Geometric interpretation of Curvature Circles in Minkowski Plane

Abstract

In this study, we investigate the geometric interpretation of the curvature circles of motion at the initial position in Minkowski plane. We consider the equations of the circling-point and centering-point curves of one-parameter motion in Minkowski plane and then determine the positions of these curves relative to each other.

Keywords

• Centering-point curve,Circling-point curve,Minkowski plane

Kaynakça

1. [1] O. Bottema, On instantaneous invariants, Proceedings of the International Conference for Teachers of Mechanisms, New Haven (CT): Yale University, 1961, 159–164.
2. [2] O. Bottema, On the determination of Burmester points for five distinct positions of a moving plane; and other topics, Advanced Science Seminar on Mechanisms, Yale University, July 6-August 3, 1963.
3. [3] O. Bottema, B. Roth, Theoretical Kinematics, New York (NY), Dover, 1990.
4. [4] B. Roth, On the advantages of instantaneous invariants and geometric kinematics, Mech. Mach. Theory, 89 (2015), 5–13.
5. [5] F. Freudenstein, Higher path-curvature analysis in plane kinematics, ASME J. Eng. Ind., 87 (1965), 184–190.
6. [6] F. Freudenstein and G. N. Sandor, On the Burmester points of a plane, ASME J. Appl. Mech., 28 (1961), 41–49.
7. [7] G. R. Veldkamp, Curvature theory in plane kinematics [Doctoral dissertation], Groningen: T.H. Delft, 1963.
8. [8] G. R. Veldkamp, Some remarks on higher curvature theory, J. Manuf. Sci. Eng., 89 (1967), 84–86.

9. [9] G. R. Veldkamp, Canonical systems and instantaneous invariants in spatial kinematics, J. Mech., 2 (1967) 329–388.
10. [10] K. Eren, S. Ersoy, Circling-point curve in Minkowski plane, Conference Proceedings of Science and Technology, 1(1), (2018), 1–6.
11. [11] K. Eren, S. Ersoy, A comparison of original and inverse motion in Minkowski plane, Appl. Appl. Math., Special Issue No.5 (2019), 56–67.