Kinematics of the Mechanism Consisting of Three Mobile Links Connected by Ball or Flat Joints
Authors: Ioffe M.L. | Published: 08.04.2016 |
Published in issue: #4(673)/2016 | |
Category: Calculation and Design of Machinery | |
Keywords: kinematics of parallel manipulators, spatial three-link mechanism, Bennett mechanism, number of degrees of freedom, generalized coordinates, direction cosine matrix |
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.