In this thesis a novel spatial model of an overhead crane was developed. The model includes: bridge, trolley, driving and follower wheels for the bridge and trolley, drum, cable, and the payload. The model accounts for the winding/unwinding of the cable around the drum as the payload is raised/lowered. The cable and the payload were considered as rigid bodies with uniformly distributed mass. First, the kinematic equations of the model were developed by using constraint equations. Second, the dynamic equations were derived through use of Newton’s Laws. Developing the rotational dynamic equations required the determination of the angular momentum vectors of the rigid bodies as expressed with respect to an inertial frame. However, the orientations of the rigid bodies were described using Euler angles, which are neither absolute angular coordinates nor described with respect to an inertial frame. Hence, a novel derivation of the angular momentum vector with respect to an inertial frame in terms of Euler angles and local parameters was developed. In addition, a new approach for deriving the dynamic equilibrium torque of the drum was developed; this method used the constraints forces instead of the positions, velocities, and accelerations of the bodies. The motion of the system was simulated with bang-bang inputs and the results prove that the model is stable.