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Creating the form of a complicated treadmill

  • Y. S. TemirbekovEmail author
  • B. O. Bostanov
  • B. A. Karassayev
  • G. A. Tukeshova
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

The problem of creating a smooth complex trajectory and determining the position of the points of connection, providing the conditions of tangency, continuity and equality of the radius of curvature, is considered. When conjugation trajectory in the form of arcs of curves, there are non-smoothness at the junction, a centrifugal force jump occurs due to the inequality of the radii of curvature, which will lead to the impact. Known methods and methods for continuous, smooth connection of trajectories, which include lines, splines, as well as specially designed transition curves, such as a majorant curve, clothoid, elastic line, lemniscate and velocity curve. However, the proposed methods are less accurate and approximate. With such conjugations, the condition of equality of the radii of curvature of these curves at the junction point is not satisfied. To eliminate the undesirable effect of impact, the method of inserting a transition section is used, the model of which is a second-order curve (conic). An original method is proposed for analytically determining a smooth (smooth second order) transition region in the form of a conic. A mathematical condition has been established that ensures a smooth connection without a jump in the radius of curvature. By setting the start point of connection and using mathematical condition for smooth connection can determine the finish point of connection. The process of determining the smoothness of conjugation is proposed to be modeled by a link mechanism. The proposed method makes it possible to construct complex technical forms and to create on their basis new models of a smooth trajectory from arcs of high-order curves with a conical transition section.

Keywords

smooth treadmill conic radius of curvature transition curve curvature jump conjugation point 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Y. S. Temirbekov
    • 1
    Email author
  • B. O. Bostanov
    • 1
  • B. A. Karassayev
    • 1
  • G. A. Tukeshova
    • 1
  1. 1.Institute of Mechanics and EngineeringMinistry of Education and ScienceAlmatyKazakhstan

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