Skip to main content
SpringerLink
Log in

Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

This paper investigates various topologies and mobility of a class of metamorphic parallel mechanisms synthesized with reconfigurable rTPS limbs. Based on the reconfigurable Hooke (rT) joint, the rTPS limb has two phases which result in parallel mechanisms having ability of mobility change. While in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane which is used to demonstrate different topologies of the nrTPS metamorphic parallel mechanisms by investigating various relations (parallel or intersecting) among the n constraint planes (n = 2,3,..,6). Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals mobility and redundant geometric conditions of the mechanism topologies. By altering the limbs into the non-constraint phase without constraint plane, new mechanism phases are deduced with mobility change based on each mechanism topology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. M. Gan, J. S. Dai and Q. Z. Liao, Mobility analysis of two types of metamorphic parallel mechanisms, ASME Journal of Mechanisms and Robotics, 1 (2009) 041007_1–9.

    Google Scholar 

  2. J. P. Merlet, Parallel robots, 2nd Edition. Springer (2008).

    MATH  Google Scholar 

  3. C. Gosselin, Determination of the workspace of 6-dof parallel manipulators, ASME J. Mech. Des., 112 (1990) 331–336.

    Article  Google Scholar 

  4. Z. Huang and Y. F. Fang, Kinematic characteristics analysis of 3-DOF in-parallel actuated pyramid mechanisms, Mech. Mach. Theory, 31(8) (1996) 1009–1018.

    Article  Google Scholar 

  5. F. Gao, W. M. Li and X. C. Zhao, New kinematic structures for 2-, 3-, 4-, and 5-dof parallel manipulator designs, Mech. Mach. Theory, 37 (2002) 1395–1411.

    Article  Google Scholar 

  6. L. W. Tsai and S. A. Joshi, Kinematic analysis of 3 DOF position mechanisms for use in hybrid kinematic machines, ASME J. Mech. Des., 124(2) (2002) 245–253.

    Article  Google Scholar 

  7. J. Angeles, G. L. Yang and I-M. Chen, Singularity analysis of three-legged, six-DOF platform manipulators with URS legs, IEEE/ASME Transactions on Mechatronics, 8(4) (2003) 469–475.

    Article  Google Scholar 

  8. H. J. Su, P. Dietmaier and J. M. McCarthy, Trajectory planning for constrained parallel manipulators, ASME Journal of Mechanical Design, 125(4) (2003) 709–716.

    Article  Google Scholar 

  9. X. J. Liu, J. Wang and G. Pritschow, A new family of spatial 3-DoF fully-parallel manipulators with high rotational capability, Mech. Mach. Theory, 40(4) (2005) 475–494.

    Article  MathSciNet  Google Scholar 

  10. D. M. Gan, Q. Z. Liao, J. S. Dai, S. M. Wei and L. D. Seneviratne, Forward displacement analysis of the general 6-6 Stewart mechanism using Grobner bases, Mech. Mach. Theory, 44(9) (2009) 1640–1647.

    Article  Google Scholar 

  11. J. M. Hervé and F. Sparacino, Structural synthesis of parallel robots generating spatial translation, Proc. of the Fifth International Conference on Advanced Robotics, Pisa, Italy (1991) 808–813.

    Google Scholar 

  12. M. Carricato and V. Parenti-Castelli, A family of 3-DOF translational parallel manipulators, ASME J. Mech. Des., 125(2) (2003) 302–307.

    Article  Google Scholar 

  13. T. L. Yang, A. X. Liu, Q. Jin, Y. F. Luo, H. P. Shen and L. B. Hang, Position and orientation characteristic equation for topological design of robot mechanisms, ASME Journal of Mechanical Design, 131(2) (2009) 021001_(1–17).

    Article  Google Scholar 

  14. L. Cui and J. S. Dai. Axis constraint analysis and its resultant 6R double-centered overconstrained mechanisms. ASME Journal of Mechanisms and Robotics, 3(3) (2011) 031004_1–9.

    Google Scholar 

  15. Z. Huang and Q. C. Li, General methodology for the type synthesis of lower-mobility symmetrical parallel manipulators and several novel manipulators, Int. J. Robot. Res., 21(2) (2002) 131–145.

    Article  Google Scholar 

  16. D. Kim and W. K. Chung, Kinematic condition analysis of three-DOF pure translational parallel manipulators, ASME J. Mech. Des., 125(2) (2003) 323–331.

    Article  Google Scholar 

  17. X. Kong and C. M. Gosselin, Type synthesis of 3-DOF spherical parallel manipulators based on screw theory, ASME J. Mech. Des., 126(1) (2004) 101–108.

    Article  Google Scholar 

  18. J. S. Dai, Z. Huang and Harvey Lipkin, Mobility of overconstrained parallel mechanisms. ASME J. Mech. Des., 128 (2006) 220–229.

    Article  Google Scholar 

  19. C. W. Wampler, On a rigid body subject to point-plane constraints, ASME J. Mech. Des., 128(1) (2006) 151–158.

    Article  Google Scholar 

  20. C. W. Wampler, Locating N points of a rigid body on N given planes, Proc. ASME Design Engineering Technical Conf., Salt Lake City, USA (2004).

    Google Scholar 

  21. J. M. Selig, Quadratic constraints on rigid-body displacements. ASME J. Mech. Robot., 2(4) (2010) 041009.

    Article  Google Scholar 

  22. J. M. Selig, On the geometry of point-plane constraints on rigid-body displacements. Acta Appl. Math. (2011) 1–23.

    Google Scholar 

  23. M. Karouia and J. M. Hervé, A family of novel orientational 3-DOF parallel robots, Proc. 14thCISM-IFToMM RoManSy, Springer (2002) 359–368.

    Chapter  Google Scholar 

  24. P. Huynh and J. M. Hervé, Equivalent kinematic chains of three degree-of-freedom tripod mechanisms with Planar-Spherical Bonds, ASME J. Mech. Des., 127(1) (2005) 95–102.

    Article  Google Scholar 

  25. C. C. Lee and J. M. Hervé, Uncoupled 6-dof tripods via Group Theory, Proc. of the 5th International Workshop on Computational Kinematics, Andrés Kecskeméthy, Andreas Müller, eds. Springer (2009) 201–208.

    Chapter  Google Scholar 

  26. Q. Li and J. M. Hervé, 1T2R parallel mechanisms without parasitic motion, IEEE Transactions on Robotics, 26(3) (2010) 401–410.

    Article  Google Scholar 

  27. D. M. Gan and J. S. Dai, A reconfigurable Hooke joint, China Patent CN102152303A (2011).

    Google Scholar 

  28. D. M. Gan, J. S. Dai and Q. Z. Liao, Constraint analysis on mobility change of a novel metamorphic parallel mechanism, Mechanism and Machine Theory, 45(12) (2010) 1864–1876.

    Article  Google Scholar 

  29. D. M. Gan, J. S. Dai and D. G. Caldwell, Constraint-based limb synthesis and mobility-change aimed mechanism construction, ASME J. Mech. Des., 133(5) (2011) 051001_1–9.

    Article  Google Scholar 

  30. H. S. Yan and C. H., Kuo, Topological representations and characteristics of variable kinematic joints, ASME J. Mech. Des., 128(2) (2006) 384–391.

    Article  Google Scholar 

  31. K. T. Zhang, J. S. Dai and Y. F. Fang, Topology and constraint analysis of phase change in the metamorphic chain and its evolved mechanism, ASME J. Mech. Des., 132(12) (2010) 121001(1–11).

    Article  Google Scholar 

  32. K. Zhang, J. S. Dai and Y. Fang, Geometric constraint and mobility variation of two 3SvPSv metamorphic parallel mechanisms, ASME Transactions, Journal of Mechanical Design, 135(1) (2013) 011001–1.

    Article  Google Scholar 

  33. J. S. Dai and J. J. Rees, Mobility in metamorphic mechanisms of foldable/erectable kinds, ASME J. Mech. Des., 121(3) (1999) 375–382.

    Article  Google Scholar 

  34. M. Leonesio, G. Bianchi and P. Manara, A general approach for self-locking analysis in closed kinematic chains, Proc. of the 12th World Congress in Mechanism and Machine Theory, Besancon, France (2007) 141–147.

    Google Scholar 

  35. G. Wei, J. S. Dai, S. Wang and H. Luo, Kinematic analysis and prototype of a metamorphic anthropomorphic hand with a reconfigurable palm, International Journal of Humanoid Robotics, 8(3) (2011) 459–479.

    Article  Google Scholar 

  36. X. Kong and C. Gosselin, Classification of 6-SPS parallel manipulators according to their components, Proc. of ASME Design Engineering Technical Conferences, Baltimore, Mariland, USA (2000) DETC2000/MECH-14105.

    Google Scholar 

  37. C. Zhang and S. Song, Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions, IEEE International Conference on Robotics and Automation, Sacramento, CA, USA (1991) 2676–2681.

    Google Scholar 

  38. D. M. Gan, J. S. Dai, Jorge Dias and L. D. Seneviratne, Reconfigurability and unified kinematics modeling of a 3rTPS metamorphic parallel mechanism with perpendicular constraint screws, Robotics and Computer Integrated Manufacturing, 29(4) (2013) 121–128.

    Article  Google Scholar 

  39. D. M. Gan, J. S. Dai, Jorge Dias and L. D. Seneviratne, Unified kinematics and singularity analysis of a metamorphic parallel mechanism with bifurcated motion, ASME: Journal of Mechanisms and Robotics, 5(3) (2013) 041104_1–11.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Robotics Institute, Khalifa University of Science, Technology & Research, 127788, Abu Dhabi, UAE

    Dongming Gan, Jorge Dias & Lakmal Seneviratne

  2. School of Natural and Mathematical Sciences, King’s College London, University of London, London, WC2R2LS, UK

    Jian S. Dai & Lakmal Seneviratne

  3. Institute of Systems and Robotics, University of Coimbra, Faculty of Science and Technology, Coimbra, 3000-315, Portugal

    Jorge Dias

Authors
  1. Dongming Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian S. Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jorge Dias
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lakmal Seneviratne
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongming Gan.

Additional information

Recommended by Associate Editor Ki-Hoon Shin

Dongming Gan received his Ph.D. based on a joint program with Beijing University of Posts and Telecommunications and King’s College London in 2009. He is currently an Assistant Professor in Mechanical Engineering and Robotics at Khalifa University of Science, Technology and Research, Abu Dhabi, UAE. His research interests include mechanism modeling and design, reconfigurable mechanisms and robots with applications on automation, rehabilitation and manufacturing.

Jian S Dai received his Ph.D. from the University of Salford in UK in 1993. He is currently a chair Professor in mechanisms and robotics in King’s College London. Professor Dai’s research and teaching are in the area of kinematics, mechanisms, robotics, and their application to rehabilitation, surgical robotics and industrial packaging particularly reconfigurable mechanisms with four books, over 400 publications and a number of best paper awards in journals and conferences. He is ASME fellow, IMechE fellow and received a number of service awards including outstanding service award from ASME and IEEE.

Jorge Dias received the Ph.D. in electrical engineering with specialization in control and instrumentation from the University of Coimbra, Coimbra, Portugal, in 1994. He holds his research activities at the Insti tute of Systems and Robotics (ISR), University of Coimbra, and also at the Khalifa University of Science, Technology and Research. His current research areas are computer vision and robotics, with activities and contributions in these fields since 1984. Dr. Dias is currently in the Board of Officers from the Portuguese Chapter for the IEEE Robotics and Automation Society.

Lakmal D. Seneviratne received B.Sc.(Eng.) and Ph.D. degrees in Mechanical Engineering from King’s College London (KCL), London, U.K. He is currently a Professor in Mechanical Engineering and the Director of the Robotics Institute at Khalifa University. He is also an Emeritus Professor at King’s College London. His research interests are focused on robotics and autonomous systems. He has published over 300 refereed research papers related to these topics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gan, D., Dai, J.S., Dias, J. et al. Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms. J MECH SCI TECHNOL 28, 4179–4191 (2014). https://doi.org/10.1007/s12206-014-0931-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-014-0931-7

Keywords

Search

Navigation