## 1 Introduction  
A locomotion interface (LI) can support walking and running through appropriately generated ground surfaces to provide active participation in virtual environments (VEs) with realistic spatial sensations [1]. Therefore, an LI provides a sense of mobility based on energy input/consumption of actual walking [2]. To create more immersive locomotion, a LI system should allow the user to arbitrarily change not only the walking speed, but also the walking direction. Such features may motivate a user to participate more actively in VR experiences, such as military training programs, physical education programs, disaster preparedness training, and rehabilitation programs [3]. To simulate omnidirectional locomotion, several types of devices have been suggested, such as balls [4], large spheres [5], mobile robots [6], a rotating one-dimensional (1D) treadmill [7], and a robotic foot platform [8; 9; 10]. However, these devices have limitations with respect to omnidirectional walking. As the most natural mechanism for two-dimensional (2D) LI, an omnidirectional treadmill (ODT) can simulate the over-ground walking of humans [11; 12; 13]. An ODT or 2D treadmill usually consists of \"unit segments\" (transverse treadmills) installed in such a way as to form a continuous loop (Figure 1). Each unit segment is a narrow treadmill with its own belt. In an ODT, as shown in Figure 1, the X-axis translational motion is generated by the rotation of all the unit segments along \(\overset{\rightarrow}{\text{A}}_{\text{X}}\) vector, while the Y-axis translational motion is generated by rotational actuation of the belt of each segment along \(\overset{\rightarrow}{\text{A}}_{\text{Y}}\) vector. Thus, the 2D treadmill combines small treadmills assembled orthogonally to create a single, large treadmill. An ODT provides an infinite ground plane by generating independent belt motions along two orthogonal axes (X and Y). In the cases of Cyberwalk [12] and Torus treadmill [14], Y-axis translational motion is generated by individual actuators attached directly to each unit segment. This increases the inertia of the segments; thus, this design requires a very large amount of power to rotate all the segments (X-axis motion). As the weight of each segment is increased, the acceleration performance is greatly reduced. The ODTs developed by the United States Army Research Institute (US ARL) ODT [15] and the InfinaDeck treadmill [16] use a different mechanism to generate Y-axis motion. The transverse treadmill belt (segment belt) is actuated by stationary actuator(s) through  
Figure 1: Omnidirectional treadmill (ODT) concept (see Figure 2 for the cross-sectional view), and the geared omni-pulley (GOP)-based actuation scheme of the proposed ODT to generate infinite 2D ground. Figure 2: Cross-sectional view of the Y-axis motion of a 2D treadmill (unit segment): (**a**) Transversal treadmill actuated directly by an actuator (Torus or Cyberwalk treadmill), (**b**) Frictional transmission mechanism based on the Omni-wheel via the frame-fixed motor (US army ODT), (**c**) The proposed mechanism based on gear-driven transmission via a frame-fixed motor. a special transmission system. This design, due to the light weight of the individual segments, may improve the maximum speed and acceleration of the systems during X-axis translational motion as compared to those of the Cyberwalk and Torus treadmill. To drive each segment belt while allowing free movement in the X-axis direction, these ODTs use a frictional transmission mechanism composed of omni-wheels. However, since the omni-wheels-based frictional transmission mechanism has a low power transmission efficiency, the maximum speed and acceleration of these ODTs for Y-axis translational motion are limited. Thus, due to the high inertia of the unit segment treadmills for X-axis translational motion and the low efficiency of power transmission for Y-axis translational motion, the currently available 2D treadmills are only able to accommodate slow human walking speeds and accelerations.