Skip to main content
SpringerLink
Log in

Optimal design of a new spatial 3-DOF parallel robot with respect to a frame-free index

  • Published:
Science in China Series E: Technological Sciences Aims and scope Submit manuscript

Abstract

Optimal design is one of the most important issues in robots. Since the very beginning, the concepts of the Jacobian matrix, manipulability and condition number, which are used successfully in the field of serial robots, have been applied to parallel robots. Unlike serial robots, parallel robots are good for motion/force transmission. Their performance evaluation and design should be correspondingly different. This paper is an attempt to optimally design a novel spatial three-degree-of-freedom (3-DOF) parallel robot by using the concept of motion/force transmission. Accordingly, three indices are defined. The suggested indices are independent of any coordinate frame and could be applied to the analysis and design of a parallel robot whose singularities can be identified wholly by using the relative angle between the output and adjacent links, and by using the relative angle between the input and adjacent links.

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. Huang Z, Li Q C. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. Int J Robot Res, 2003, 22: 59–79

    Google Scholar 

  2. Li Y, Xu Q. A novel design and analysis of a 2-DOF compliant parallel micromanipulator for nanomanipulation. IEEE Trans Automat Sci Eng, 2006, 3: 248–254

    Google Scholar 

  3. Gosselin C, Angeles J. The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator. J Mech Transm Autom Des, 1989, 111: 202–207

    Article  Google Scholar 

  4. Ottaviano E, Ceccarelli M. Optimal design of CaPaMan (Cassino Parallel Manipulator) with a specified orientation workspace. Robotica, 2002, 20: 159–166

    Article  Google Scholar 

  5. Merlet J P. Jacobian, manipulability, condition number, and accuracy of parallel robots. ASME J Mech Des, 2006, 128: 199–206

    Article  Google Scholar 

  6. Gosselin C, Angeles J. A global performance index for the kinematic optimization of robotic manipulators. ASME J Mech Des, 1991, 113: 220–226

    Article  Google Scholar 

  7. Alt Von H. Der uberstragungswinkel und seine bedeutung fur dar konstruieren periodischer getriebe. Werksstattstechnik, 1932, 26(4): 61–65

    Google Scholar 

  8. Balli S S,. Chand S. Transmission angle in mechanisms. Mech Mach Theory, 2002, 37: 175–195

    Article  MATH  MathSciNet  Google Scholar 

  9. Eschenbach P W, Tesar D. Link length bounds on the four bar chain. J Eng Ind Trans ASME Ser B, 1971, 93: 287–293

    Google Scholar 

  10. Hall A S. Kinematics and Linkage Design. Englewood Cliffs: Prentice-Hall 1961. 41

  11. Hartenberg R S, Denavit J. Kinematic Synthesis of Linkages. New York: McGraw-Hill, 1964. 46–47

    Google Scholar 

  12. Tao D C. Applied Linkage Synthesis. Reading: Addison-Wesley, 1964. 7–12

    Google Scholar 

  13. Kimbrella J T. Kinematics Analysis and Synthesis. New York: McGraw-Hill, 1991. 14–15

    Google Scholar 

  14. Sutherland G H, Siddall J N. Dimensional synthesis of linkage by multifactor optimization. Mech Mach Theory, 1974, 9: 81–95

    Article  Google Scholar 

  15. Soylu R. Analytical synthesis of mechanism part-I, transmission angle synthesis. Mech Mach Theory, 1993, 28: 825–833

    Article  Google Scholar 

  16. Liu X-J, Wang J, Gao F, et al. On the analysis of a new spatial three degrees of freedom parallel manipulator. IEEE Trans Rob Autom, 2001, 17: 959–968

    Article  Google Scholar 

  17. Hain K. Applied Kinematics. New York: McGraw-Hill, 1967

    Google Scholar 

  18. Ting K L, Tsai G H. Mobility and synthesis of five-bar programmable linkages. In: Proceedings of 9th OSU Applied Mechanisms Conf, Kansas City, MO. Stillwater: Oklahoma State University 1985. III-1–III-8.

  19. Stanley R. Five-bar loop synthesis. Mach Design, 1961, 189-195.

  20. Balli S S, Chand S, Synthesis of a five-bar mechanism of variable topology type with transmission angle control. ASME J Mech Des, 2004, 126: 128–134

    Article  Google Scholar 

  21. Philipp M R E, Preudenstein F. Synthensis of two-degree-of-freedom linkages-a feasibility study of numerical methods of synthesis of bivariate function generators. J Mech, 1965, 1: 9–21

    Article  Google Scholar 

  22. Söylemez E, Freudenstein F. Transmission optimization of spatial 4-link mechanisms. Mech Mach Theory, 1982, 17: 263–283

    Article  Google Scholar 

  23. Alizade R I, Mohan Rao A V, Sandor G. Optimum synthesis of two degree of freedom planar and spatial function generating mechanism using the penalty function approach. J Eng Ind Trans ASME, 1975, 629-634

  24. Gosselin C M, Angeles J. Singularity analysis of closed loop kinematic chains. IEEE Trans Rob Autom, 1990, 6: 281–290

    Article  Google Scholar 

  25. Park F C, Kim J W. Singularity analysis of closed kinematic chains. ASME J Mech Des, 1999, 121: 32–38

    Article  Google Scholar 

  26. Liu G. Lou Y, Li Z. Singularities of parallel manipulators: a geometric treatment. IEEE Trans Rob Autom, 2003, 19: 579–594

    Article  Google Scholar 

  27. Liu X-J, Wang J, Pritschow G. Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms. Mech Mach Theory, 2006, 41: 145–169

    Article  MATH  MathSciNet  Google Scholar 

  28. Funabashi H, Takeda Y. Determination of singular points and their vicinity in parallel manipulators based on the transmission index. In: Proc 9th World Congr on the Theory of Machines and Mechanisms, Milan, Italy. Milano: Edizioni Unicopli, 1995. 1977–1981

    Google Scholar 

  29. Ma O, Angeles J. Architecture singularities of platform manipulators. In: Proceedings of the IEEE International Conf on Robotics and Automation, Sacramento, California, 1991. 1542–1547

  30. Zlatanov D, Bonev I A, Gosselin C M. Constarint singularities of parallel mechanisms. In: Proceedings of the IEEE International Conf. on Robotics and Automation, Washington, DC, 2002. 496-502

  31. Pittens K H, Podhorodeski R P. A family of Stewart platforms with optimal dexterity. J Rob Syst, 1993, 10: 463–479

    Article  MATH  Google Scholar 

  32. Stoughton R, Arai T. A modified Stewart platform manipulator with improved dexterity. IEEE Trans Rob Autom, 1993, 9: 166–173

    Article  Google Scholar 

  33. Voglewede P A, Ebert-Uphoff I. Measuring ‘closeness’ to singularities for parallel manipulators. In: Proc. IEEE Int. Conf. on Robotics and Automation, New Orleans, 2004. 4539–4544.

  34. Chablat D. Wenger P, Merlet J-P. Workspace analysis of the orthoglide using interval analysis. In: Proc. of International Symposium on Advances in Robot Kinematics, Caldes de Malavalla, Spain. London: Kluwer Academic, 2002. 397–406

    Google Scholar 

  35. Lou Y J, Liu G F, Chen N, et al. Optimal design of parallel manipulators for maximum effective regular workspace. In: Proc. of IEEE/RSJ International Conf. on Intelligent Robots and Systems, Edmonton, Canada, 2005. 1208–1213

  36. Sutherland G, Roth B. A transmission index for spatial mechanism. ASME J Eng Ind Trans, 1973. 589-597

  37. Takeda Y, Funabashi H, Ichimaru H. Development of spatial in-parallel actuated manipulators with six degrees of freedom with high motion transmissibility. JSME Int J, Ser C, 1997, 40: 299–308

    Google Scholar 

  38. Liu X-J, Wang J, Kim J. Determination of the link lengths for a spatial 3-DoF parallel manipulator. ASME J Mech Des, 2006, 128: 365–373

    Article  Google Scholar 

  39. Liu X-J, Wang J, Pritschow G. On the optimal kinematic design of the PRRRP 2 DoF parallel mechanism. Mech Mach Theor, 2006, 41: 1111–1130

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Precision Instruments, Tsinghua University, Beijing, 100084, China

    JinSong Wang, XinJun Liu & Chao Wu

Authors
  1. JinSong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. XinJun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chao Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to XinJun Liu.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 50775118), High Technology Research and Development Program of China (863 Program) (Grant No. 2006AA04Z227), and National Basic Research Program of China (973 Program) (Grant No. 2007CB714000)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Liu, X. & Wu, C. Optimal design of a new spatial 3-DOF parallel robot with respect to a frame-free index. Sci. China Ser. E-Technol. Sci. 52, 986–999 (2009). https://doi.org/10.1007/s11431-008-0305-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-008-0305-4

Keyword

Search

Navigation