Control constraints can be used to prescribe the motion in the inverse dynamics of multibody systems. If the number of control inputs is lower than the degrees of freedom, this kind of mechanical system is called underactuated system. The solution of such partly specified system is a challenging task due to the underactuation property. The description of underactuated systems can be based on either minimal coordinates or redundant coordinates. The resulting governing equations show the form of differential-algebraic equations (DAEs) with a mixed set of holonomic and control constraints. The index of the DAEs may exceed three and alternative projection methods will be applied to reduce the index to three. Numerical examples are used to compare the alternative projection methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)