Hyperbolic Number Forms of Euler-Savary Equation

This study deals with hyperbolic number forms of Euler-Savary Equation (ESE) to find either the four special points on the pole ray. While obtaining the hyperbolic ESE forms, one-parameter planar motion is considered according to the osculating circles contacting at three infinitesimally close points. This approach with the hyperbolic number method gives more detailed information than the traditional method. As a final part, examples are given to show the utility of the practical way in the application.