Multiloop theory of the self-aligning mechanisms formation in machine engineering and practical construction of the complete atlas for the two-degree-of-freedom mechanism K-chains

The paper provides a new approach to representing the mechanisms design in the form of a structural mathematical model calculated on the basis of the integer solutions, it is a kind the multi-loop kinematic chain outer shell filled with all possible calculated sets of the mutually independent closed loops to create various mechanisms without the redundant connections. The proposed approach efficiency was confirmed by examples of its application in designs created at the invention levels: a manipulator mechanism for group operations and a four-capacitance vibration mixer synthesized on the basis of a floating parallelogram without special uncontrolled and dead center positions. An extended example is considered of constructing a comprehensive analysis of a systematized complete atlas that consists of sixty closed circuits to create the two-degree-of-freedom self-aligning lever mechanisms in mechanical engineering and contains twenty new structural diagrams without the redundant connections. Performance of the new two-degree-of-freedom lever mechanisms was confirmed experimentally and by calculating their mobility based on the new universal structural formulas.

References

[1] Artobolevskiy I.I. Mekhanizmy v sovremennoy tekhnike [Mechanisms in modern technics]. Moscow, LENAND Publ., 2019. 500 p. (In Russ.).

[2] Glazunov V.A., ed. Novye mekhanizmy v sovremennoy robototekhnike [New mechanisms in modern robotics]. Moscow, Tekhnosfera Publ., 2018. 316 p. (In Russ.).

[3] Mudrov A.G., Mudrova A.A., Sakhapov R.L. Prostranstvennye apparaty s meshalkoy i smesiteli [Spatial apparatuses with agitators and mixers]. Moscow, Knorus Publ., 2021. 190 p. (In Russ.).

[4] Markovets K.I., Polotebnov V.O. Synthesis of mechanisms of material handling mechanism with a toothed bar straight line section of the movement. Izvestiya vysshikh uchebnykh zavedeniy. Tekhnologiya legkoy promyshlennosti [The News of Higher Educational Institutions. Technology of Light Industry], 2018, vol. 39, no. 1, pp. 117–121. (In Russ.).

[5] Smelyagin A.I., Prikhodko A.A. Structural synthesis of reciprocating rotational mixing device complex actuator. Izvestiya vysshikh uchebnykh zavedeniy. Pishchevaya tekhnologiya [Izvestiya Vuzov. Food Technology], 2014, no. 5–6, pp. 85–88. (In Russ.).

[6] Pozhbelko V.I. A unified theory of structure, synthesis and analysis of multibody mechanical systems with geometrical, flexible and dynamic connections. Part 1. Basic structural equations and universal structure tables. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2020, no. 9, pp. 24–23, doi: https://doi.org/10.18698/0536-1044-2020-9-24-43 (in Russ.).

[7] Nesmeyanov I.A. Structural synthesis of self-aligning gears of industrial robots with parallel kinematics. Vestnik Bryanskogo GTU [Bulletin of Bryansk State Technical University], 2019, no. 4, pp. 4–13, doi: https://doi.org/10.30987/article_5cb58f4ed2c444.85435034 (in Russ.).

[8] Pozhbelko V. Type synthesis method of planar and spherical mechanisms. In: IFToMM WC-2019. Springer, 2019, pp. 1517–1526, doi: https://doi.org/10.1007/978-3-030-20131-9_150

[9] Sun W. A joint-joint matrix representation of planar kinematic chains. Adv. Mech. Eng., 2018, vol. 10, no. 6, doi: https://doi.org/10.1177/1687814018778404

[10] Zou Y., He P., Pei Y. Automatic topological structural synthesis algorithm. Adv. Mech. Eng., 2016, vol. 8, no. 3, doi: https://doi.org/10.1177/1687814016638055

[11] Ding H.F., Hou F.M., Kecskemethy A. et al. Synthesis of the whole family of 1-DOF kinematic chains. Mech. Mach. Theory, 2012, vol. 47, pp. 1–15, doi: https://doi.org/10.1016/j.mechmachtheory.2011.08.011

[12] Pozhbelko V. A unified structure theory of multibody open-, closed-, and mixed-loop mechanical systems with simple and multiple joint kinematic chains. Mech. Mach. Theory, 2016, vol. 100, no. 6, pp. 1–16, doi: https://doi.org/10.1016/j.mechmachtheory.2016.01.001

[13] Rao A.C. Loop based detection of isomorphism among chains, inversions and type of freedom in multi degree of freedom chain. J. Mech. Des., 2000, vol. 122, no. 1, pp. 31–42, doi: https://doi.org/10.1115/1.533543

[14] Muller A. Kinematic topology and constraints of multi-loop linkages. Robotica, 2018, vol. 36, no. 11, pp. 1641–1663, doi: https://doi.org/10.1017/S0263574718000619

[15] Talaba D. Mechanical models and the mobility of robots and mechanisms. Robotica, 2015, vol. 33, no. 1, pp. 181–193, doi: https://doi.org/10.1017/S0263574714000149

[16] Evgrafov A.N., Petrov G.N. Computer simulation of mechanisms. In: Advances in mechanical engineering. Springer, 2017, pp. 45–56, doi: https://doi.org/10.1007/978-3-319-53363-6_6

[17] Kozhevnikov S.N. Osnovaniya strukturnogo sinteza mekhanizmov [Fundamentals of structural synthesis of mechanisms.]. Kiev, Naukova Dumka Publ., 1979. 232 p. (In Russ.).

[18] Reshetov L.N. Samoustanavlivayushchiesya mekhanizmy [Self-aligning mechanisms]. Moscow, Mashinostroenie Publ., 1991. 288 p. (In Russ.).

[19] Umnov N.V., Silvestrov E.E. [Using homotopy methods in mechanism synthesis]. Sb. dok. mezhd. konf. po teorii mekhanizmov i mashin [Proc. Int. Conf. on Mechanisms and Machines Theory]. Krasnodar, Kubanskiy GTU Publ., 2006, pp. 47–48. (In Russ.).

[20] Kraynev A.F. Mekhanika mashin. Fundamentalnyy slovar [Mechanics of machines. A fundamental dictionary]. Moscow, Mashinostroenie Publ., 2000. 904 p. (In Russ.).

[21] Peysakh E.E. Atlas of structural schemes of eight-link planar articulated mechanisms. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2006, vol. 4, no. 1, pp. 3–17. (In Russ.).

[22] Timofeev G.A., ed. Teoriya mekhanizmov i mashin [Mechanisms and machines theory]. Moscow, Bauman MSTU Publ., 2017. 566 p. (In Russ.).

[23] Pozhbelko V.I. Platformennyy mekhanizm otnositelnogo manipulirovaniya [Relative manipulation platform]. Patent RU 2758391. Appl. 25.02.2021, publ. 28.10.2021. (In Russ.).

[24] Pozhbelko V.I. Mekhanizm plavayushchego sharnirnogo parallelogramma [Mechanism of floating articulate parallelogram]. Patent RU 2765387. Appl. 19.08.2021, publ. 28.01.2022.

[25] Pozhbelko V.I. Universal algorithm for the synthesis of structural schemes of complex single and multi-moving lever mechanisms. Sovremennoe mashinostroenie. Nauka i obrazovanie, 2022, no. 11, pp. 91–100. (In Russ.).

[26] Pozhbelko V.I., Kuts E.N. A new general methodology for the topological structure analysis of multiloop mechanisms with multiple joints and crossing links. In: MTM&Robotics 2020. Springer, 2020, pp. 155–163, doi: https://doi.org/10.1007/978-3-030-60076-1_14

[27] Pozhbelko V. Advanced technique of type synthesis and construction of veritable complete atlases of F-DOF generalized kinematic chains. In: EnCoMes-2018. Springer, 2019, vol. 59, pp. 207–214, doi: https://doi.org/10.1007/978-3-319-98020-1_24