The significance of control to induction coil constant speed movement when the induction hardening to planar cam contour carring out is expounded.The complex cam contour is simplied suitably by using broken line replacing the curve and geometrical relation and movement relation between the cam and induction coil in planar cam induction hardening installation are analyzed.The mathematical relation of movement parameter is established.The random planar cam induction hardening speed basic invariant to the general induction coil is realized.