The relation between a curve and its involute suggests the idea of a pair of curves such that the binormals of one cut the other orthogonally. Let r be the position vector of the current point P on the first curve C and t, n, b the unit vectors in the directions of the tangent, the principal normal and the binormal at P These are functions of the arc-length s of the curve. Since the binormals of C intersect the second curve C1 the position vector of the point P1 of the second curve which lies on the binormal at P is given by

r1= r + ab,.....(1)

in which a is a scalar.