Kinematics of the Mechanism Consisting of Three Mobile Links Connected by Ball or Flat Joints

In recent years the geometry and kinematics of parallel manipulators have been given considerable attention. The most interest amongst researchers has been generated by Stewart-Gough type manipulators that are widely used in various fields. The manipulator consists of a moving platform and a base that are connected by 6 moving links and 12 joints. The kinematics and geometry of such a mechanism can be easily understood by studying a simpler mechanism consisting of three moving links connected by ball or flat joints, an example of which can be the well-known Bennett mechanism. In this article the kinematics of the mechanism are analyzed, and an algorithm of parameter selection is proposed.

References

[1] Bennett G.T. A new mechanism. Engineering, 1903, vol. 76, pp. 777–778.

[2] Bennett G.T. The scew isogram-mechanism. Proceedings of the London Mathematical Society, 1913–1914, vol. 13, pp. 151–173.

[3] Hunt K.H. Kinematic Geometry of Mechanisms. Oxford engineering science series, University Press, Oxford. 1978. 484 p.

[4] Perez A., McCarthy J.M. Dimensional synthesis of Bennett linkages. Proceedings of the ASME Design Engineering Technical Conferences, 2000, Baltimore, Maryland, USA, paper ETC2000/MECH-14069.

[5] Brunnthaler K., Schrocker H.-P., Husty M. A New Method for the Synthesis of Bennett Mechanisms, Proceedings of CK2005, International Workshop on Computational Kinematics, Cassino, May 4–6, 2005, pp. 1–8.

[6] Iarullin M.G., Mingazov M.R. Sintez strukturnykh modifikatsii mekhanizma Bennetta [Synthesis of structural modifications mechanism Bennett]. Available at: http://www.mmf.spbstu.ru/mese/2014/129.pdf (accessed 2 November 2015).

[7] Iarullin M. G., Mingazov M. R. Kratkii analiz modifikatsii mekhanizmov Bennetta [A brief analysis of the modification arrangements Bennett]. Problemy mekhaniki sovremennykh mashin. Materialy 5 mezhdunarodnoi konferentsii [Problems of modern machines. Proceedings of the 5 International Conference]. Ulan-Ude, VSGUTU publ., 2012, vol. 1, pp. 177–181.

[8] Iarullin M.G., Mingazov M.R. Strukturnyi sintez dvukhpodvizhnogo prostranstvennogo 5R mekhanizma i elementy slediashchego upravleniia [Structure Synthesis of Differential 5R Linkage and Tracking Control Elements]. Izvestiia Samarskogo nauchnogo tsentra Rossiiskoi akademii nauk [Proceedings of the Samara Scientific Center of the Russian Academy of Sciences]. 2014, no. 6, pp. 214–220.