Pedal curves obtained from Frenet vector of a space curve and Smarandache curves belonging to these curves

Abstract

In this study, first the pedal curves as the geometric locus of perpendicular projections to the Frenet vectors of a space curve were defined and the Frenet vectors, curvature, and torsion of these pedal curves were calculated. Second, for each pedal curve, Smarandache curves were defined by taking the Frenet vectors as position vectors. Finally, the expressions of Frenet vectors, curvature, and torsion related to the main curves were obtained for each Smarandache curve. Thus, new curves were added to the curve family.

Keywords

• pedal curves
• frenet apparatus
• t-pedal curve
• n-pedal curve
• b-pedal curve
• smarandache curves