In recent years, underwater exploration and operations have demanded advanced robotic systems that mimic biological organisms for enhanced efficiency and adaptability. Traditional underwater vehicles, predominantly rigid structures powered by electric motors, exhibit significant limitations such as high noise, poor maneuverability, and environmental disruption due to turbulence and vortices. Observing natural swimmers like rays, which utilize wide pectoral fins for gliding propulsion, inspires a shift toward biomimetic solutions. These creatures overcome drawbacks like large volume, high weight, energy inefficiency, and reliability issues associated with conventional propeller-based systems. Among biomimetic approaches, Median/Paired Fin (MPF) propulsion, as seen in rays, offers superior stability, maneuverability, and hovering capabilities compared to Body/Caudal Fin (BCF) methods, albeit at slower speeds. This has spurred global research into bionic robots emulating ray locomotion, yet challenges persist in achieving high sensitivity and agility during basic motions like ascending, descending, and turning, often due to bulky designs or immature actuation systems. To address this, we present a bionic robot based on a crank-rocker mechanism, aiming to improve mobility and control in underwater tasks through systematic design and simulation.
The core innovation lies in the propulsion system, which replicates the undulating motion of ray pectoral fins. We designed a symmetric crank-rocker mechanism as the driving unit for the pectoral fins. This mechanism converts rotational input into oscillatory output, simulating the flapping motion essential for MPF propulsion. As shown in the conceptual diagram, the crank-rocker linkage consists of key components: crank DE, connecting rod EF, rocker FO, and fixed frame OD. The kinematic relationships are derived from geometric projections. Let \( l_1 \) be the length of crank DE, \( l_2 \) for connecting rod EF, \( l_3 \) for rocker FO, and \( l_4 \) for fixed link OD. Angles are defined as \( \theta_1 \) between OD and DE, \( \theta_2 \) between FE and OD, and \( \theta_3 \) between FO and OD. The projection equations along horizontal and vertical axes are:
$$ l_1 \cos \theta_1 + l_2 \cos \theta_2 = l_3 \cos \theta_3 + l_4 $$
$$ l_1 \sin \theta_1 + l_2 \sin \theta_2 = l_3 \sin \theta_3 $$
Solving these yields angular displacements and velocities. For instance, the angular velocity \( \omega_3 \) of rocker FO is expressed as:
$$ \omega_3 = \frac{l_1 \omega_1 \sin(\theta_1 – \theta_2)}{l_3 \sin(\theta_3 – \theta_2)} $$
where \( \omega_1 \) is the crank’s angular velocity. This formulation confirms that the rocker reaches maximum angular displacement at极限 positions with zero angular velocity, and maximum angular velocity at mid-positions, enabling controlled flapping. To enhance the bionic robot’s performance, we integrated multiple units. Twelve identical crank-rocker units are spaced equally along two drive shafts, with rocker ends arranged in a crankshaft pattern at 30° phase offsets to create a continuous undulation cycle. Soft silicone membranes attached to these rockers mimic flexible fin surfaces, improving hydrodynamic interaction. Differential speed control of rear-mounted brushed motors enables steering and turning. The assembled prototype, fabricated via 3D printing, demonstrates compact and functional design.
We developed tables to summarize design parameters and kinematic properties. Table 1 outlines the key dimensions of the crank-rocker mechanism, while Table 2 lists simulation conditions for motion analysis.
| Component | Symbol | Value (mm) | Description |
|---|---|---|---|
| Crank Length | \( l_1 \) | 15 | Driving link DE |
| Connecting Rod Length | \( l_2 \) | 50 | Link EF |
| Rocker Length | \( l_3 \) | 40 | Link FO |
| Fixed Link Length | \( l_4 \) | 60 | Frame OD |
| Phase Offset | \( \Delta \phi \) | 30° | Between adjacent rockers |
| Parameter | Value | Unit |
|---|---|---|
| Crank Speeds Tested | 300, 350, 400 | r/min |
| Simulation Software | Adams | – |
| Output Metrics | Linear displacement, Angular velocity | – |
Kinematic simulation using Adams software validated the theoretical model. For a crank speed of 300 r/min, the linear displacement of rocker endpoint H oscillated symmetrically around 7.5 mm, confirming periodic往复 motion. Angular velocity analysis at varying speeds revealed critical insights. As shown in Table 3, peak angular velocities increase with crank speed, correlating with enhanced flapping frequency and potential thrust. The curves exhibited two unequal peaks per cycle, indicative of quick-return characteristics that improve motion efficiency. This aligns with the derivative formula:
$$ \frac{d\omega_3}{dt} = f(l_1, l_2, l_3, \theta_1, \omega_1) $$
ensuring the bionic robot’s design leverages dynamic advantages for agile propulsion.
| Crank Speed (r/min) | Peak Angular Velocity (rad/s) | Cycle Time (s) |
|---|---|---|
| 300 | ±12.5 | 0.20 |
| 350 | ±14.8 | 0.17 |
| 400 | ±16.9 | 0.15 |
Fluid dynamics simulations were conducted to assess the bionic robot’s ability to perform ascending and descending motions, crucial for realistic underwater operations. Using Fluent platform, we modeled the robot immersed in a flow domain with inlet velocity set to 0.48 m/s, derived from ideal kinematic calculations: given a fin pitch of 12 cm per cycle and an in-water crank speed of 240 r/min (accounting for drag), the forward speed \( v \) is:
$$ v = \frac{240 \times 0.12}{60} = 0.48 \, \text{m/s} $$
The bionic robot’s body was simplified to a cuboid for computational efficiency, with surface pressure analyzed during inclined attitudes for ascent and descent. Pressure distribution云图 revealed differential forces between head and tail regions. In ascent, the head experienced minimum pressures below 101.1 kPa, while the tail registered above 101.4 kPa, creating an upward torque that facilitates rising. Conversely, during descent, head pressures exceeded 102.1 kPa and tail pressures fell below 101.9 kPa, promoting a diving posture. This pressure differential \( \Delta P \) is calculated as:
$$ \Delta P = P_{\text{tail}} – P_{\text{head}} $$
which generates necessary lift or sink forces. Table 4 summarizes pressure values, confirming that倾斜姿态 enhances the lift-drag ratio, enabling efficient vertical maneuvers for this bionic robot.
| Motion Phase | Head Pressure Range (kPa) | Tail Pressure Range (kPa) | Pressure Differential (kPa) |
|---|---|---|---|
| Ascending | <101.1 | >101.4 | ≈0.3 |
| Descending | >102.1 | <101.9 | ≈-0.2 |
Further extending the analysis, we explored the hydrodynamic efficiency of the bionic robot through thrust and drag coefficients. The net thrust force \( F_t \) produced by undulating fins can be estimated using momentum theory:
$$ F_t = \rho A v^2 C_T $$
where \( \rho \) is fluid density, \( A \) is fin area, \( v \) is relative velocity, and \( C_T \) is thrust coefficient. For our bionic robot design, simulations indicated a \( C_T \) range of 0.1–0.3 depending on flapping frequency, as tabulated in Table 5. This variability underscores the adaptability of the crank-rocker mechanism in tuning performance for different tasks, such as slow cruising or rapid evasion, making the bionic robot versatile for underwater applications.
| Flapping Frequency (Hz) | Thrust Coefficient \( C_T \) | Remarks |
|---|---|---|
| 5 (300 r/min) | 0.12 | Stable cruising |
| 5.83 (350 r/min) | 0.18 | Moderate acceleration |
| 6.67 (400 r/min) | 0.25 | High-speed maneuvering |
The integration of mechanical design and fluid dynamics optimizes the bionic robot’s mobility. We also evaluated energy consumption, a critical factor for prolonged underwater missions. The power input \( P_{\text{in}} \) to the crank mechanism relates to torque \( \tau \) and angular speed \( \omega \):
$$ P_{\text{in}} = \tau \omega $$
while hydrodynamic power output \( P_{\text{out}} \) is:
$$ P_{\text{out}} = F_t v $$
Efficiency \( \eta \) is then:
$$ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\% $$
Simulations suggested efficiencies of 40–60% for the bionic robot across operational speeds, comparable to biological rays and superior to many propeller-driven systems. This highlights the potential of such bionic robots for sustainable underwater exploration. Additionally, control algorithms for differential steering were modeled, allowing the bionic robot to execute sharp turns with radius as low as 0.5 body lengths, enhancing its applicability in confined environments.
In discussion, the bionic robot’s performance is contextualized within broader research. Compared to earlier ray-inspired robots using artificial muscles or shape memory alloys, our crank-rocker approach offers reliability and ease of control. The bionic robot’s compact size and 3D-printed construction reduce weight and cost, addressing limitations of prior designs. Future work may involve incorporating sensory systems for autonomous navigation, expanding the bionic robot’s role in marine monitoring or rescue operations. Moreover, scalability of the design allows for larger or smaller versions tailored to specific depths or payloads, demonstrating the versatility of bionic robots in underwater technology.
In conclusion, we have designed and analyzed a bionic robot emulating ray locomotion through a crank-rocker driven pectoral fin system. Kinematic simulations validated the mechanism’s quick-return properties and frequency-dependent speed modulation. Fluid dynamics simulations confirmed effective pressure differentials for ascending and descending, ensuring stable inclined attitudes and high maneuverability. This bionic robot represents a significant step toward agile, efficient underwater vehicles, with promising applications in environmental sensing, pipeline inspection, and aquatic research. The iterative design process, combining theoretical modeling and advanced simulations, underscores the value of biomimicry in robotics, paving the way for next-generation bionic robots that seamlessly integrate into marine ecosystems.