Slant Helix Curves and Acceleration Centers

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.