# Development of a Novel Variable-Diameter Wheel
## 1 Introduction  
Wheeled rovers are one of the best candidates for planetary surface exploration due to their power-efficient performance [1]. Wheels are essential in improving the mobility of wheeled rovers, including trafficability and obstacle-surmounting capability on unstructured environments [2]. On soft terrain, conventional circular wheels slip and cause poor rover mobility [3]. Therefore, to optimize mobility on unknown and soft terrain, growing research interest has focused on various unconventional wheels [4; 5; 6]. However, despite the satisfactory trafficability of rovers with unconventional wheels, their obstacle-surmounting capabilities remain insufficient.  
By increasing its diameter, a wheel can enhance the tractive performance and obstacle-surmounting capability of a vehicle [7; 8]. Therefore, expandable wheels were developed. Expandable mechanisms allow the adjustment of wheel diameter, and different types have been proposed in recent years. The diagrams of the principles behind these mechanisms are provided in [9]. These mechanisms can be categorized into rigid-body mechanisms [10; 11; 12; 13] and compliant mechanisms [14; 15; 16]. Compliant mechanisms perform movement through their part deflections and usually have reduced weight [17; 18]. Moreover, these traditional mechanisms can be classified as expandable in the axial and radial planes of the wheels. Unlike the former, the ratio of the wheel width to diameter is unconstrained forthe latter. However, several of these mechanisms are only capable of expanding once. By contrast, repeatedly expandable mechanisms with real-time self-locking can continuously adjust the wheel diameter according to different terrain conditions.  
A repeatedly deployable compliant mechanism in the radial plane is desired for an expandable wheel. The mechanism in a variable-diameter wheel, which is an expandable wheel, is an example [9; 19; 20].  
Previous studies had only considered mechanisms in the design of expandable wheels. Despite the importance of deployable mechanism in such designs, wheel performance cannot be ignored. At the least, the mechanism should not affect the normal operation of the wheel (e.g., maneuverability). Wheel performance is crucial for reliability and availability in real situations. Thus, the design of variable-diameter wheels should consider not only the mechanism but also meet the requirements of wheel performance.  
In the existing variable-diameter wheel [9], the wheel feet may deviate from the initial orientation position because of the relative rotation between two hubs in the mechanism movement, resulting in a torque action on each foot. Moreover, because the supporting structure of each wheel foot consists of two spoke links that are not on the same plane, the support easily causes wheel camber or inclination. These conditions may influence the maneuverability of a wheeled rover. Every wheel leg has four flexure pivots on the radial plane of the wheels. Hence, with the compliance of the torsion springs, a single wheel leg approaches a four-bar mechanism. As a result, the structure of the wheel spoke may not transmit sufficient torque from the wheel's hub to its feet.  
To address these issues of the existing variable-diameter wheel, we designed a novel variable-diameter wheel in this study. Wheel performance was considered and improved in the new design. First, to increase stability of the supporting structure and avoid additional moment, the novel wheel configuration and its transmission system were considered. Kinematic equations of the mechanism were then established and applied to synthesize the wheel dimensions. The load-deflection relationship of the mechanism was analytically obtained by building a modified pseudo-rigid-body model (PRBM). Finally, finite element analysis (FEA) simulations were performed to validate the design and analysis.