<p>A three-cable suspension manipulator is an underactuated multibody system that has more degrees of freedom than independent control inputs. The outputs, equal in number to the control inputs, are specified in time and expressed in terms of the system state variables. The outputs lead to servo constraints on the system. The use of servo constraints is an effective approach to solve the inverse dynamics problem of an underactuated mechanical system. The servo-constraint problem is then a specific model inversion in which an input control strategy needs to be determined. The feedforward control strategy steers the underactuated mechanical system along the prescribed trajectory. To formulate the servo-constraint problem of the three-cable suspension manipulator, the rotationless formulation in terms of redundant coordinates (direction-cosine matrix) is employed to circumvent the use of rotational variables such as Euler or Bryan angles. The control problem can thus be viewed as a mechanical system subject to both standard holonomic constraints and servo constraints. The governing equations of the servo-constraint problem arise as a set of differential-algebraic equations (DAEs) with high index. It is generally challenging to solve the DAEs with high index, such as the index-5 DAEs. In this paper, a specific index reduction approach, known as the index reduction by minimal extension method, is applied to solve the servo-constraint problem of the three-cable suspension manipulator. The manipulator is modeled as an ideal mechanical system without friction or damping. Under this assumption, it can be classified as a differentially flat system. Extensions to non-ideal effects are beyond the scope of the present study. Several numerical simulations are conducted to demonstrate the applicability of the index reduction by minimal extension method to the rotationless formulation. The numerical results are presented and discussed.</p>