Kinematic analysis of a planetary mechanism with the oval gearwheels

Researchers, inventors and engineers are interested in mechanical transmissions with the non-circular gearwheels due to their significant compactness and implementation of a wide range of the transmission functions. The paper presents kinematic analysis of a planetary transmission with the oval gearwheels, which, depending on the gearwheels’ size, allows for various types of the output shaft motion, i.e. reciprocating, intermittent and one-way uneven rotation. It proposes the mechanism kinematic model and determines the law of motion as an analogue of the speed and position function of the output link. An experimental stand was designed and developed for the proposed planetary transmission. Four options of the mechanism with different kinematic parameters were studied on its basis. The position function was constructed by measuring rotation angles of the mechanism input and output shafts using the absolute encoders. Results of the measurement error statistical analysis indicate adequacy of the constructed kinematic model allowing it to be introduced in dynamic force studies and design of machines based on the proposed planetary transmission.
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References

[1] Addomine M., Figliolini G., Pennestrì E. A landmark in the history of non-circular gears design: The mechanical masterpiece of Dondi’s astrarium. Mech. Mach. Theory, 2018, vol. 122, pp. 219–232, doi: https://doi.org/10.1016/j.mechmachtheory.2017.12.027

[2] Pozhbelko V.I., Shagiakhmetov A.I., Akhmetshin N.I. A new way to regulate the angle of standstill and classification of adjustable toothed-lever mechanisms of periodic rotation. Vestnik YuUrGU. Ser. Mashinostroenie [Bulletin of the South Ural State University. Ser. Mechanical Engineering Industry], 2005, no. 1, pp. 181–184. (In Russ.).

[3] Tarabarin V.B., Tarabarina Z.I. Model gears with variable ratios collected in Bauman Moscow State Technical University. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2014, no. 12, pp. 84–91, doi: https://doi.org/10.18698/0536-1044-2014-12-84-91 (in Russ.).

[4] Zheng F., Hua L., Han X. et al. Synthesis of indexing mechanisms with non-circular gears. Mech. Mach. Theory, 2016, vol. 105, pp. 108–128, doi: https://doi.org/10.1016/j.mechmachtheory.2016.06.019

[5] Figliolini G., Angeles J. Synthesis of the base curves for N-lobed elliptical gears. J. Mech. Des., 2005, vol. 127, no. 5, pp. 997–1005, doi: https://doi.org/10.1115/1.1901707

[6] Ottaviano E., Mundo D., Danieli G.A. et al. Numerical and experimental analysis of non-circular gears and cam-follower systems as function generators. Mech. Mach. Theory, 2008, vol. 43, no. 8, pp. 996–1008, doi: https://doi.org/10.1016/j.mechmachtheory.2007.07.004

[7] Litvin F.L. Nekruglye zubchatye kolesa [Non-round gears]. Moscow, Leningrad, Mashgiz Publ., 1956. 312 p. (In Russ.).

[8] Jang H.S., Lee C.H., Park G.Y. et al. Study on design of non-circular gears for speed control of the squid belly opening and gutting machine (SBOGM). Appl. Sci., 2021, vol. 11, no. 7, art. 3268, doi: https://doi.org/10.3390/app11073268

[9] Doege E., Hindersmann M. Optimized kinematics of mechanical presses with noncircular gears. CIRP Annals, 1997, vol. 46, no. 1, pp. 213–216, doi: https://doi.org/10.1016/S0007-8506(07)60811-7

[10] Doege E., Meinen J., Neumaier T. et al. Numerical design of a new forging press drive incorporating non-circular gears. Proc. Inst. Mech. Eng. B: J. Eng. Manuf., 2001, vol. 215, no. 4, pp. 465–471, doi: https://doi.org/10.1243/0954405011518430

[11] Prikhod’ko A.A. Kinematics of a two-stage transmission with elliptical gears for nonuniform motion. Russ. Eng. Res., 2022, vol. 42, no. 10, pp. 1033–1036, doi: https://doi.org/10.3103/S1068798X22100264

[12] Prikhodko A.A. Experimental kinematic analysis of an intermittent motion planetary mechanism with elliptical gears. J. Meas. Eng., 2020, vol. 8, no. 3, pp. 122–131, doi: https://doi.org/10.21595/jme.2020.21583

[13] Litvin F.L., Fuentes A. Gear geometry and applied theory. Cambridge University Press, 2004. 800 p.

[14] Kireev S.O., Ershov Yu.V., Padalko N.A. Determination parameters of centroid oval tooth wheels. Izvestiya vysshikh uchebnykh zavedeniy. Severo-kavkazskiy region. Tekhnicheskie nauki [Bulletin of Higher Educational Institutions. North Caucasus Region. Technical Sciences], 2009, no. 6, pp. 90–91. (In Russ.).

[15] Barash V.Ya. Uncertainty and error in modern metrology. Zakonodatelnaya i prikladnaya metrologiya [Legal and Applied Metrology], 2009, no. 5, pp. 15–20. (In Russ.).

[16] Hall B.D., White D.R. An introduction to measurement uncertainty. Measurement Standards Laboratory of New Zealand, 2020. 50 p.

[17] Possolo A., Meija J. Measurement uncertainty: a reintroduction. Montevideo, Sistema Interamericano de Metrologia, 2022. 107 p.