Screw Representation of Flexible Elements

  • Chen QiuEmail author
  • Jian S. Dai
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 139)


As discussed in Sect.  2.4, the definitions of the twist and wrench describe the instantaneous velocity (infinitesimal displacement) of a rigid body and the external load applied at it in the framework of screw theory. Also, an example is given to demonstrate their application in describing the degrees of freedom and constraints of a compliant parallel mechanism in Sect.  2.4.3. Further screw theory is utilized to systematically design compliant mechanisms based on the mechanism-equivalence principle. According to this principle, the design of a compliant mechanism can be categorized into two steps: the design of flexible elements and the integration of them. We begin with flexible elements in this chapter and explore their performance both qualitatively and quantitatively through their internal compliance/stiffness. Particularly, flexible elements are categorized according to their feasible degrees of freedom (DOF). Single DOF flexible elements are examined first in Sect. 3.2, followed by multiple DOF flexible elements in Sect. 3.3.


  1. 1.
    Huang, S., Schimmels, J.M.: The bounds and realization of spatial stiffnesses achieved with simple springs connected in parallel. IEEE Trans. Robot. Autom. 14(3), 466–475 (1998)CrossRefGoogle Scholar
  2. 2.
    Shigley, J.E., Mischke, C.R., Budynas, R.G., Liu, X., Gao, Z.: Mechanical Engineering Design, vol. 89. McGraw-Hill, New York (1989)Google Scholar
  3. 3.
    Parise, J.J., Howell, L.L., Magleby, S.P.: Ortho-planar linear-motion springs. Mech. Mach. Theory 36(11), 1281–1299 (2001)zbMATHGoogle Scholar
  4. 4.
    Awtar, S., Slocum, A.H.: Constraint-based design of parallel kinematic XY flexure mechanisms. J. Mech. Des. 129(8), 816–830 (2007)Google Scholar
  5. 5.
    Blanding, D.L.: Exact constraint: machine design using kinematic processing. American Society of Mechanical Engineers (1999)Google Scholar
  6. 6.
    Pashkevich, A., Chablat, D., Wenger, P.: Stiffness analysis of overconstrained parallel manipulators. Mech. Mach. Theory 44(5), 966–982 (2009)CrossRefGoogle Scholar
  7. 7.
    Pashkevich, A., Klimchik, A., Chablat, D.: Enhanced stiffness modeling of manipulators with passive joints. Mech. Mach. Theory 46(5), 662–679 (2011)CrossRefGoogle Scholar
  8. 8.
    Duffy, J.: Statics and Kinematics with Applications to Robotics. Cambridge University Press (1996)Google Scholar
  9. 9.
    Hale, L.C.: Principles and techniques for designing precision machines. Technical Report, Lawrence Livermore National Lab., CA, US (1999)Google Scholar
  10. 10.
    Tuma, J.J.: Handbook of Structural and Mechanical Matrices. McGraw-Hill Inc., New York, NY, USA (1987)Google Scholar
  11. 11.
    Ciblak, N., Lipkin, H.: Design and analysis of remote center of compliance structures. J. Robot. Syst. 20(8), 415–427 (2003)CrossRefGoogle Scholar
  12. 12.
    Young, W.C., Budynas, R.G.: Roark’s Formulas for Stress and Strain, vol. 6. McGraw-Hill, New York (2002)Google Scholar
  13. 13.
    Howell, L.L., Magleby, S.P., Olsen, B.M., Wiley, J.: Handbook of Compliant Mechanisms. Wiley Online Library (2013)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Innovation CentreNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of InformaticsKing’s College LondonLondonUK

Personalised recommendations