Modeling of a light-fueled self-paddling boat with a liquid crystal elastomer-based motor

Active materials possess unique properties of being able to respond autonomously to external stimuli, yet realizing and regulating the motion behavior of active machines remains a major challenge. Conventional control approaches, including sensor control and external device control, are both complex and difficult to implement. In contrast, active materials–based self-oscillators offer distinct properties such as periodic motion and ease of regulation. Inspired by paddle boats, we have proposed a conceptual light-fueled self-paddling boat with a photothermally responsive liquid crystal elastomer (LCE)–based motor that operates under steady illumination and incorporates an LCE fiber. Based on the well-established dynamic LCE model and rotation dynamics, the dynamic equations for governing the self-paddling of the LCE-steered boat are derived, and the driving torque of the LCE-based motor and the paddling velocity of the LCE-steered boat are formulated successively. The numerical results show that two motion modes of the boat under steady illumination: the static mode and the self-paddling mode. The self-paddling regime arises from the competition between the light-fueled driving torque and the frictional torque. Moreover, the critical conditions required to trigger the self-paddling are quantitatively examined as well as the significant system parameters affecting the driving torque, angular velocity, and paddling velocity. The proposed conceptual light-fueled self-paddling LCE-steered boat exhibits benefits including customizable size and being untethered and ambient powered, which provides valuable insights into the design and application of micromachines, soft robotics, energy harvesters, and beyond.

Figure 1

Schematic diagram of the LCE-based motor in the self-paddling boat system (a) Top view of LCE steered boat; (b) Side view of LCE steered boat; (c) Reference state of the LCE fiber; (d) Current state of the LCE-based motor; (e) Force analysis of the boat; (f) Force analysis of the wheels. The self-paddling boat system is capable of self-paddling under steady illumination.

Figure 2

Effect of maximum frictional torque ${\overline{M}}_{\mathrm{frict}}$ on (a) net driving torque ${\overline{M}}_{\mathrm{net}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. A critical maximum frictional torque of ${\overline{M}}_{\mathrm{frict}}=0.305$ exists for triggering the self-paddling. An increase in the maximum frictional torque ${\overline{M}}_{\mathrm{frict}}$ leads to a decline in the angular velocity and paddling velocity of the self-paddling.

Figure 3

Effect of heat flux $\overline{q}$ on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. A threshold value of $\overline{q}=0.234$ for heat flux to trigger the self-paddling is witnessed. As the heat flux increases, both the angular velocity and paddling velocity of the self-paddling undergo gradual increments.

Figure 4

Effect of contraction coefficient $C$ on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. A critical contraction coefficient of $C=0.311$ is observed to be responsible for initiating the self-paddling. In addition, an increment in the contraction coefficient leads to an increase in both the angular velocity and paddling velocity of the self-paddling.

Figure 5

Effect of initial stretch rate ${\lambda }_0$ on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. A critical initial stretch rate of ${\lambda }_0=1.282$ is present to trigger the self-paddling. Moreover, when raising the initial stretch rate, both the angular velocity and paddling velocity of the self-paddling exhibit an increase.

Figure 6

Effect of radius ${\overline{R}}_1$ of wheel 1 on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. The self-paddling mode is triggered when ${\overline{R}}_1$ reaches 1.198. Furthermore, a larger ${\overline{R}}_1$ corresponds to an increase in both the angular velocity and paddling velocity of the self-paddling.

Figure 7

Effect of paddle length $\overline{l}$ on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. An increase in the paddle length leads to a gradual decrease in both the angular velocity and paddling velocity of the self-paddling boat.

Figure 8

Effect of rotational damping coefficient ${\overline{\beta }}_1$ of paddle on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. As the damping coefficient of paddle increases, the angular velocity of the self-paddling decreases, while the velocity of boat is unchanged.

Figure 9

Effect of rotational damping coefficient ${\overline{\beta }}_2$ of boat on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. With the increase in the rotational damping coefficient of boat, both the angular velocity and paddling velocity of the self-paddling boat undergo gradual declines.

Figure 10

Effect of elastic coefficient ${\overline{k}}_{\mathrm{L}}$ of LCE fiber on (a) driving torque ${\overline{M}}_{\mathrm{drive}}$ and (b) angular velocity of the wheel and paddling velocity of the LCE-steered boat. Self-paddling is initiated at a critical elastic coefficient of ${\overline{k}}_{\mathrm{L}}=6.802$. Furthermore, the increase in elastic coefficient of the LCE fiber results in a simultaneous increase in both the angular velocity and paddling velocity of the self-paddling boat.