Universal L0-algorithm of structural synthesis and analysis of the family of the new platform parallel-structure manipulators

Structural synthesis of various multi-circuit and multi-link mechanisms in a parallel structure appears to be one of the most complicated problems both in the theory of mechanisms and machines, and in the mechanical engineering for various robotics areas. The paper considers directed structural synthesis and analysis based on the universal L0-algorithm. Examples of its application are provided to create the relative manipulation mechanisms for group operations, multi-platform manipulators, anti-parallelogram and parallelogram tripod manipulators without special provisions and with the increased number of controlled degrees of freedom up to 12. Common properties of the entire family of articulated platform manipulators created at the invention level include the separate motion kinematics and the absence of harmful redundant connections in all the closed loops of flat and spatial synthesized mechanisms. Their performance and effectiveness were confirmed both experimentally and theoretically according to the new universal structural mobility formula.

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] 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] 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] 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

[17] 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

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

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

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

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

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

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

[24] 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

[25] 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

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

[27] 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, 2027, vol. 100, no. 6, pp. 1–16, doi: https://doi.org/10.1016/j.mechmachtheory.2016.01.001

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

[29] 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.).

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

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

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

[33] 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.).

[34] 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.).

[35] Vyshnegradskiy I.A. Publichnye populyarnye lektsii o mashinakh. O teorii mekhanizmov bez formul [Public popular lections on machines. On mechanisms theory without formulas]. Moscow, Librikom Publ., 2015. 448 p. (In Russ.).

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

[37] Pozhbelko V.I. Prostranstvennyy manipulyator [Spatial manipulator]. Patent RU 2758377. Appl. 24.02.2021, publ. 28.10.2021. (In Russ.).

[38] Pozhbelko V.I. Prostranstvennyy parallelogrammnyy mekhanizm manipulyatora [Spatial parallelogram mechanism of manipulator]. Patent RU 2784764. Appl. 07.04.2022, publ. 29.11.2022. (In Russ.).

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

[40] Pozhbelko V.I. Platformennyy robot [Platform robot]. Patent RU 2751778. Appl. 07.07.2020, publ. 16.07.2021. (In Russ.).

[41] Pozhbelko V.I. Prostranstvennyy platformennyy VIP-manipulyator [Spatial platform VIP-manipulator]. Patent RU 2722165. Appl. 19.11.2019, publ. 27.05.2020. (In Russ.).

[42] Pozhbelko V.I. Universal structural method in synthesis and constructing the complete atlas of the multiloop orthogonal structures of the self-adjusting linkages in mechanical engineering. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2023, no. 3, pp. 25–40, doi: http://dx.doi.org/10.18698/0536-1044-2023-3-55-72 (in Russ.).

[43] Kolovsky M.Z., Evgrafov A.N., Semenov Yu.A. et al. Advanced theory of mechanisms and machines. Springer, 2000. 396 p.