Bobillier Formula for the Elliptical Harmonic Motion

In this study, we have considered the elliptical harmonic motion which is the superposition of two simple harmonic motions in perpendicular directions with the same angular frequency and phase difference of π/2 . It is commonly recognized that a convenient formulation for problems in planar kinematics is obtained by using number systems. Here the elliptical numbers are used to derive the Bobillier formula with two different methods for aforesaid motion; the first method depends on the Euler-Savary formula and the second one uses the usual relations of the velocities and accelerations.