Ball and Burmester points in Lorentzian sphere kinematics

ABDULLAH INALCIK, SOLEY ERSOY

Abstract


In this work, we study Lorentzian spherical motion of rigid bodies by usinginstantaneous invariants and define Lorentzian inflection curve, Lorentzian circlingpoints curve and Lorentzian cubic of twice stationary curve, which are the loci ofpoints having the same properties during Lorentzian spherical motion of rigid bodies.Also, the intersection points of these curves are called Ball points and Burmesterpoints. We define Lorentzian Ball and Burmester points on Lorentzian sphere.

Keywords


Ball points; Burmester points; instantaneous invariants; Lorentz spherical kinematics.

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References


Ayyıldız, N. & Yalçın, Ş. N. 2010. On instantaneous invariants in dual Lorentzian space kinematics,

Archives of Mechanics., 62, 3, 223–238.

Chiang, C. H. 1992. Spherical kinematics in contrast to planar kinematics, Mechanism and Machine

Theory, 27, 243–250.

Gupta, K. C. 1978. A direct method for the evaluation of instantaneous invariants of a given method,

Mechanism and Machine Theory, 13, 567–576.

Kamphuis, H. J. 1969. Application of spherical instantaneous kinematics to the spherical slider-crank

mechanism, Journal of Mechanisms, 4, 43–56.

Karadağ, H. B., Kılıç, E. & Karadağ, M. 2014. On the developable ruled surfaces kinematically

generated in Minkowski 3-Space, Kuwait Journal of Science, 41(1), 21–34.

Korolko, A. & Leite, F. S. 2011. Kinematics for rolling a Lorentzian sphere, 2011 50th IEEE Conference

on Decisions and Control and European Control Conference (CDC-ECC), Orlando, FL, USA.

O’Neill, B. 1983. Semi-Riemannian Geometry, Academic Press, New York.

Özçelik, Z. & Şaka, Z. 2010. Ball and Burmester points in spherical kinematics and their special cases,

Forschung im Ingenieurwesen, 74, 111–122.

Özçelik, Z. 2008. Design of spherical mechanisms by using instantaneous invariants, Ph.D. Dissertation,

Selcuk University, Mechanical Engineering Department (in Turkish).

Roth, B. & Yang, A. T. 1977. Application of instantaneous invariants to the analysis and synthesis of

mechanisms, Journal of Engineering for Industry-Transactions of the ASME, 99, 97–103.

Roth, B. & Yang, A. T. 1973. Higher–order path curvature in spherical kinematics, Journal of Engineering

for Industry ASME, 95(2), 612–616.

Ting, K. L. & Wang, S. C. 1991. Fourth and fifth order double Burmester points and the highest attainable

order of straight lines, Journal of Engineering for Industry ASME, 113(1), 213–219.

Uğurlu, H. H. & Topal, A. 1996. Relation between Darboux instantaneous rotation vectors of curves on a

timelike surface, Mathematical & Computational Applications, 1(2), 149–157.

Veldkamp, G. R. 1967. Canonical systems and instantaneous invariants in spatial kinematics, Journal of

Mechanisms, 2(3), 329–388.


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