On the Choice of Parameters of the Bennett Mechanism and Modelling It in MATLAB

The article deals with the analysis of the so-called Bennett mechanism representing a four-link mechanism consisting of four links connected by flat hinges. From the point of view of mathematical apparatus and practical application, the approach proposed by the author is considerably simpler than those described in the literature. When such a mechanism is implemented, the choice of parameters that ensure its mobility plays a significant role as the number of degrees of freedom is negative. A method for the mechanism analysis and the choice of the mechanism parameters is proposed. The method comprises two approaches based on the generalized coordinates and the generalized velocities respectively. Using the proposed method, the author has obtained parameters of the mechanism that are essentially different from the ones proposed by Bennett. The kinematic model of the mechanism is developed in the MATLAB environment.

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 DETC2000/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 September 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.