A combined method for the kinematic and force analysis of complex mechanical systems

Methods for the kinematic and stress analysis of simple linkages with second-class Assur groups are currently most fully developed. However, there are many other, more complex mechanisms of practical interest. Therefore, the development of methods for the kinematic and force analysis of mechanisms with Assur groups of high classes is an important task. A universal method for the graphical analysis of mechanical systems (mechanisms) and statically determinate trusses including Assur groups of high classes is proposed. The mechanism under study is represented by a truss in which the output link connected to the fixed member is conventionally replaced with a hinged support. The reaction of the imaginary support to a unit moment applied to the input link of the mechanism under consideration is determined. The value of the reaction moment about the original link support defines relative angular velocities of the input and output links. The kinematic transfer functions of the real mechanism are determined from these velocities. If the reactions in the truss are difficult to determine, the truss is idealized by a mechanism in which one more link is removed and the reactions are determined by the kinematics of this simplified mechanism. If the resultant mechanism is also too complex to analyze, a new simpler truss should be considered. This process is continued until the simplified structure is represented only by dyads. Thus, the algorithm for the kinematic analysis is a linear chain of transformations from a mechanism to a truss and from a truss to a mechanism with a final return to the original mechanism along the same path. Similarly, the algorithm for the force analysis of a statically determinate truss implies the same recursion starting with a truss and ending with a mechanism. The proposed algorithm for the kinematic and force analysis allows developers to study mechanisms and mechanical systems with Assur groups of high classes used in carrying and lifting machines, structures, and equipment.

References

[1] Drong V.I., Dubinin V.V., Il’in M.M. Kurs teoreticheskoi mekhaniki [Course of Theoretical Mechanics]. Moscow, Bauman Press, 2011. 758 p.

[2] Kolovskii M.Z., Evgrafov A.N., Semenov Iu.A., Sloushch A.V. Teoriia mekhanizmov i mashin [Theory of Mechanisms and Machines]. Moscow, Izdatel’skii tsentr «Akademiia» publ., 2006. 560 p.

[3] Leont’ev N.N., Sobolev D.N., Amosov A.A. Osnovy stroitel’noi mekhaniki sterzhnevykh system [Basics of structural mechanics of rod systems]. Moscow, Assotsiatsii stroitel’nykh vuzov publ., 1996. 541 p.

[4] Peisakh E.E. Sborki rychazhnykh mekhanizmov [Linkage assembly]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2005, no. 4, pp. 17–24.

[5] Levitskii N.I. Teoriia mekhanizmov i mashin [Theory of Mechanisms and Machines]. Moscow, Nauka publ., 1990. 592 p.

[6] Smeliagin A.I. Struktura mekhanizmov i mashin [The structure of mechanisms and machines]. Novosibirsk, NNSTU publ., 2003. 305 p.

[7] Dzholdasbekov U.A. Grafoanaliticheskie metody analiza i sinteza mekhanizmov vysokikh klassov [Graphic analytical methods of analysis and synthesis of mechanisms of high classes]. Alma-Ata, Nauka, 1983. 256 p.

[8] Konstruirovanie mashin [Construction machinery]. Vol. 1. Ed. Frolov K.V. Moscow, Mashinostroenie, 1994. 528 p.

[9] Dvornikov L.T., Zhivago E.Ia. Osnovy teorii kinematicheskikh par [Fundamentals of the theory of kinematic pairs]. Novokuznetsk, SIBSIU publ., 1999. 105 p.

[10] Pozhbelko V.I. Universal’nye formuly strukturnogo analiza i sinteza mekhanizmov proizvol’noi struktury s pozitsii «chernogo iashchika» [Universal formula of structural analysis and synthesis of mechanisms of any structure from the perspective of «black box»]. Problemy mekhaniki sovremennykh mashin. Materialy vtoroi mezhdunarodnoi konferentsii [Problems in Mechanics of modern machines. Proceedings of the Second International Conference]. Ulan-Ude, ESSUTM publ., 2003, vol. 1, pp. 31–34.

[11] Peisakh E.E. Metodika avtomatizirovannogo strukturnogo sinteza ploskikh sharnirnykh mekhanizmov [Automated technique of structural synthesis of planar hinged mechanisms]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2009, no. 1, pp. 73–82.

[12] Dzholdasbekov U.A., Dzholdasbekov S.U., Temirbekov E.S., Savel’ev E.I. Teoreticheskii I eksperimental’nyi silovoi analiz sharnirno-rychazhnogo pod"emnika [Theoretical and experimental power analysis toggle the lift]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2004, no. 6, pp. 91–94.

[13] Starikov S.P., Dvornikov L.T. Novye resheniia v zadachakh kinematicheskogo issledovaniia ploskikh grupp Assura vysokikh klassov [New solutions in problems of plane kinematic study groups Assur high classes]. Mezhdunarodnaia konferentsiia po teorii mekhanizmov i mekhanike mashin. 2006. Sbornik dokladov [International Conference on Theory of mechanisms and mechanics of machines. 2006. Collection of reports]. Krasnodar, KubGTU publ., 2006, pp. 63–64.

[14] Teoriia mekhanizmov i mekhanika mashin [Theory of mechanisms and mechanics of machines]. Ed. Timofeev G.A. Moscow, Bauman Press, 2012. 655 p.