Abstract: A rationally designed motion system with four Mecanum wheels can move in omni-direction on flat floor, but not any arbitrarily composed system with four Mecanum wheels can do so. In order to find the conditions of the system with four Mecanum wheels to move in omni-direction, the motion model of the general system is put forward and the inverse velocity Jacobian matrix is analyzed, considering the request of the system driving and controllability. The conclusion is presented that the omi-directional motion conditions not only depend on the full rank of inverses Jacobian matrix, but also depend on the wheel structure and the layout of the four wheels of the system. Then six typical layouts of four Mecanum wheels are illustrated and the optimal layout is picked out by calculating the Jacobian matrix rank of the six typical layouts.

Key words: Inverse Jacobian matrix, Motion performance, Optimal layout, System with four Mecanum wheels