Rolling Circles of Motions: Yesterday and Today

  • Murat Tosun
  • Soley ErsoyEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)


In this chapter, we give a short historical survey of basic events which had happened during the development of models depend on a rolling circles around circles. The first seeds of these models can be seen at the couple of Tusi which was derived for stating his astronomical theory in the 13th century. Tusi’s model generates just a straight line. Nowadays, it is well known the curves traced out by a point on a circle rolling on the inside and outside of another circle are hypocycloids and epicycloids, respectively. These curves are used for practical engineering problems such as the slider-crank mechanism or design of the rotary engine. One of the degenerate case of hypocycloidal motion is elliptic motion and recently it is called Cardan motion. In this chapter, we deal with elliptic and cycloidal (epicycloid or hypocycloid) motion by use of the complex forms of Bottema’s instantaneous invariants characterizing the infinitesimal properties of motion.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Arts and Sciences, Department of MathematicsSakarya UniversitySakaryaTurkey

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