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 𝔼3is given by moving the coordinate frame {𝑵, 𝑪, 𝑾} instead ofthe Frenet frame {𝑻, 𝑵, 𝑩} along a unit speed curve 𝛼(𝑡), where 𝑵, 𝑪 and 𝑾 correspond,respectively, to unit principal normal vector field, derivative vector field of the unit principalnormal vector field and Darboux vector field of the unit speed curve 𝛼(𝑡). Also the concepts fixedaxode, striction curve, instantaneous pole points, acceleration pole points (or acceleration centers)and instant screw axis (ISA) of this alternative one-parameter motion are studied.