Flatness of Mechanical Systems with 3 Degrees of Freedom

We study flatness of two-input mechanical systems with 3 degrees of freedom. Our goal is to describe the geometry of this class of systems from the point of view of differential weight. We completely characterize flatness of differential weight 8 and 9. We show that a mechanical systems with 3 degrees of freedom is flat of differential weight 8 or 9 if and only if it is config-flat or vel-flat of differential weight 8 or 9 and we describe config-flatness of differential weight 10.