Passive Rotation of Rotational Joints and Its Computation Method

  • Shucen DuEmail author
  • Josef Schlattmann
  • Stefan Schulz
  • Arthur Seibel
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


This paper discusses the equivalence condition of the input and output rotation of a passive rotational joint and provides a general method to compute the output rotation angle. In a Stewart-Gough platform, the fixed base platform is usually connected to the moveable manipulator platform by six identical kinematic chains consisting of rotational joints and linear actuators. When using lead screws for the linear actuators, possible passive rotations of the rotational joints can be harmful because they may lead to additional length variations of the linear actuators or cause extra stresses if the rotations are obstructed. This paper provides a for computing these passive rotations by using vector comparison and demonstrates its application on the examples of a universal joint, a Rzeppa joint, and a Tracta joint.


Passive rotation Rotational joint Constant-velocity joint 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the German Research Foundation (DFG) under grant SCHL 275/15-1.


  1. 1.
    Du, S., Schlattmann, J., Schulz, S., Seibel, A.: Passive rotation compensation in parallel kinematics using quaternions. Applied Mathematics and Mechanics 16(1), 51–52 (2016)Google Scholar
  2. 2.
    Du, S., Schlattmann, J., Schulz, S., Seibel, A.: Comparison of three methods of length compensation in a parallel kinematic and their equivalence conditions. MEAE 2018, MATEC Web Conf. p. 198 02003 (2018)Google Scholar
  3. 3.
    Fenaille, M.P.: Double cardan sph´erique pour automobiles a` roues avant motrices et di-rectrices (1927). Patent. FR 628309.Google Scholar
  4. 4.
    Geisthoff, H.: Double hookes joint (1986). Patent. DE 3636194C1.Google Scholar
  5. 5.
    Gogu, G.: Structural synthesis of parallel robots: part 1 – methodology. Springer-Verlag, Dordrecht (2008)Google Scholar
  6. 6.
    Hunt, K.H.: Constant velocity shaft coupling: a general theory. Journal of Engineering for Industry 95(2), 455–464 (1973)Google Scholar
  7. 7.
    Molly, H., Bengisu, O.: Das Gleichgang-Gelenk im Symmetriespiegel. Automob. Ind. 14(2), 45–54 (1969). In German.Google Scholar
  8. 8.
    Orain, M.: Die Gleichlaufgelenke, allgemeine Theorie und experimentelle Forschung. Glaenzer-Spicer, Paris (1976)Google Scholar
  9. 9.
    Pennestr`ı, E., Rossi, V., Salvini, P., Valentini, P.P., Pulvirenti, F.: Review and kinematics of Rzeppa-type homokinetic joints with straight crossed tracks. Mechanism and Machine Theory 90(1), 142–161 (2015)Google Scholar
  10. 10.
    Riebe, S., Ulbrich, H.: Modelling and online computation of the dynamics of a parallel kinematic with six degrees-of-freedom. Archive of Applied Mechanics 72(11–12), 817–829 (2003)Google Scholar
  11. 11.
    Rzeppa, A.H.: Constant velocity universal joint (1928). Patent. US 1665280.Google Scholar
  12. 12.
    Schmelz, F., Seherr-Thoß, H.C.: Die Entwicklung der Gleichlaufgelenke für den Frontantrieb. VDI-Report 418, 197–207 (1981). In German.Google Scholar
  13. 13.
    Schulz, S., Seibel, A., Schlattmann, J.: Closed-form solution for the direct kinematics problem of planar 3-RPR parallel mechanisms. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 968–973. Brisbane, Australia (2018)Google Scholar
  14. 14.
    Schulz, S., Seibel, A., Schlattmann, J.: Solution for the direct kinematics problem of the general Stewart-Gough platform by using only linear actuators’ orientations. In: J. Lenarčič, V. Parenti-Castelli (eds.) Advances in Robot Kinematics 2018, pp.56–64. Springer, The Netherlands (2019)Google Scholar
  15. 15.
    Schulz, S., Seibel, A., Schreiber, D., Schlattmann, J.: Sensor concept for solving the direct kinematics problem of the Stewart-Gough platform. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1959–1964. Vancouver, BC, Canada (2017)Google Scholar
  16. 16.
    Seherr-Thoß, H.C., Schmelz, F., Aucktor, E.: Universal joints and driveshafts: analysis, design, applications. Springer-Verlag, Berlin Heidelberg New York (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Shucen Du
    • 1
    Email author
  • Josef Schlattmann
    • 1
  • Stefan Schulz
    • 1
  • Arthur Seibel
    • 1
  1. 1.Workgroup on System Technologies and Engineering Design Methodology, Hamburg University of TechnologyHamburgGermany

Personalised recommendations