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Year 2019, Volume: 32 Issue: 1, 256 - 271, 01.03.2019

Murat Bekar Yusuf Yaylı

Abstract

References

  • [1] O. Bottema, B. Roth, Theoretical kinematics, Dover Publications, Inc.,1979.
  • [2] J. Angeles, The angular-acceleration tensor of a rigid-body kinematics and its properties, Archive of Applied Mechanics 69 (1999) 204-214.
  • [3] M. Skreiner, A study of the geometry and the kinematics of instantaneous spatial motion, J. Mech. 1 (1966) 115-143.
  • [4] De Lun Wang, Jian Liu, Da Zhun Xiao, Kinematic differential geometry of a rigid body in spatial motion—II. A new adjoint approach and instantaneous properties of a line trajectory in spatial kinematics, Mech. Mach. Theory 32 (4) (1997) 419-432.
  • [5] M.G. Mohammed, Kinematics of rigid bodies in general spatial motion: second-order motion properties, Appl. Math. Model. 21 (8) (1997) 471-479.
  • [6] G.R. Veldkamp, Canonical systems and instantaneous invariants in spatial kinematics, J. Mech. 3 (3) (1967) 329-388.
  • [7] J. Angeles, Rotational kinematics, Springer- Verlag, New York, 1988.
  • [8] D.J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Publishing Company, Inc., 1961.
  • [9] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004) 531–537.
  • [10] B. Uzunoglu, I. Gok, Y. Yayli, A New Approach on Curves of Constant Precession, 2013, Arxic: 1311.4730v1 (math.DG).
  • [11] J.H. Choi, Y.H. Kim, Associated curves of a Frenet curve and their applicatins, Applied Mathematics and Computation 218 (2012) 9116-9124.
  • [12] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Pretice Hall, 1976.
  • [13] A. Turgut, H.H. Hacisalihoglu, Time-like ruled surfaces in the Minkowski 3-space, Far East J. Math. Sci. 5 (1) (1997) 83–90.
  • [14] Y. Yayli, S. Saracoglu, On Timelike and Spacelike Developable Ruled Surfaces, 2012, Arxic: 1202.0138v1 (math.DG).
  • [15] W. Clifford, J.J. Mc Mahon, The Rolling of One Curve or Surface Upon Another, The American Mathematical Monthly 68 (1961) 338-341.
  • [16] H.H. Hacisalihoglu, On the geometry of motion in the Euclidean n-space, Communications de la faculte des sciences de l’universite d’ankara 23 (1974) 95-108.
  • [17] Y. Yayli, B. Bükcü, Homothetic motions at E^8 with Cayley numbers, Mech. Mach. Theory 30 (1995) 417-420.
  • [18] F. Frenet, Sur les courbes a ̀ double courbure, Jour. De Math. 17 (1852) 437-447.
  • [19] P.D. Scofield, Curves of Consant Precession, The American Mathematical Monthly 102 (1995) 531-537.

Slant Helix Curves and Acceleration Centers

Year 2019, Volume: 32 Issue: 1, 256 - 271, 01.03.2019

Murat Bekar Yusuf Yaylı

Abstract

In
this study, an alternative one-parameter
motion to Frenet motion of a rigid-body in 3-dimensional Euclidean space E3 is given by moving the coordinate
frame {N, C, W} instead of the Frenet frame {T, N, B} along a unit speed curve a(t), where, N, C and W correspond, respectively, to unit principal normal vector field,
derivative vector field of the unit principal normal vector field and Darboux
vector field of the unit speed curve a(t). Also the concepts fixed axode,
striction curve, instantaneous
pole points, acceleration pole points (or acceleration centers) and instant
screw axis (ISA) of this alternative one-parameter motion are studied.

Keywords

Cylindrical helix C-Slant helix Striction curve Rigid-body motion Acceleration center

References

  • [1] O. Bottema, B. Roth, Theoretical kinematics, Dover Publications, Inc.,1979.
  • [2] J. Angeles, The angular-acceleration tensor of a rigid-body kinematics and its properties, Archive of Applied Mechanics 69 (1999) 204-214.
  • [3] M. Skreiner, A study of the geometry and the kinematics of instantaneous spatial motion, J. Mech. 1 (1966) 115-143.
  • [4] De Lun Wang, Jian Liu, Da Zhun Xiao, Kinematic differential geometry of a rigid body in spatial motion—II. A new adjoint approach and instantaneous properties of a line trajectory in spatial kinematics, Mech. Mach. Theory 32 (4) (1997) 419-432.
  • [5] M.G. Mohammed, Kinematics of rigid bodies in general spatial motion: second-order motion properties, Appl. Math. Model. 21 (8) (1997) 471-479.
  • [6] G.R. Veldkamp, Canonical systems and instantaneous invariants in spatial kinematics, J. Mech. 3 (3) (1967) 329-388.
  • [7] J. Angeles, Rotational kinematics, Springer- Verlag, New York, 1988.
  • [8] D.J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Publishing Company, Inc., 1961.
  • [9] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004) 531–537.
  • [10] B. Uzunoglu, I. Gok, Y. Yayli, A New Approach on Curves of Constant Precession, 2013, Arxic: 1311.4730v1 (math.DG).
  • [11] J.H. Choi, Y.H. Kim, Associated curves of a Frenet curve and their applicatins, Applied Mathematics and Computation 218 (2012) 9116-9124.
  • [12] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Pretice Hall, 1976.
  • [13] A. Turgut, H.H. Hacisalihoglu, Time-like ruled surfaces in the Minkowski 3-space, Far East J. Math. Sci. 5 (1) (1997) 83–90.
  • [14] Y. Yayli, S. Saracoglu, On Timelike and Spacelike Developable Ruled Surfaces, 2012, Arxic: 1202.0138v1 (math.DG).
  • [15] W. Clifford, J.J. Mc Mahon, The Rolling of One Curve or Surface Upon Another, The American Mathematical Monthly 68 (1961) 338-341.
  • [16] H.H. Hacisalihoglu, On the geometry of motion in the Euclidean n-space, Communications de la faculte des sciences de l’universite d’ankara 23 (1974) 95-108.
  • [17] Y. Yayli, B. Bükcü, Homothetic motions at E^8 with Cayley numbers, Mech. Mach. Theory 30 (1995) 417-420.
  • [18] F. Frenet, Sur les courbes a ̀ double courbure, Jour. De Math. 17 (1852) 437-447.
  • [19] P.D. Scofield, Curves of Consant Precession, The American Mathematical Monthly 102 (1995) 531-537.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Murat Bekar

Yusuf Yaylı

Publication Date March 1, 2019
Published in Issue Year 2019 Volume: 32 Issue: 1

Cite

APA Bekar, M., & Yaylı, Y. (2019). Slant Helix Curves and Acceleration Centers. Gazi University Journal of Science, 32(1), 256-271.
AMA Bekar M, Yaylı Y. Slant Helix Curves and Acceleration Centers. Gazi University Journal of Science. March 2019;32(1):256-271.
Chicago Bekar, Murat, and Yusuf Yaylı. “Slant Helix Curves and Acceleration Centers”. Gazi University Journal of Science 32, no. 1 (March 2019): 256-71.
EndNote Bekar M, Yaylı Y (March 1, 2019) Slant Helix Curves and Acceleration Centers. Gazi University Journal of Science 32 1 256–271.
IEEE M. Bekar and Y. Yaylı, “Slant Helix Curves and Acceleration Centers”, Gazi University Journal of Science, vol. 32, no. 1, pp. 256–271, 2019.
ISNAD Bekar, Murat - Yaylı, Yusuf. “Slant Helix Curves and Acceleration Centers”. Gazi University Journal of Science 32/1 (March 2019), 256-271.
JAMA Bekar M, Yaylı Y. Slant Helix Curves and Acceleration Centers. Gazi University Journal of Science. 2019;32:256–271.
MLA Bekar, Murat and Yusuf Yaylı. “Slant Helix Curves and Acceleration Centers”. Gazi University Journal of Science, vol. 32, no. 1, 2019, pp. 256-71.
Vancouver Bekar M, Yaylı Y. Slant Helix Curves and Acceleration Centers. Gazi University Journal of Science. 2019;32(1):256-71.