Wheels have been commonly used for locomotion in mobile robots and transportation systems because of their simple structure and energy efficiency. However, the performance of wheels in overcoming obstacles is limited compared with their advantages in driving on normal flat ground. Here, we present a variable-stiffness wheel inspired by the surface tension of a liquid droplet. In a liquid droplet, as the cohesive force of the outermost liquid molecules increases, the net force pulling the liquid molecules inward also increases. This leads to high surface tension, resulting in the liquid droplet reverting to a circular shape from its distorted shape induced by gravitational forces. Similarly, the shape and stiffness of a wheel were controlled by changing the traction force at the outermost smart chain block. As the tension of the wire spokes connected to each chain block increased, the wheel characteristics reflected those of a general circular-rigid wheel, which has an advantage in high-speed locomotion on normal flat ground. Conversely, the modulus of the wheel decreased as the tension of the wire spoke decreased, and the wheel was easily deformed according to the shape of obstacles. This makes the wheel suitable for overcoming obstacles without requiring complex control or sensing systems. On the basis of this mechanism, a wheel was applied to a two-wheeled wheelchair system weighing 120 kilograms, and the state transition between a circular high-modulus state and a deformable low-modulus state was realized in real time when the wheelchair was driven in an outdoor environment.

Coordinate reduction has been widely used for efficient simulation of flexible multibody dynamics. To achieve the reduction of flexible bodies with reasonable accuracy, the appropriate number of dominant modes used for the reduction process must be selected. To handle this issue, an iterative coordinate reduction strategy is introduced. In the iteration step, more dominant modes of flexible bodies are selected than the ones in the previous step. Among the various methods, the conventional frequency cut-off rule is here considered. As a stop criterion, a novel a posteriori error estimator that can evaluate the relative eigenvalue error between full and reduced flexible bodies is proposed. Through the estimated relative eigenvalue error obtained, the number of dominant modes is automatically selected to satisfy the error tolerance up to the desired mode range. The applicability to the automation process is verified through numerical examples. It is also evaluated that efficient and accurate flexible multibody dynamics simulation is available with the reduced flexible body, generated by the proposed algorithm.