Evolutoids and pedaloids of plane curves

Evolutes and pedals of plane curves have been well investigated since the beginning of the history of differential geometry. However, there might be no direct relationships between the pedal and the evolute of a curve. We introduce families of relatives of pedals and evolutes and investigate some relationships between these families curves. Moreover, we generalize these notions to the category of frontal curves. Then the relation can be completely described in this category.