Pedal and Contrapedal Curves of Framed Immersions in the Euclidean 3-Space

In this paper, we define pedal and contrapedal curves of framed immersions, which can have singularities, in the Euclidean 3-space and investigate the sufficient conditions that they are framed base curves. Moreover, we give the relations among pedal curves, contrapedal curves, evolutes and involutes of framed immersions.