Slant Helix Curves and Acceleration Centers 1 Murat Bekar 1,∗ and Yusuf Yaylı 2 Necmettin Erbakan University, Department of Mathematics and Computer Sciences, Turkey 2 Ankara University, Department of Mathematics, Turkey [email protected] Abstract In the study, an alternative one-parameter motion to Frenet motion of a rigid-body in 3-dimensional Euclidean space is given by moving the coordinate frame N,C,W instead of the Frenet frame T,N,B along a unit speed curve, where N, C and W correspond to, respectively, unit principal normal vector field, derivative vector field of the unit principal normal vector field and Darboux vector field of the unit speed curve. 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 analyzed. Keywords: C-Slant helix; Striction curve; Rigid-body motion; Acceleration center Karatekin Mathematics Days 2014, C ¸ ankırı, TURKEY

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