Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T08:53:30.442Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

Published online by Cambridge University Press:  24 August 2018

Abhilash Nayak ,
Stéphane Caro Open the ORCID record for Stéphane Caro [Opens in a new window]  and
Philippe Wenger
Abhilash Nayak
Affiliation:
École Centrale de Nantes, Laboratoire des Sciences du Numérique de Nantes (LS2N), Nantes, France
Stéphane Caro*
Affiliation:
Centre National de Recherche Scientifique (CNRS), Laboratoire des Sciences du Numérique de Nantes (LS2N), Nantes, France, UMR CNRS 6004 Emails: stephane.caro@ls2n.fr, philippe.wenger@ls2n.fr
Philippe Wenger
Affiliation:
Centre National de Recherche Scientifique (CNRS), Laboratoire des Sciences du Numérique de Nantes (LS2N), Nantes, France, UMR CNRS 6004 Emails: stephane.caro@ls2n.fr, philippe.wenger@ls2n.fr
*
*Corresponding author. E-mail: stephane.caro@ls2n.fr
Get access Rights & Permissions [Opens in a new window]

Summary

This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Keywords

Series–parallel ManipualtorsS–PMSingularitiesCharacteristic tetrahedronInverse kinematicsDirect kinematics
Type
Articles
Information
Robotica , Volume 37 , Special Issue 7: Computational Kinematics Conference, CK 2017 , July 2019 , pp. 1240 - 1266
Copyright
© Cambridge University Press 2018 

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.)

References

Merlet, J. P., Parallel Robots (Springer Science & Business Media, Netherlands, 2006).Google Scholar
Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & Sons, New York, USA, 1999).Google Scholar
Tanev, T. K., “Kinematics of a hybrid (parallelserial) robot manipulator,” J. Mech. Mach. Theory 35 (9), 1183–1196 (2000).CrossRefGoogle Scholar
Cheng, H. H., Lee, J. J. and Penkar, R., “Kinematic analysis of a hybrid serial-and-parallel-driven redundant industrial manipulator,” Int. J. Rob. Aut. 10 (4), 159–166 (1995).Google Scholar
Shahinpoor, M., “Kinematics of a parallel-serial (hybrid) manipulator,” J. Rob. Syst. 10 (4), 159–166 (1995).Google Scholar
Waldron, K. J., Raghavan, M. and Roth, B., “Kinematics of a hybrid series-parallel manipulation system,” J. Dyn. Sys. Meas. Control 111 (2), 211–221 (1989).CrossRefGoogle Scholar
Zhang, C. and Song, S.-M., “Geometry and Position Analysis of a Novel Class of Hybrid Manipulators,” Proceedings of ASME Design Technical Conference (1994) pp. 1–9.Google Scholar
Romdhane, L., “Design and analysis of a hybrid serial-parallel manipulator,” J. Mech. Mach. Theory 34 (7), 1037–1055 (1999).CrossRefGoogle Scholar
Zheng, X. Z., Bin, H. Z. and Luo, Y. G., “Kinematic analysis of a hybrid serial-parallel manipulator,” Int. J. Adv. Manuf. Tech. 23 (11), 925–930 (2004).CrossRefGoogle Scholar
Hu, B., Yu, J., Lu, Y., Sui, C. and Han, J., “Statics and stiffness model of serial-parallel manipulator formed by k parallel manipulators connected in series,” ASME. J. Mech. Rob. 4 (2), pp. 021012–021012–8 (2012).CrossRefGoogle Scholar
Lu, Y. and Hu, B., “Analysis of kinematics/statics and workspace of a 2(SP+SPR+SPU) serial–parallel manipulator,” J. Multibody Syst. Dyn. 21 (4), 361–70 (1999).CrossRefGoogle Scholar
Alvarado, J. G., Njera, C. R. A., Rosas, L. C., Martnez, J. M. R. and Islam, M. N., “Kinematics and dynamics of 2(3-RPS) manipulators by means of screw theory and the principle of virtual work,” J. Mech. Mach. Theory 43 (10), 1281–1294 (2008).CrossRefGoogle Scholar
Hu, B., Yi, L., Yu, J. J. and Zhuang, S., “Analyses of Inverse Kinematics, Statics and Workspace of a Novel 3-RPS-3-SPR Serial-Parallel Manipulator,” J. Mech. Eng. M1 (6), 65–72 (2012).Google Scholar
Hu, B., “Formulation of unified Jacobian for serial-parallel manipulators,” Robotics and Computer-Integr. Manuf. 30 (5), 460–467 (2014).CrossRefGoogle Scholar
-Alvarado, J. G., -González, L. P., Mondragón, G. R., Garduño, H. R. and Villagómez, A. T., “Mobility and Velocity Analysis of a Limited-dof Series-Parallel Manipulator,” Conference: XVII COMRob 2015, Mexican Robotics Congress (2015)Google Scholar
Hunt, K. H., Kinematic Geometry of Mechanisms (Oxford University Press, Oxford, UK, c. 1978).Google Scholar
Nayak, A., Caro, S. and Wenger, P., “Local and Full-Cycle Mobility Analysis of a 3-RPS-3-SPR Series-Parallel Manipulator,” Proceedings of the 7th International Workshop on Computational Kinematics (2018) pp. 499–507.Google Scholar
Husty, M. L., Pfurner, M., Schröcker, H. P. and Brunnthaler, K., “Algebraic methods in mechanism analysis and synthesis,” J. Robotica 25 (6), 661–675 (2007).CrossRefGoogle Scholar
Husty, M. L. and Schr, H. P., “Kinematics and Algebraic Geometry,” Proceedings of the 21st Century Kinematics (2013) pp. 85–123.Google Scholar
Stigger, T. and Husty, M. L., “Constraint Equations of Inverted Kinematic Chains,” Proceedings of the 7th International Workshop on Computational Kinematics (2018) pp. 491–498.Google Scholar
Schadlbauer, J., Walter, D. R. and Husty, M. L., “The 3-RPS parallel manipulator from an algebraic viewpoint,” J. Mech. Mach. Theory 75, 161–176 (2014).CrossRefGoogle Scholar
Ebert-Uphoff, I., Lee, J. K. and Lipkin, H., “Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs,” Proc. Inst Mech. Eng., Part C: J. Mech. Eng. Sci. 216 (1), 81–93 (2002).CrossRefGoogle Scholar
Joshi, S. A. and Tsai, L. W., “Jacobian analysis of limited-DOF parallel manipulators,” ASME J. Mech. Des. 124 (2), 254–258 (2002).CrossRefGoogle Scholar
Nayak, A., Nurhami, L., Wenger, P. and Caro, S., “Comparison of 3-RPS and 3-SPR Parallel Manipulators Based on Their Maximum Inscribed Singularity-Free Circle,” New Trends in Mechanism and Machine Science (2017) pp. 121–130.Google Scholar
Kalla, R., Nurhami, L., Bandyopadhay, S., Wenger, P. and Caro, S., “A Study of Σ2 Singularities in the 3-RPS Parallel Manipulator,” Proceedings of the 2nd International and 17th National Conference on Machines and Mechanisms, India (2015).Google Scholar
Schadlbauer, J., Husty, M. L., Caro, S. and Wenger, P., “Self-motions of 3-RPS manipulators,” ASME J. Frontiers Mech. Eng. 8 (1), 62–69 (2013).CrossRefGoogle Scholar
Amine, S., Mokhiamar, O. and Caro, S., “Classification of 3T1R parallel manipulators based on their wrench graph,” ASME. J. Mech. Rob. 9 (1), 011003-011003-10 (2017).Google Scholar
Amine, S., Caro, S., Wenger, P. and Kanaan, D., “Singularity analysis of the H4 robot using Grassmann Cayley algebra,” J. Robotica 9 (1), 1109–1118 (2012).CrossRefGoogle Scholar
Amine, S., Masouleh, M. T., Caro, S., Wenger, P. and Gosselin, C., “Singularity conditions of 3T1R parallel manipulators with identical limb structures,” ASME. J. Mech. Rob. 4 (1), 011011-1 011011-11 (2012).Google Scholar
Maraje, S., Nurhami, L. and Caro, S., “Operation Modes Comparison of a Reconfigurable 3-PRS Parallel Manipulator Based on Kinematic Performance,” Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016, Charlotte, North Carolina, USA, Aug. 21–24 (2016).CrossRefGoogle Scholar
Caro, S., Moroz, G., Gayral, T., Chablat, D. and Chen, C., “Singularity Analysis of a Six-dof Parallel Manipulator using Grassmann–Cayley Algebra and Groebner Bases,” Symposium on Brain, Body and Machine, Montreal, QC, Canada, November 10–12. (2010) pp. 341–352.Google Scholar
Merlet, J. P., “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Geometry and Robotics: Workshop, Toulouse, France (1989) pp. 194–212.Google Scholar
Pottmann, H. and Wallner, J., Computational Line Geometry (Springer-Verlag New York, Inc., 2001).Google Scholar
Bonev, I. A., Zlatanov, D. and Gosselin, C. M., “Advantages of the Modified Euler Angles in the Design and Control of PKMs,” Proceedings of the Parallel Kinematic Machines International Conference (2002) pp. 171–188.Google Scholar
Weiss, E. A., Einführung in Die Liniengeometrie und Kinematik (Teubner, B. G., Leibzig, 1935).Google Scholar
Shum, J. C. F., and Zsombor-Murray, P. J., “Direct Kinematics of the Double-Triangular Manipulator: An Exercise in Geometric Thinking.” In: Advances in Robot Kinematics. (Lenarčič, J. and Stanišić, M. M. eds.) (Springer, Dordrecht, 2000).Google Scholar