0
Research Papers

Kinematic Analysis of a Novel Kinematically Redundant Spherical Parallel Manipulator

[+] Author and Article Information
Jérôme Landuré

Départment de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: jerome.landure.1@ulaval.ca

Clément Gosselin

Départment de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: gosselin@gmc.ulaval.ca

Manuscript received September 20, 2017; final manuscript received December 6, 2017; published online February 12, 2018. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 10(2), 021007 (Feb 12, 2018) (10 pages) Paper No: JMR-17-1303; doi: 10.1115/1.4038971 History: Received September 20, 2017; Revised December 06, 2017

This paper introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters, which are chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Cox, D. J. , and Tesar, D. , 1989, “ The Dynamic Model of a Three Degree of Freedom Parallel Robotic Shoulder Module,” Advanced Robotics, Springer, Berlin, pp. 475–487. [CrossRef]
Sefrioui, J. , and Gosselin, C. M. , 1994, “ Étude et représentation des lieux de singularité des manipulateurs parallelles sphériques a trois degrés de liberté avec actionneurs prismatiques,” Mech. Mach. Theory, 29(4), pp. 559–579. [CrossRef]
Kong, X. , Gosselin, C. M. , and Ritchie, J. M. , 2011, “ Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator,” ASME J. Mech. Rob., 3(12), p. 011007. [CrossRef]
Gosselin, C. M. , and Lavoie, E. , 1993, “ On the Kinematic Design of Spherical Three-Degree-of-Freedom Parallel Manipulators,” Int. J. Rob. Res., 12(4), pp. 393–402. [CrossRef]
Gosselin, C. M. , St-Pierre, E. , and Gagné, M. , 1996, “ On the Development of the Agile Eye: Mechanical Design, Control Issues and Experimentation,” IEEE Rob. Autom. Soc. Mag., 3(4), pp. 29–37. [CrossRef]
Gosselin, C. M. , Perreault, L. , and Vallancourt, C. , 1995, “ Simulation and Computer-Aided Kinematic Design of Three-Degree-of-Freedom Spherical Parallel Manipulators,” J. Rob. Syst., 12(12), pp. 857–869. [CrossRef]
Cammarata, A. , and Sinatra, R. , 2008, “ The Elastodynamics of the 3-CRU Spherical Robot,” Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Montpellier, France, Sept. 21–22, pp. 159–165.
Li, R. , and Guo, Y. , 2014, “ Research on Dynamics and Simulation of 3-RRP Spherical Parallel Mechanism,” Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Tianjin, China, July 7–8, pp. 1–8.
Huda, S. , Takeda, Y. , and Hanagasaki, S. , 2008, “ Kinematic Design of 3-URU Pure Rotational Parallel Mechanism to Perform Precise Motion Within a Large Workspace,” Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Montpellier, France, Sept. 21–22, pp. 49–56.
Hervé, J. M. , and Karouia, M. , 2002, “ The Novel 3-RUU Wrist With No Idle Pair,” First International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Quebec City, QC, Canada, Oct. 3–4, pp. 284–286. https://www.researchgate.net/publication/279197277_The_Novel_3-RUU_Wrist_with_No_Idle_Pair
Yu, J. , Lu, D. , and Hao, G. , 2014, “ Design and Analysis of a 2-DOF Compliant Parallel Pan-Tilt Platform,” Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Tianjin, China, July 7–8, pp. 1–8. https://www.researchgate.net/publication/264128915_Design_and_Analysis_of_a_2-DOF_Compliant_Parallel_Pan-Tilt_Platform
Shen, H. , Yang, L. , Deng, J. , Li, J. , and Zhang, X. , 2014, “ A Parallel Shoulder Rehabilitation Training Mechanism and Its Kinematics Design,” Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Tianjin, China, July 7–8, pp. 1–8.
Congzhe, W. , Yuefa, F. , Sheng, G. , and Zhihong, C. , 2014, “ Design and Kinematics of a Reconfigurable Robot for Ankle and Knee Rehabilitation,” Third International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Tianjin, China, July 7–8, pp. 1–10.
Hayes, M. J. D. , Weiss, A. , and Langlois, R. G. , 2008, “ Atlas Motion Platform Generalized Kinematic Model,” Second International Workshop on Fundamental Issues and Future Directions for Parallel Mechanisms and Manipulators, Montpellier, France, Sept. 21–22, pp. 227–234. https://www.researchgate.net/publication/225466236_Atlas_motion_platform_generalized_kinematic_model_Atlas_motion_platform
Wu, G. , Caro, S. , and Wang, J. , 2015, “ Design and Transmission Analysis of an Asymmetrical Spherical Parallel Manipulator,” Mech. Mach. Theory, 94, pp. 119–131. [CrossRef]
Stanisic, M. M. , and Duta, O. , 1990, “ Symmetrically Actuated Double Pointing Systems: The Basis of Singularity-Free Robot Wrists,” IEEE Trans. Rob. Autom., 6(5), pp. 562–569. [CrossRef]
Leguay-Durand, S. , and Reboulet, C. , 1997, “ Optimal Design of a Redundant Spherical Parallel Manipulator,” Robotica, 15(4), pp. 399–405. [CrossRef]
Di Gregorio, R. , 2002, “ A New Family of Spherical Parallel Manipulators,” Robotica, 20(4), pp. 353–358. [CrossRef]
Bai, S. , 2010, “ Optimum Design of Spherical Parallel Manipulators for a Prescribed Workspace,” Mech. Mach. Theory, 45(2), pp. 200–211. [CrossRef]
Liu, X.-J. , Jin, Z.-L. , and Gao, F. , 2000, “ Optimum Design of 3-DOF Spherical Parallel Manipulators With Respect to the Conditioning and Stiffness Indices,” Mech. Mach. Theory, 35(9), pp. 1257–1267. [CrossRef]
Lum, M. J. , Rosen, J. , Sinanan, M. N. , and Hannaford, B. , 2006, “ Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot: Theoretical and Experimental Approaches,” IEEE Trans. Biomed. Eng., 53(7), pp. 1440–1445. [CrossRef] [PubMed]
Kurtz, R. , and Hayward, V. , 1992, “ Multiple-Goal Kinematic Optimization of a Parallel Spherical Mechanism With Actuator Redundancy,” IEEE Trans. Rob. Autom., 8(5), pp. 644–651. [CrossRef]
Gosselin, C. M. , Laliberté, T. , and Veillette, A. , 2015, “ Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability,” IEEE Trans. Rob., 31(2), pp. 457–467. [CrossRef]
Bonev, I. A. , Zlatanov, D. , and Gosselin, C. M. , 2002, “ Advantages of the Modified Euler Angles in the Design and Control of PKMs,” Third Chemnitz Parallel Kinematics Seminar/2002 Parallel Kinematic Machines International Conference, Chemnitz, Germany, Apr. 23–25, pp. 171–188.
Gosselin, C. M. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Wang, J. , and Gosselin, C. M. , 2004, “ Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators,” ASME J. Mech. Des., 126(2), pp. 319–326. [CrossRef]
Bonev, I. A. , and Gosselin, C. M. , 2005, “ Singularity Loci of Spherical Parallel Mechanisms,” IEEE International Conference on Robotics and Automation (ICRA), Barcelona, Spain, Apr. 18–22, pp. 2968–2973.
Bonev, I. A. , and Gosselin, C. M. , 2006, “ Analytical Determination of the Workspace of Symmetrical Spherical Parallel Mechanisms,” IEEE Trans. Rob., 22(5), pp. 2968–2973. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Architecture of the proposed 4DOF kinematically redundant spherical robot

Grahic Jump Location
Fig. 2

Kinematic modeling of the 4DOF redundant spherical parallel robot

Grahic Jump Location
Fig. 8

Determinant of matrix j during trajectory 2 for the redundant architecture and the nonredundant architecture. The determinant for the redundant architecture is multiplied by 10 for scale considerations.

Grahic Jump Location
Fig. 7

Determinant of matrix j during trajectory 1 for the redundant architecture and the nonredundant architecture. The determinant for the redundant architecture is multiplied by 10 for scale considerations.

Grahic Jump Location
Fig. 6

Joint coordinates of the robot during trajectory 2 with optimized redundancy

Grahic Jump Location
Fig. 5

Joint coordinates of the robot during trajectory 1 with optimized redundancy

Grahic Jump Location
Fig. 4

Particular architecture of a spherical 4DOF redundant parallel robot. Vector z (not represented) is collinear with vectorn.

Grahic Jump Location
Fig. 3

Illustration of the admissible values for parameter β

Grahic Jump Location
Fig. 9

Architecture of the RPR leg and of the equivalent RRR leg

Grahic Jump Location
Fig. 10

Prototype of the spherical parallel manipulator

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In