Construction of flat inputs for mechanical systems

For observed mechanical systems, we study the problem of constructing flat inputs that are consistent with the mechanical structure of the systems. Such inputs will be called mechanical flat inputs. We show that contrary to flat inputs, that exist (almost) everywhere, in general, for the existence of mechanical flat inputs, additional structural conditions are needed. We provide necessary and sufficient conditions for the existence of mechanical inputs for observed mechanical systems with n degrees of freedom, where n is arbitrary, and n − 1 measurements.