Abstract
The problem of creating a smooth combined trajectory and determining the position of the connection points ensuring the conditions of tangency, continuity and equality of the radius of curvature are considered. When the circular and conical arcs are conjoined at the junction point, there are nonsmoothness, there is a jump in the centrifugal force due to the inequality of the radii of curvature, which will lead to a strike. A method is used to insert a transitional section, the model of which is a conic, in order to exclude the undesirable impact effect. There are known methods of continuous, smooth connection of trajectories, which include contours, splines. The condition of equality of the radii of curvature is not fulfilled at such conjugations of these curves at the junction point. The mathematical condition of unstressed connection of trajectories is established. You can define the final connection point by specifying the starting point of the connection and using the condition of the unstressed connection. The proposed method allows to design complex technical forms and create on their basis new models of a smooth trajectory from conical arcs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tari, E., Baykal, O.: A new transition curve with enhanced properties. Can. J. Civil Eng. 32(5), 913–923 (2005). https://doi.org/10.1139/105-051
Eliou, N., Kaliabetsos, G.: A new, simple and accurate transition curve type, for use in road and railway alignment design. Eur. Transp. Res. Rev. 6(2), 171–179 (2014). https://doi.org/10.1007/s12544-013-0119-8
Long, E.X.-Y., Weil, Q.-C., Zheng, F.-Y.: Dynamic analysis of railway transition curves. Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Trasit 224(1), 1–14 (2010)
Lipicnik, M.: New form of Road/RailwayTransition curve. J. Transp. Eng. 124(6), 546–556 (1998). https://doi.org/10.1061/(asce)0733-947x
Foks A., Pratt, M.: Computational Geometry. Applications in Design and Manufacturing. Mir (1982). 304 s
Temirbekov, E.S., Bostanov, B.O.: Analytical definition of the correct transition of the contours of the details of clothing. News of higher educational institutions. Technology of the textile industry, Ivanovo, No. 5(365), pp. 160–165 (2016)
Arslan, A., Tari, E., Ziatdinov, R., Nabiyev, R.I.: Transition curve modeling with kinematical properties: research on log-aesthetic curves. Comput. Aided Des. Appl. 11(5), 509–517 (2014). https://doi.org/10.1080/16864360.2014.902680
Shen, T.I., Chang, Ch-H, Lu, Ch-Ch.: A numerical study of cubic parabolas on railway transition curves. J. Mar. Sci. Technol. 21(2), 191–197 (2013). https://doi.org/10.6119/jmst-012-0403-1
Farin, G.: Curves and Surfaces for Computer-aided Geometric Design: A Practical Guide, 4th edn, p. 447. Academic Press Inc., Cambridge (1997)
Hooke, R., Jeeves, T.A.: «Direct Search » solution of numerical and statistical problems. J. ACM 8(2), 212–229 (1961). https://doi.org/10.1145/321062.321069
A Policy on Geometric Design of Highways and Streets. 2011, published by American association of the state highway and transportation officials, Washington D.C
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Temirbekov, E.S., Bostanov, B.O., Dudkin, M.V., Kaimov, S.T., Kaimov, A.T. (2019). Combined Trajectory of Continuous Curvature. In: Carbone, G., Gasparetto, A. (eds) Advances in Italian Mechanism Science. IFToMM ITALY 2018. Mechanisms and Machine Science, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-030-03320-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-03320-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03319-4
Online ISBN: 978-3-030-03320-0
eBook Packages: EngineeringEngineering (R0)