The high-speed motions of mobile manipulators can dynamically disturb their vehicles, even to the point where they can cause a vehicle to tip over. A planning method is presented which insures that such dynamic disturbances do not exceed the capabilities of a vehicle, and compromise its stability, while permitting a mobile manipulator to perform its tasks quickly. The method is an extension of an algorithm for fixed-base manipulators and has been implemented in a CAD system with extensive computer graphics. The technique can also determine if any proposed manipulator motion plan, optimal or conventional, results in dynamic forces which exceed the capabilities of a vehicle and result in either a statistically or dynamically unstable system. The technique is applied to a representative system in which there is significant friction between the vehicle and ground. The results suggest that the algorithm may be an effective planning tool for such mobile manipulators. The technique has also been found to be effective for planning the motions of spacecraft-mounted manipulators.>