# Development of a Novel Variable-Diameter Wheel
## 2 Wheel Configuration and Transmission System  
### Wheel Configuration  
As mentioned in Section 1, various expandable mechanisms have been invented to facilitate changes in the diameter of expandable wheels. In the present study, the traditional expandable mechanisms are classified into diverse types according to their different characteristics before summarizing their advantages. These characteristics are integrated in the proposed mechanism for the new variable-diameter wheel.  
In compliant mechanisms, flexural pivots or hinges perform the function of pin joints for rigid-body kinematics [21; 22; 23]. Helical torsion springs serve as flexural hinges and can achieve large angular deformations, as shown in Figure 1. In addition, the springs are used with pins to maintain alignment and provide buckling resistance when necessary. Therefore, springs that can simplify the assembly are applied to the new mechanism in the wheel.  
The proposed wheel with six circumferentially arranged wheel legs is composed of three hubs that house a planetary gear train system, helical torsion springs (the spring arms serve as the spokes), and 12 wheel feet. A single wheel leg consists of two wheel feet and geometrically symmetric helical torsion springs (Figure 2). These springs (including four spoke links) and the two wheel feet in a single wheel leg are connected by two concentric pins. One of the two wheel feet is fixed to two middle spoke bars, whereas the other foot is fixed to the two spoke bars on both sides. This setting allows the two wheel feet to rotate around each other. The ends of the middle two torsion springs in the wheel leg are positioned at the middle wheel hub, whereas the ends of the two torsion springson both sides are positioned at the two wheel hubs on both sides. Therefore, when the middle hub rotates around the side hubs with the same speed, the helical torsion springs experience angular deflections, and the mechanism gains mobility (i.e., changes in wheel diameter). The relative rotation between the three hubs can prevent the movement interferences between the spoke bars and remove the additional moments on the wheel feet. Moreover, the supporting structure of the two wheel feet in each wheel leg, which is supported by four spoke links, has greater stability than that of the existing variable-diameter wheel.  
Each wheel leg can be treated as a triangular structure with three flexure pivots in the radial plane of the wheel. Hence, the structural stiffness of the wheel leg increases compared with that of the conventional variable-diameter wheel. In addition, the structure with the three flexure pivots reduces the linkages in the movement plane, which simplifies the design and analysis of the wheel.  
Note that each wheel foot comprises three spaced metal cleats with segmented circular-arc outer edges. For its folded limit position, the wheel is circular with an outer contour that comprises the segmented circular-arc cleats. This condition provides good ride performance on flat and rigid terrains. Moreover, the spacing between these cleats creates a longer shearing surface that extends deep into soft terrains and thus develops more traction than the continuous wheel foot of the existing variable-diameter wheel [4]. When the wheel exits the folded limit position, the wheel feet separate from each other, except for the two wheel feet in the same wheel leg. As the wheel diameter increases, the angle between the two fixed wheel feet on the spoke links in a single wheel leg decreases and vice versa.  
Figure 1: Two limit working positions of new variable-diameter wheel prototype.  
Figure 2: Single wheel leg configuration.