  We introduce circular evolutes and involutes of framed curves in the
Euclidean space. Circular evolutes of framed curves stem from the curvature
circles of Bishop directions and singular value sets of normal surfaces of
Bishop directions. On the other hand, involutes of framed curves are direct
generalizations of involutes of regular space curves and frontals in the
Euclidean plane. We investigate properties of normal surfaces, circular
evolutes, and involutes of framed curves. We can observe that taking circular
evolutes and involutes of framed curves are opposite operations under suitable
assumptions, similarly to evolutes and involutes of fronts in the Euclidean
plane. Furthermore, we investigate the relations among singularities of normal
surfaces, circular evolutes, and involutes of framed curves.
