Theoretical Modeling of a Bionic Arm with Elastomer Fiber as Artificial Muscle Controlled by Periodic Illumination

Abstract

Liquid crystal elastomers (LCEs) have shown great potential in the field of soft robotics due to their unique actuation capabilities. Despite the growing number of experimental studies in the soft robotics field, theoretical research remains limited. In this paper, a dynamic model of a bionic arm using an LCE fiber as artificial muscle is established, which exhibits periodic oscillation controlled by periodic illumination. Based on the assumption of linear damping and angular momentum theorem, the dynamics equation of the model oscillation is derived. Then, based on the assumption of linear elasticity model, the periodic spring force of the fiber is given. Subsequently, the evolution equations for the cis number fraction within the fiber are developed, and consequently, the analytical solution for the light-excited strain is derived. Following that, the dynamics equation is numerically solved, and the mechanism of the controllable oscillation is elucidated. Numerical calculations show that the stable oscillation period of the bionic arm depends on the illumination period. When the illumination period aligns with the natural period of the bionic arm, the resonance is formed and the amplitude is the largest. Additionally, the effects of various parameters on forced oscillation are analyzed. The results of numerical studies on the bionic arm can provide theoretical support for the design of micro-machines, bionic devices, soft robots, biomedical devices, and energy harvesters.

Keywords: bionic arm; dynamic model; forced oscillation; light-fueled; liquid crystal elastomer; periodic illumination.

Figure 1

Schematic diagram of the bionic arm using an LCE fiber as artificial muscle controlled by periodic illumination. (a) Schematic diagram; (b) Initial state; (c) Illuminated state; (d) Non-illuminated state. The rotation angle is positive in a counterclockwise direction from the horizontal line. Periodic illumination leads to the periodic contraction and relaxation of the fiber, driving the bionic arm to oscillation periodically.

Figure 2

The variation of the dimensionless cis number fraction $\overline{\varphi }$ as a function of time $\overline{t}$ under a periodic illumination with given light intensity ${\overline{I}}_0=0.35$.

Figure 3

The forced vibration of the bionic arm for six different nondimensionalized illumination periods with given parameters: ${\overline{L}}_{\mathrm{AB}}=1.0$ ${\overline{L}}_{\mathrm{BC}}=0.5$, ${\overline{T}}_{\mathrm{on}}/{\overline{T}}_{\mathrm{L}}=0.5$, $\overline{k}=18$, $\overline{g}=1.2$, $C_0=-0.28$, ${\overline{I}}_0=0.35$, $\overline{c}=0.2$, ${\overline{\dot{\theta }}}_{\overline{t}=0}=0$, and ${\theta }_{\overline{t}=0}=0$. From (a–f), ${\overline{T}}_{\mathrm{L}}=1$, $2$, $4$, $5$, $15$, and $30$, respectively. The shaded regions in (d–f) indicate periods of illumination, the non-shaded regions represent periods of non-illumination. The stable forced vibration period of the system is consistent with the illumination period.

Figure 4

Mechanism of the forced vibration of the bionic arm controlled by periodic illumination. The parameters are ${\overline{L}}_{\mathrm{AB}}=1.0$${\overline{L}}_{\mathrm{BC}}=0.5$, ${\overline{T}}_{\mathrm{L}}=2$, ${\overline{T}}_{\mathrm{on}}/{\overline{T}}_{\mathrm{L}}=0.5$, $\overline{k}=18$, $\overline{g}=1.2$, $C_0=-0.28$, ${\overline{I}}_0=0.35$, $\overline{c}=0.2$, ${\overline{\dot{\theta }}}_{\overline{t}=0}=0$, and ${\theta }_{\overline{t}=0}=0$. (a) Time-dependent change in rotation angle $\theta$; (b) The relationship between angular velocity $\overline{\dot{\theta }}$ and time; (c) Evolution of fiber length ${\overline{L}}_1$ over time; (d) Number fraction of cis-isomers $\overline{\varphi }$ change with time; (e) Variation in the spring force $\overline{F}$ with time; (f) The relationship between the spring force $\overline{F}$ and the length of the fiber ${\overline{L}}_1$. The shaded regions in (a–e) indicate periods of illumination, and the non-shaded regions represent periods of non-illumination.

Figure 5

Effect of the dimensionless illumination period on the amplitude and equilibrium position of the oscillation with given parameters ${\overline{L}}_{\mathrm{AB}}=1.0$ ${\overline{L}}_{\mathrm{BC}}=0.5$, ${\overline{T}}_{\mathrm{on}}/{\overline{T}}_{\mathrm{L}}=0.5$, $\overline{k}=18$, $\overline{g}=1.2$, $C_0=-0.28$, ${\overline{I}}_0=0.35$, $\overline{c}=0.2$, ${\overline{\dot{\theta }}}_{\overline{t}=0}=0$, and ${\theta }_{\overline{t}=0}=0$. An optimal illumination period ${\overline{T}}_{\mathrm{op}}=1.98$ exists that maximizes the amplitude of the oscillation, while a critical illumination period ${\overline{T}}_{\mathrm{cr}}=1.88$ exists that minimizes the equilibrium position of the oscillation.

Figure 6

Effect of the illumination time rate on the amplitude and equilibrium position of the oscillation with given parameters ${\overline{L}}_{\mathrm{AB}}=1.0$, ${\overline{L}}_{\mathrm{BC}}=0.5$, ${\overline{T}}_{\mathrm{L}}=2$, $\overline{k}=18$, $\overline{g}=1.2$, $C_0=-0.28$, ${\overline{I}}_0=0.35$, $\overline{c}=0.2$, ${\overline{\dot{\theta }}}_{\overline{t}=0}=0$, and ${\theta }_{\overline{t}=0}=0$. An optimum illumination time rate ${\overline{T}}_{\mathrm{on}}/{\overline{T}}_{\mathrm{L}}=0.36$ can be identified to achieve the maximum amplitude of oscillation.

Figure 7

Effects of (a) the dimensionless light intensity ${\overline{I}}_0$ (b) the dimensionless contraction coefficient $C_0$, (c) the dimensionless elastic coefficient $\overline{k}$, (d) the dimensionless gravitational acceleration $\overline{g}$, (e) the dimensionless length from point A to point B ${\overline{L}}_{AB}$, (f) the dimensionless length from point B to point C ${\overline{L}}_{BC}$, (g) the dimensionless damping coefficient $\overline{c}$, and (h) the initial rotation angle ${\theta }_{\overline{t}=0}$ on the amplitude and equilibrium position of the oscillation. The computational parameters are labeled in the figure, and the other parameters are ${\overline{T}}_{\mathrm{L}}=2$, ${\overline{T}}_{\mathrm{on}}/{\overline{T}}_{\mathrm{L}}=0.36$, and ${\overline{\dot{\theta }}}_{\overline{t}=0}=0$. An optimum elastic constant $\overline{k}=16.6$, gravitational acceleration $\overline{g}=1.08$, and length from point B to point C ${\overline{L}}_{BC}=0.48$ can be identified to achieve the maximum amplitude of oscillation.