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

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