Universal structural method in synthesis and constructing the complete atlas of the multiloop orthogonal structures of the self-adjusting linkages in mechanical engineering

The paper considers theory and practice of structural synthesis, classification of assembly and construction of a complete atlas of the new class multi-loop mechanisms, where the multi-hinge linkages are made with all hinges positioned on the same line, such mechanisms are called the orthogonal mechanisms. Original universal method is proposed for structural synthesis of these multi-hinge linkage mechanisms with a given large number of independent closed loops in the kinematic chain to create a variety of mechanisms with the given different number of degrees of freedom of their drive. Using this method to create new efficient multilink mechanisms does not require introduction of complex computer programs and consideration of tens of thousands of the Assur groups in order to build complete atlases in closed chains of the parallel structure mechanisms reliably not containing any harmful redundant links. This makes it possible to solve the problem of structural synthesis of the self-adjusting orthogonal mechanisms, including both single and multiple hinged joints of the lever links. Based on the orthogonal structural synthesis proposed algorithm, a complete atlas of 20 non-isomorphic three-circuit orthogonal eight-link basic kinematic chains was constructed for the first time, which formed the basis for synthesizing 27 new schemes of single-moving flat hinged mechanisms with simple hinges. This increases the possible composition of their database to 180 closed structures. Effectiveness of the proposed universal synthesis method is confirmed by examples of inventions of various multi-loop orthogonal self-adjusting lever mechanisms and manipulators of the parallel structure.

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. 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] Kuts E.N. Structural synthesis of multiloop lever mechanisms with multiple hinges and the most complex double hinge link. Sovremennoe mashinostroenie. Nauka i obrazovanie, 2019, no. 8, pp. 201–214. (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] Chen L.M. Digital and discrete geometry. Springer, 2014. 322 p.

[13] Norton R.L. Design in machinery. McGraw Hill, 2011. 857 p.

[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] Peisakh E.E. Technique of automated structural synthesis of planar jointed mechanisms. J. Mach. Manuf. Reliab., 2009, vol. 38, no. 1, pp. 62–70, doi: https://doi.org/10.3103/S1052618809010129

[16] Peysakh E.E. Structural synthesis of closed kinematic chains (Gr?bler chains). Part 1. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2008, vol. 6, no. 1, pp. 4–14. (In Russ.).

[17] Peysakh E.E. Structural synthesis of closed kinematic chains (Gr?bler chains). Part 2. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2008, vol. 6, no. 2, pp. 3–17. (In Russ.).

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

[19] Peysakh E.E. To the discussion of the problem of structural synthesis of planar articulated mechanisms. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2006, vol. 4, no. 1, pp. 49–54. (In Russ.).

[20] 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

[21] Babichev D., Evgrafov A., Lebedev S. Lever mechanisms: the new approach to structural synthesis and kinematic analysis. In: IFToMM WC-2019. Springer, 2019, pp. 1030–1050, doi: https://doi.org/10.1007/978-3-030-20131-9_56

[22] Peisakh E.E. An algorithmic description of the structural synthesis of planar Assur group. J. Mach. Manuf. Reliab., 2007, vol. 36, no. 6, pp. 505–514, doi: https://doi.org/10.3103/S1052618807060015

[23] Vicker J.J., Pennock G.R., Shingley J.E. Theory of mechanisms. Oxford University Press, 2017. 950 p.

[24] Ceccarelli M. Fundamentals of mechanisms of robotic manipulations. Springer, 2004. 312 p.

[25] Kong X., Gosselin C.M. Type synthesis of parallel mechanisms. Springer, 2007. 268 p.

[26] Gogu G. Structural synthesis of parallel robots. Part 1: Methodology. Springer, 2008. 706 p.

[27] Tsai L.W. Robot Analysis. The mechanics of serial and parallel manipulators. Wiley, 1999. 520 p.

[28] Aefattani R., Luck C.A. A lamina-emergent frustum using a bistable collapsible compliant mechanism. Mech. Des., 2018, vol. 140, no. 12, art. 125001, doi: https://doi.org/10.1115/1.4037621

[29] Ding H., Hou F., Kecskemethy A. et al. Synthesis of a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible DOFs. Mech. Mach. Theory, 2011, vol. 46, no. 11, pp. 1588–1600, doi: https://doi.org/10.1016/j.mechmachtheory.2011.07.012

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

[31] Pozhbelko V. Advanced technique of type synthesis and construction og 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

[32] 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, vol. 100, no. 6, pp. 1–16, doi: https://doi.org/10.1016/j.mechmachtheory.2016.01.001

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

[34] 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.).

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

[36] Pozhbelko V.I. The method of topological structural analysis and new criteria for the identification of complex multi-circuit mechanical systems. Teoriya mekhanizmov i mashin, 2014, vol. 12, no. 2, pp. 50–65. (In Russ.).

[37] Pozhbelko V.I. Universal method of topological synthesis of multiloop structures and atlas of kinematic chains of eight-link mechanisms and their invariants. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2014, vol. 12, no. 2, pp. 66–80. (In Russ.).

[38] Dvornikov L.T. Experience of structural synthesis of mechanisms. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2004, vol. 2, no. 2, pp. 3–17. (In Russ.).

[39] Dvornikov L.T. Polnyy sostav ploskikh sharnirnykh vosmizvennykh mekhanizmov [Full composition of flat articulated eight-link mechanisms]. Patent RU 2015620078. Appl. 19.11.2014, publ. 15.01.2015. (In Russ.).

[40] Dvornikov L.T., Gudimova L.N. Justifications of a universal synthesis method of kinematic chains. Fundamentalnye issledovaniya [Fundamental research], 2015, no. 4, pp. 48–54. (In Russ.).

[41] Romantsev A.A. To the question of creating structural schemes of flat articulated groups of links. Teoriya mekhanizmov i mashin [Theory of Mechanisms and Machines], 2014, vol. 12, no. 1, pp. 81–90. (In Russ.).

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

[43] 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.).

[44] 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.).

[45] Pozhbelko V.I. Sharnirnyy trekhkrivoshipnyy mekhanizm [Hinged crank mechanism]. Patent RU 2740526. Appl. 07.07.2020, publ. 15.01.2021. (In Russ.).

[46] Pozhbelko V.I. Rychazhnyy pyatizvennyy dvukhporshnevoy mekhanizm [Lever five-link mechanism]. Patent RU 2751011. Appl. 08.12.2020, publ. 07.07.2021. (In Russ.).

[47] Pozhbelko V.I. Skladyvayushchiysya gruzopodemnyy manipulyator parallelnoy struktury [Folding lifting manipulator of parallel structure]. Patent RU 2780824. Appl. 27.10.2021, publ. 04.10.2022. (In Russ.).

[48] Pozhbelko V.I. Sfericheskiy V-manipulyator [Spherical V-manipulator]. Patent RU 2730345. Appl. 23.01.2020, publ. 21.08.2020. (In Russ.).