Undulatory motion is an effective propulsion mechanism widely observed in nature, offering advantages in environments where traditional propulsion systems struggle, such as highly viscous fluids. This study systematically investigates how the number of links and fluid viscosity influence the propulsion characteristics of a multi-link swimmer. A fluid force model incorporating pressure and viscous drag, valid across a wide range of Reynolds numbers, was utilized. Multi-objective optimization was then performed to identify Pareto-optimal solutions for swimming speed and average power by varying the number of links and control inputs across three distinct fluid viscosities. The results reveal several key findings. First, a greater number of links enables higher speeds and more efficient propulsion, with the most significant improvement seen when increasing from four to eight links, after which the gains diminish, a phenomenon potentially linked to the uniform control strategy employed. Second, while a larger tail beat amplitude increases stride length, its effectiveness is reduced in highly viscous fluids where viscous drag becomes the dominant resistive force. Consequently, undulatory motion becomes an inefficient strategy in very low Reynolds number regimes (Re ~ 10⁻²). Finally, the robot’s optimal motion aligns with established scaling laws for aquatic animals, although the constant Strouhal number at high Reynolds numbers (~ 1.0) differs from typical biological values (~ 0.3). This discrepancy suggests that body shape and surface material, in addition to motion patterns, are critical factors for achieving high efficiency. These findings provide design guidelines for bio-inspired robots operating in diverse viscous environments.

The dynamic contact behavior of a minute liquid droplet upon collision with a high-temperature solid is investigated using total reflection imaging. An inkjet water droplet collides with a high temperature surface of a sapphire prism (and a quartz glass prism) and then splashes away. The contact behavior captured from the back side using a nanosecond lighting stroboscope varies significantly with the contact temperature T_c, as determined based on heat-conduction theory, rather than the temperature T_s of the bulk solid. The contact behavior can be classified into four regions: (I) film evaporation, (II) nucleate boiling, (III) spontaneous nucleation and (IV) supercritical state. The contact area decreases significantly in region II and exhibits a minimum at a temperature close to the superheat limit for the liquid. It then increases in region III to reach a maximum at a temperature close to the critical temperature before it decreases at higher temperatures. Even at a contact temperature so high as to exceed the critical temperature, the liquid still contacts the solid surface over a significant area for several microseconds before the surface dries out. The fine bubbles generated due to spontaneous nucleation hinder contact due to the formation of a local dried area as the contact temperature approaches the superheat limit, whereas contact is enhanced at higher temperatures due to the dynamic action of spontaneous nucleation. Similar behavior is observed for the quartz glass prism in the same range of contact temperature.

In the early stages of chassis model-based development, we needed a tire physical model that could be handled easily, and we devised the TM Tire Model. Some tire samples have verified that the TM Tire Model is superior to existing physical characteristic models. The feature of the TM Tire Model is that it enhanced the modeling of tire tread parts. This enhancement has made it possible to embody the mechanism of the cornering force in the small slip angle range. In this paper, we theoretically prove that the way of thinking of the TM Tire Model has universal validity and explains its mechanism.