Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs
DOI:
https://doi.org/10.22213/2413-1172-2021-3-97-103Keywords:
kinematic pair, constraint, equivalent mechanism, geared linkageAbstract
The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.References
Müller A. [Higher-order constraints for higher kinematic pairs and their application to mobility and shakiness analysis of mechanisms]. Meccanica, 2017, vol. 52, pp. 1669-1684. DOI: 10.1007/s11012-016-0496-x.
Fedoseev G.N., Semin A.G., Korneenko D.V. [The study of the kinematic capabilities of the gear-lever mechanism with quasi-stops]. Vestnik Vitebskogo gosudarstvennogo tekhnologicheskogo universiteta, 2015, vol. 28, pp. 111-115 (in Russ.).
Suncov A.S. [Load distribution along the length of the teeth of the wheels of a two-satellite planetary gear with a prefabricated carrier]. Vestnik IzhGTU imeni M.T. Kalashnikova, 2016, vol. 19, no. 3, pp. 7-8 (in Russ.). DOI: 10.22213/2413-1172-2016-3-7-8.
Turygin Yu.V., Zubkova Yu.V., Speranskih T.N. [Development of a mathematical model of the movement of the robot output link based on the analysis of positioning errors]. Vestnik IzhGTU imeni M.T. Kalashnikova, 2018, vol. 21, no. 1, pp. 19-22 (in Russ.). DOI: 10.22213/2413-1172-2018-1-19-22.
Zhivago E.Ya. [History of the creation and classification of kinematic pairs]. Teoriya mekhanizmov i mashin, 2008, vol. 6, no. 2, pp. 26-34 (in Russ.).
Gudimova L.N., Dvornikov L.T. [Problems of elimination of excess bonds in planar articulated mechanisms]. Fundamental’nye issledovaniya, 2013, no. 6, pp. 24-32 (in Russ.).
Ermak V.N. [A new method for identifying and eliminating excess connections in multi-circuit mechanisms]. Izvestiya vysshih uchebnyh zavedenij, 2012, no. 1, pp. 18-23 (in Russ.).
Timofeev G.A., Samojlova M.V. [Structural analysis of a planetary mechanism with two floating links]. Izvestiya vysshih uchebnyh zavedenij. Mashinostroenie, 2017, no. 6, pp. 18-27 (in Russ.). DOI: 10.18698/0536-1044-2017-6-18-27.
Timofeev G.A., Podchasov E.O. [Using the graph method in the structural analysis of a wave gear]. Vestnik nauchno-tekhnicheskogo razvitiya, 2016, no. 6, pp. 23-31 (in Russ.).
Pozhbelko V.I., Kuc E.N. [System analysis and areas of application of multi-circuit linkage mechanisms with multiple joints in modern engineering]. Izvestiya vysshih uchebnyh zavedenij, 2020, no. 2, pp. 11-25 (in Russ.). DOI: 10.18698/0536-1044-2020-2-11-25.
Kuc E.N. [Structural synthesis of multi-circuit linkage mechanisms with multiple joints and the most complex double-joint link]. Sovremennoe mashinostroenie. Nauka i obrazovanie, 2019, no. 8, pp. 201-214 (in Russ.). DOI: 10.1872/MMF-2019-17.
Pozhbelko V. [Advanced technique of type synthesis and construction of veritable complete atlaces of multiloop F-DOF generalized kinematic chains]. Mechanisms and Machine Science, 2019, vol. 59, pp. 207-214. DOI: 10.1007/978-3-319-98020-1-24.
Gregorio Di R. [On Higher-Pair Modelling in Planar Mechanisms]. Mechanisms and Machine Science, 2019, vol. 73, pp. 863-870. DOI: 10.1007/978-3-030-20131-9-86.
Pozhbelko V.I. [Structural synthesis of lever and planetary mechanisms of a given level of complexity according to the universal table of standard structure codes]. Izvestiya vysshih uchebnyh zavedenij. Mashinostroenie, 2012, no. 4, pp. 13-29 (in Russ.). DOI: 10.18698/ 0536-1044-2012-4.
Wang J., Ting K., Zhao D. [Equivalent Linkages and Dead Center Positions of Planar Single-DOF Complex Linkages]. Journal of Mechanisms and Robotics, 2013, vol. 7, pp. 48-54. DOI: 10.1115/IMECE2013-62306.
Kim M., Han M.S., Seo T. [A new instantaneous center analysis methodology for planar closed chains via graphical representation]. Control Autom. Syst., 2016, vol. 14, pp. 1528-1534. DOI: 10.1007/s12555-015-0066-3.
Zhao J., Feng Z. [Kinematic Design of Geared Five-Bar Linkage]. Design of Special Planar Linkages, 2014, pp. 51-75.
Balyakin V., Krylov E. [Cultural and Educational Significance of MMS Competitions for Future Engineers]. Springer Nature Switzerland AG 2019 J. C. García-Prada and C. Castejón (еds.): New Trends in Educational Activity in the Field of Mechanism and Machine Theory, MMS 64, 2019, pp. 38-48. DOI: 10.1007/978-3-030-00108-7-5.
