The inertial forces and moments, due to the motion of robotic arms installed on a mobile base, lead to reaction forces on the moving base which may cause its unexpected motion. In this article, a method of designing a path of motion in the Cartesian space between the initial and final positions is presented which guarantees no reaction on the moving base. To this end, developing the system dynamics model, the moment equations are derived. Based on the conservation of momentum in the absence of any external force and moments, the angular motion due to the motion of robotic arms is solved. Then, based on the definition of reaction null-space map for dynamic coupling matrix, the joint speeds are projected to the reaction null-space, to obtain the joint speeds in this space. Next, using numerical integration of the obtained joint rates, the motion in the joint space with no reaction on the base is obtained. Therefore, motion of robotic arms according to these joint specifications, the total momentum of the system remains zero, and due to no reaction forces applied on the moving base, its position and attitude remains unchanged.