Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T11:00:26.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Computation of the safe working zones of Planar and Spatial Parallel Manipulators

Published online by Cambridge University Press:  25 July 2019

Murali K. Karnam ,
Aravind Baskar ,
Rangaprasad A. Srivatsan  and
Sandipan Bandyopadhyay Open the ORCID record for Sandipan Bandyopadhyay [Opens in a new window]
Murali K. Karnam
Affiliation:
Department of Biomedical Engineering, University of Basel, 4001 Basel, Switzerland
Aravind Baskar
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN46556, USA
Rangaprasad A. Srivatsan
Affiliation:
Robotics Institute, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA15213, USA
Sandipan Bandyopadhyay*
Affiliation:
Department of Engineering Design, Indian Institute of Technology Madras, Chennai600 036, India
*
* Corresponding author. E-mail: sandipan@iitm.ac.in
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-R̲RR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

Keywords

Safe working zoneParallel manipulatorSingularitiesLink interferenceJoint limitsSingularity-free workspace
Type
Articles
Information
Robotica , Volume 38 , Issue 5 , May 2020 , pp. 861 - 885
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Murali K. Karnam contributed to the paper while working as a Project Officer at the Indian Institute of Technology Madras, India. Aravind Baskar contributed to the paper as anMS scholar at the Indian Institute of Technology Madras, India. Rangaprasad A. Srivatsan contributed to the paper while working as a Project Officer at the Indian Institute of Technology Madras, India.

References

Srivatsan, R. A. and Bandyopadhyay, S., “Determination of the Safe Working Zone of a Parallel Manipulator,” Proceedings of the International Conference on Computational Kinematics, Barcelona, Spain (2014) pp. 201–208.Google Scholar
Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Rob. Autom. 6, 281–290 (1990).CrossRefGoogle Scholar
Tsai, L., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (A Wiley-Interscience Publication, Wiley, 1999).Google Scholar
Ghosal, A. and Ravani, B., “A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators,” Trans. ASME, J. Mech. Design 123(1), 80–89 (2001).CrossRefGoogle Scholar
Bandyopadhyay, S. and Ghosal, A., “Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators,” Mech. Mach. Theory 39(5), 519–544 (2004).CrossRefGoogle Scholar
Ghosal, A., Robotics: Fundamental Concepts and Analysis (Oxford University Press, New Delhi, 2014).Google Scholar
Merlet, J.-P., Parallel Robots (Springer Science & Business Media, Springer Netherlands, Berlin/Heidelberg, 2006).Google Scholar
Bohigas, O., Henderson, M. E., Ros, L., Manubens, M. and Porta, J. M., “Planning singularity-free paths on closed-chain manipulators,” IEEE Trans. Robot . 29(4), 888–898 (2013).CrossRefGoogle Scholar
Dash, A. K., Chen, I.-M., Yeo, S. H. and Yang, G., “Workspace generation and planning singularity-free path for parallel manipulators,” Mech. Mach. Theory 40(7), 776–805 (2005).CrossRefGoogle Scholar
Sen, S., Dasgupta, B. and Mallik, A. K., “Variational approach for singularity-free path-planning of parallel manipulators,” Mech. Mach. Theory 38(11), 1165–1183 (2003).CrossRefGoogle Scholar
Leguay-Durand, S. and Reboulet, C., “Optimal design of a redundant spherical parallel manipulator,” Robotica 15(4), 399–405 (1997).CrossRefGoogle Scholar
Agarwal, A., Nasa, C. and Bandyopadhyay, S., “Dynamic singularity avoidance for parallel manipulators using a task-priority based control scheme,” Mech. Mach. Theory 96, 107–126 (2016).CrossRefGoogle Scholar
Li, H., Gosselin, C. M. and Richard, M. J., “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).CrossRefGoogle Scholar
Jiang, Q. and Gosselin, C. M., “The maximal singularity-free workspace of the Gough-Stewart platform for a given orientation,” J. Mech. Design 130(11), 1281–1293 (2008).CrossRefGoogle Scholar
Abbasnejad, G., Daniali, H. M. and Kazemi, S. M., “A new approach to determine the maximal singularityfree zone of 3-RPR planar parallel manipulator,” Robotica 30(6), 1005–1012 (2012).CrossRefGoogle Scholar
Zein, M., Wenger, P. and Chablat, D., “Singularity Surfaces and Maximal Singularity-Free Boxes in the Joint Space of Planar 3-RPR Parallel Manipulators,” Proceeding of 12th IFToMM World Congress, Besançon, France (2007) pp. 1–6.Google Scholar
Yang, Y. and O’Brien, J., “A Geometric Approach for the Design of Singularity-free Parallel Robots,” Proceedings of the IEEE International Conference on Robotics and Automation, Kobe, Japan (2009) pp. 1801–1806.Google Scholar
Pernkopf, F. and Husty, M. L., “Workspace analysis of Stewart-Gough-type parallel manipulators,” Proc. Inst. Mech. Eng. C 220(7), 1019–1032 (2006).CrossRefGoogle Scholar
Stigger, T., Pfurner, M. and Husty, M., “Workspace and Singularity Analysis of a 3-RUU Parallel Manipulator,” Proceedings of the European Conference on Mechanism Science, Aachen, Germany (2018) pp. 325–332.Google Scholar
Kaloorazi, M.-H. F., Masouleh, M. T. and Caro, S., “Determination of the maximal singularity-free workspace of 3-DOF parallel mechanisms with a constructive geometric approach,” Mech. Mach. Theory 84, 25–36 (2015).CrossRefGoogle Scholar
Nag, A., Reddy, V., Agarwal, S. and Bandyopadhyay, S., “Identifying singularity-free spheres in the position workspace of semi-regular Stewart platform manipulators,” Proceedings of the International Conference on Advances in Robot Kinematics, Bologna, Italy (2018) pp. 421–430.Google Scholar
Pott, A., “Efficient Computation of the Workspace Boundary, its Properties and Derivatives for Cable-Driven Parallel Robots,” Proceedings of the International Conference on Computational Kinematics, Poitiers, France (2018) pp. 190–197.Google Scholar
Chaudhury, A. N. and Ghosal, A., “Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method,” Mech. Mach. Theory 118, 115–138 (2017).CrossRefGoogle Scholar
Kilaru, J., Karnam, M. K., Agarwal, S. and Bandyopadhyay, S., “Optimal Design of Parallel Manipulators Based on Their Dynamic Performance,” Proceedings of the 14th IFToMM World Congress, Taipei, Taiwan (2015) pp. 406–412.Google Scholar
Patel, D., Kalla, R., Tetik, H., Kiper, G. and Bandyopadhyay, S., “Computing the Safe Working Zone of a 3-RRS Parallel Manipulator,” Proceedings of the 6th European Conference on Mechanism Science (EUCOMES), Nantes, France (2016) pp. 113–120.Google Scholar
Cao, Y., Zhang, Q., Zhou, H. and Ding, H., “Orientation-workspace analysis of the Stewart-Gough manipulator,” Discrete Cont. Dyn. B 13, 646–652 (2006).Google Scholar
Merlet, J.-P., “Designing a parallel manipulator for a specific workspace,” Int. J. Rob. Res. 16(4), 545–556 (1997).CrossRefGoogle Scholar
Macho, E., Altuzarra, O., Pinto, C. and Hernandez, A., “Workspaces associated to assembly modes of the 5R planar parallel manipulator,” Robotica 26(3), 395–403 (2008).CrossRefGoogle Scholar
Macho, E., Altuzarra, O. and Hernandez, A., “Maximal Operational Workspace of Parallel Manipulators,” In: Robot Manipulators, New Achievements (Lazinica, A. and Kawai, H., eds.) (In-tech, Croatia, 2010) pp. 577–600.Google Scholar
Bohigas, O., Zlatanov, D., Ros, L., Manubens, M. and Porta, J., “A general method for the numerical computation of manipulator singularity sets,” IEEE Trans. Rob . 30(2), 340–351 (2014).CrossRefGoogle Scholar
Hudgens, J. and Arai, T., “Planning Link-interference-free Trajectories for a Parallel link Manipulator,” Proceeding of the International Conference on Industrial Electronics, Control, and Instrumentation, New Orleans, LA (1993) pp. 1506–1511.Google Scholar
Chakraborty, N., Peng, J., Akella, S. and Mitchell, J. E., “Proximity queries between convex objects: An interior point approach for implicit surfaces,” IEEE Trans. Rob . 24(1), 211–220 (2008).CrossRefGoogle Scholar
Agarwal, S., Srivatsan, R. A. and Bandyopadhyay, S., “Analytical determination of the proximity of two right-circular cylinders in space,” J. Mech. Rob. 8(4), 041010 (2016).CrossRefGoogle Scholar
Gilbert, E. G., Johnson, D. W. and Keerthi, S. S., “A fast procedure for computing the distance between complex objects in three-dimensional space,” IEEE J. Rob. Autom . 4(2), 193–203 (1988).CrossRefGoogle Scholar
Srivatsan, R. A., Bandyopadhyay, S. and Ghosal, A., “Analysis of the degrees-of-freedom of spatial parallel manipulators in regular and singular configurations,” Mech. Mach. Theory 69(11), 127–141 (2013).CrossRefGoogle Scholar
Nag, A. and Bandyopadhyay, S., “Analytical Determination of a Sphere Inside Which the Stewart Platform Translates Without Suffering Any Leg Interference,” Proceedings of the International Conference on Advances in Robot Kinematics, Bologna, Italy (2018) pp. 74–82.Google Scholar
Research, Wolfram, Inc., Mathematica, Version 9.0 (Champaign, Illinois, 2012).Google Scholar
Bandyopadhyay, S., Srivatsan, R. A. and Mehta, T., “A reconfigurable parallel manipulator,” Indian Patent Application, 5187/CHE/2012, 2012.Google Scholar
Srivatsan, R. A. and Bandyopadhyay, S., “On the position kinematic analysis of MaPaMan: A reconfigurable three-degrees-of-freedom spatial parallel manipulator,” Mech. Mach. Theory 62, 150–165 (2013).CrossRefGoogle Scholar
Huang, C. and Tsai, K., “A general method to determine compatible orientation workspaces for different types of 6-DOF parallel manipulators,” Mech. Mach. Theory 85, 129–146 (2015).CrossRefGoogle Scholar