2.5.2. Motion Analysis in VFfs Actuated by Combination of Two Stimuli: Humidity and Temperature

By using a hydrogel-coated 3D-printed shape memory polymer (SMP), an actuator system was created that responded to a combination of two environmental stimuli. The hydrophilic terpolymer (hydrogel) at a concentration of 100 mg/mL was applied manually to the SMP midrib backbones, which had a low T<sup>G</sup> of 50 ◦C (RigurTM; Stratasys Ltd., Eden Prairie, MN, USA) (Figure 1K). After a drying step at 65 ◦C, the terpolymer was simultaneously cross-linked and surface-attached by UV irradiation at 365 nm. During drying, the surface-attached hydrogel shrank leading to a bent backbone (see Figure S7). This process thus formed a water-sensitive hydrogel network that actuated the demonstrator when exposed to higher (or different) levels of humidity. The bending angle was measured via ImageJ (version 1.53a, [26] (see Figure S9). After being crosslinked, the bent backbone was attached to a snapped-open foil VFf. The VFf full assembly (Figure S8) is described in more detail in the supplementary material section "8. Environmentally triggerable systems: Stimulus combination humidity and temperature".

In the fully assembled VFf testing scenario, the change in environmental conditions was achieved through a source of hot water vapor (REER FD 1540) that generated a constant flow of hot steam. The VFfs were positioned in the steam at a fixed distance of 5.7 cm to the outlet for 300 s. This caused hydration of the dried hydrogel and led to swelling, which reduced the bend in the now flexible backbone (heated above the T<sup>g</sup> by the hot steam). This unlocked the snapped-open VFf, the stored elastic energy was released, and the lobes moved upwards to the resting position. Thereafter, the VFf was ready for manual actuation. Nineteen backbones were tested repeatedly for five dehydration and rehydration cycles. For the identification of the threshold humidity at which the hydrogel-coated backbones straightened, ten were tested in a small climate chamber in which the humidity was raised from 20% to 80% at a constant temperature of 65 ◦C.

### *2.6. Statistics*

The open-source software RStudio (v. 1.2.5042, R Core Team 2017) and statistic programming language R were used for statistical analysis and calculations. For the pneumatic demonstrator, we used a two-way ANOVA on ranked transformed data, having checked for normal distribution (Shapiro–Wilk test) and homoscedasticity (Bartlett test). The significance levels and correlation between variable actuation times and movement speeds were determined. Post-hoc tests were performed via multiple comparisons by using Tukey's test. Data from the kinematic analysis of the magnetic demonstrator were checked for normal distribution (Shapiro–Wilk test) and homoscedasticity (Bartlett test). Significant differences between movement speed and actuation rpm were determined using the Wilcoxon signedrank test. For the hydrogel- and SMA-based demonstrator, we used a paired Wilcoxon signed-rank test, having checked for normal distribution (Shapiro–Wilk test) and variance homogeneity (Kruskal–Wallis test).

#### **3. Results**

### *3.1. Movement Characteristics of the Biological Model D. muscipula*

The movement of the trap leaves of the biological model *D. muscipula* was observed from two perspectives (Figure 3A), and the leaf rim was tracked in order to calculate movement speed (Figure 3B). The closing time of the five tested plants ranged from 148 ms to 1821 ms with a mean value of 599.1 ms (SD = 487.7 ms). During the three-week testing period, mean closing time increased each week of testing from 549 ms in the first week to 683.9 ms in the third week (Figure 3C). Of the closing events, 56.1% took place in less than 500 ms (Figure 3D). Closing times above 1000 ms were the result of a delay between the initiations of the closing motions of the two lobes (Figure 3). Speed values of the closing motion ranged from 0.016 m/s to 0.245 m/s with an average movement speed of 0.088 m/s. The corresponding raw data is shown in Table S1 in the supplementary material section "Materials and Methods: 3. Kinematic analysis of the biological role model". *Biomimetics* **2022**, *7*, x FOR PEER REVIEW 9 of 27 ms to 1821 ms with a mean value of 599.1 ms (SD = 487.7 ms). During the three-week testing period, mean closing time increased each week of testing from 549 ms in the first week to 683.9 ms in the third week (Figure 3C). Of the closing events, 56.1% took place in less than 500 ms (Figure 3D). Closing times above 1000 ms were the result of a delay between the initiations of the closing motions of the two lobes (Figure 3). Speed values of the closing motion ranged from 0.016 m/s to 0.245 m/s with an average movement speed of 0.088 m/s. The corresponding raw data is shown in Table S1 in the supplementary material section "Materials and Methods: 3. Kinematic analysis of the biological role model".

**Figure 3.** *Cont*.

ms to 1821 ms with a mean value of 599.1 ms (SD = 487.7 ms). During the three-week testing period, mean closing time increased each week of testing from 549 ms in the first week to 683.9 ms in the third week (Figure 3C). Of the closing events, 56.1% took place in less than 500 ms (Figure 3D). Closing times above 1000 ms were the result of a delay between the initiations of the closing motions of the two lobes (Figure 3). Speed values of the closing motion ranged from 0.016 m/s to 0.245 m/s with an average movement speed of 0.088 m/s. The corresponding raw data is shown in Table S1 in the supplementary material section "Materials and Methods: 3. Kinematic analysis of the biological role model".

**Figure 3.** High-speed recording of the Venus flytrap from two angles gave a good impression of the overall movement (**A**). The path of motion was tracked at the base of the marginal teeth (orange and green lines) (**B**), and the movement speed was measured for these particular trajectories. Average closing time ranged from 550 to 680 ms for the three weeks of testing (**C**), whereas over half of the closing events needed less than 500 ms. The box plots represent 12, 8, and 8 measurements for week one, two, and three, respectively (**D**). Lobe tips reached velocities of between 0.016 and 0.24 m/s during closing. Each plot includes 28 measurements (**E**).

#### *3.2. Motion Analysis of Generation of Discrete Repetitive Motion by Pneumatic Actuation*

The kinematic analysis of three pneumatically actuated VFfs showed that a movement cycle consisting of one closing and opening movement could be separated into five separate phases (Figure 4A), with a curvature inversion and unrolling movement of the lobes during the snap opening of the VFfs (Figure 4B). During actuation, the highest velocities were observed during the opening movement (Figure 4C). The closing movement lasted between 132 ms and 311 ms (Figure 4D). The opening time ranged from 19 ms to 56 ms, depending on the time delay between the opening events of the two lobes. The fastest opening times were observed when both lobes moved simultaneously in parallel. Opening time is defined as the time needed from the first sign of the opening movement to the passing of the horizontal line of the backbone. After opening, with a still-inflated central cushion, the demonstrator remained locked in the open position. When all pressure was released from the system, the VFf returned to its initial position. The closing velocity showed a dependence on actuation time (AT) (a longer AT of 200, 300, and 400 ms gave slower closing) (Figure 4E). In contrast, the AT had almost no significant effect on the opening velocity of each lobe (Figure 4F). The measured speeds of the lobe tips during opening ranged from 3.05 m/s to 4.91 m/s (Figure 4F). Demonstrator three showed faster opening times because of the simultaneous opening of the two lobes (Figure 4F). The applied pressure ranged between 0.75 and 0.79 bar for the outside cushions and 0.66 and 0.69 bar for the single central pneumatic cushion.

*Biomimetics* **2022**, *7*, x FOR PEER REVIEW 11 of 27

**Figure 4.** Kinematic analysis of the five phasic motions of the pneumatic VFf. After activation of the outside cushions, the VFf closes, and the opening movement is triggered when the central cushion is inflated. Examination of the lobe movement reveals five phases (**A**) starting with the closing movement (**A1**). The second phase is the opening movement (**A2**) that begins with a slight outward movement of the base of the lobe leading to a rolled-up intermediate state that is followed by a fastunrolling movement (**B**). After opening, the lobes oscillate in the locked open position (**A3**). Following air release, the VFf snaps back into its original position and is ready for the next actuation (**A4**) with the lobes oscillating around the initial position (**A5**). In (**B**), a time-delayed opening of both lobes shows the unrolling movement of one of the lobes. The five phases are characterized by their different movement speeds (**C**), an example of which is shown here for a motion cycle at 400 ms AT. During actuation, the highest velocities (up to 4.9 m/s) are observed during the opening movement (**D**). Closing times depend on the overall actuation time (**E**). Significant differences above 40 ms for opening times are attributable to a delayed and non-parallel opening movement of the two lobes. Faster opening times represent simultaneous opening (**F**). Each boxplot corresponds to five measurements during which the three demonstrators have each completed eight movement cycles. Significance levels are indicated by the capital letters next to each boxplot. Different letters represent significant differences from other results with *p*-values below 0.05. **Figure 4.** Kinematic analysis of the five phasic motions of the pneumatic VFf. After activation of the outside cushions, the VFf closes, and the opening movement is triggered when the central cushion is inflated. Examination of the lobe movement reveals five phases (**A**) starting with the closing movement (**A1**). The second phase is the opening movement (**A2**) that begins with a slight outward movement of the base of the lobe leading to a rolled-up intermediate state that is followed by a fastunrolling movement (**B**). After opening, the lobes oscillate in the locked open position (**A3**). Following air release, the VFf snaps back into its original position and is ready for the next actuation (**A4**) with the lobes oscillating around the initial position (**A5**). In (**B**), a time-delayed opening of both lobes shows the unrolling movement of one of the lobes. The five phases are characterized by their different movement speeds (**C**), an example of which is shown here for a motion cycle at 400 ms AT. During actuation, the highest velocities (up to 4.9 m/s) are observed during the opening movement (**D**). Closing times depend on the overall actuation time (**E**). Significant differences above 40 ms for opening times are attributable to a delayed and non-parallel opening movement of the two lobes. Faster opening times represent simultaneous opening (**F**). Each boxplot corresponds to five measurements during which the three demonstrators have each completed eight movement cycles. Significance levels are indicated by the capital letters next to each boxplot. Different letters represent significant differences from other results with *p*-values below 0.05.

#### *3.3. Motion Analysis of Contactless Demonstrator Actuation by a Rotating Magnetic Field*

During actuation at low speed (rounds per minute) of the magnetic stirrer, the VFf lobes showed shivering movements, while the permanent magnet moved up and down depending on the speed of the magnetic stirrer (Figure 5A). The motion accelerated in association with an increase in actuation velocity, transforming into a fast, nearly regular, oscillating flapping motion around 800–900 rpm with a stable motion frequency of 15.6 Hz at 900 rpm (Figure S3 and Table S4). At 1000 rpm, the bent lobes tended to buckle and quickly returned to their original shape thereafter (Figure 5C); the highest observed velocity

at this time was 3.56 m/s (Figure 5B). The average speed of lobe tips increased with rising actuation velocity ranging from 0.33 m/s to 2.37 m/s. In correspondence the motion frequency also increased from 3.67 Hz to 44 Hz, with an observed decrease as the motion became more erratic at higher rpm (Figure S3 and Table S4). The movement of the lobes was delayed compared with the perpendicular motion of the magnet (Figure 5C). *Biomimetics* **2022**, *7*, x FOR PEER REVIEW 13 of 27

**Figure 5.** Motion analysis of magnetically driven oscillating VFfs with velocities approximating to **Figure 5.** natural frequency. With higher actuation velocity Motion analysis of magnetically driven oscillating VFfs with velocities approximating to (higher rpm), the movement speed and amplitude natural frequency. With higher actuation velocity (higher rpm), the movement speed and amplitude increase (motion tracks indicated by orange and blue lines) (**A**). Three VFfs were tested at six different actuation speeds (**B**). Significance levels are indicated by the capital letters next to each boxplot. Different letters represent significant differences from other results with *p*-values below 0.05. Recording frame-rate of 1000 fps for a video duration of 3 s resulted in 3000 values for each speed (*n* = 3000) of the movement of the three tested VFfs. Highest velocities were observed when a lobe bent during the outward and downward movement and then snapped back into its original curvature (**C**). The images illustrate the difference in speed of the left and the right lobe of demonstrator 3 at 1000 rpm. \* indicates the fastest snapping lobe in (**B**,**C**).
