The exploration and sustainable utilization of marine resources are pivotal for national development strategies. Traditional underwater vehicles, predominantly propelled by screw propellers or impellers, exhibit significant limitations in stealth, maneuverability within complex environments, and energy efficiency. Their pronounced acoustic signature and flow disturbance are less than ideal for sensitive ecological monitoring or covert operations. In contrast, biological swimmers like the flatworm exhibit elegant and efficient locomotion through the undulatory motion of their lateral fins. This Median and/or Paired Fin (MPF) propulsion mode offers a compelling blueprint for the next generation of underwater bionic robots. Such robots promise lower noise, reduced flow disturbance, enhanced stability, and superior agility, making them ideal for tasks in delicate coral reefs or confined underwater structures.
However, current research on MPF-based bionic robots often grapples with challenges related to system complexity, volume, weight, and motion performance. Many designs rely on multiple independently actuated fin rays, leading to bulky systems with complex control requirements. Others may use single driving elements or mechanical connections that introduce inefficient parasitic motions or compromise stability. This paper presents the design, analysis, and experimental validation of a novel bionic underwater robot inspired by the flatworm. Our core innovation lies in employing a specialized crank-rocker linkage mechanism with no quick-return characteristic as the fundamental propulsion unit. Multiple such units are arrayed along a flexible, drivable spine to transmit power and generate a stable, traveling wave along a continuous silicone fin membrane. This approach aims to create a compact, lightweight, and high-performance bionic robot capable of efficient underwater locomotion.
1. Mechanical Design of the Bionic Robot
The flatworm possesses an extremely flattened, flexible body capable of traversing narrow crevices with wave-like body motions. Emulating this key morphology and propulsion strategy, our bionic robot is architected into three integrated units: the Propulsion Mechanism Array, the Drivable Flexible Vertebral Column, and the Tail-mounted Drive and Payload Module.
1.1 Propulsion Mechanism Array Design
The propulsion system is the core of this bionic robot. It consists of an array of identical sub-mechanisms, each a four-bar crank-rocker linkage. The rocker in each linkage acts as a discrete support point for a continuous flexible fin. When the crank rotates, it drives the rocker in an oscillatory motion. By physically connecting the output points (rocker tips) of several such mechanisms with a flexible material (e.g., silicone membrane), a traveling wave is synthesized along the fin’s length.
The phase difference between adjacent sub-mechanisms is critical for forming a smooth wave. A phase angle that is too small increases material strain and internal friction; one that is too large reduces wave resolution and thrust efficiency. Based on prior research and our own analysis, a phase angle between 45° and 90° is optimal. We selected a 60° phase difference for this design. This is conveniently achieved by connecting the cranks of adjacent units via a hexagonal prism coupler, ensuring mechanical simplicity and robustness. The kinematic principle is illustrated below, where the oscillating rockers (link c) drive the fin.
The key dimensions for a single propulsion unit are summarized in Table 1.
| Parameter | Symbol | Value (mm) | Description |
|---|---|---|---|
| Crank Length | a | 15 | Input driving link |
| Coupler Length | b | 50 | Connecting link |
| Rocker Length | c | 30 | Output oscillating link / Fin ray |
| Frame Length | d | 56.4 | Fixed ground link |
| Rocker Swing Angle | 2θ | ≈ 60° | Total angular displacement of the rocker |
| Phase Difference | Δφ | 60° | Angular offset between adjacent crank phases |
1.2 Drivable Flexible Vertebral Column
To enhance the agility and functionality of the bionic robot beyond simple forward swimming, we incorporated a biomimetic, actively bendable spine. This spine serves a dual purpose: it structurally links the propulsion modules, and it allows for controlled body flexion, enabling maneuvers such as diving or turning.
The spine is constructed from a series of modular vertebral segments. Each pair of segments is connected by springs, which provide compliance, shock absorption, and restore the spine to a neutral position. For active bending, two nylon cords are routed through channels along the upper and lower sides of the spine. These cords are anchored at the tail and wound in opposite directions onto a spool connected to a servo motor in the head module. Activating the servo motor winds one cord while releasing the other, causing the entire spine to bend in the corresponding direction. This cable-driven approach allows for effective control of the bionic robot’s posture with a single actuator.
1.3 Tail-mounted Drive and Sealing System
Housing the primary power and control electronics in a separate, streamlined tail module improves hydrodynamic shape and simplifies maintenance. A 370-type DC geared motor (model JGA25-370-1285) was selected for its sufficient starting torque (>0.5 N·m), appropriate operational speed (>60 RPM), and compact size. This motor directly drives the interconnected cranks of the propulsion array.
Watertight integrity is paramount. The main tail housing and its end cap employ a dual O-ring flange seal, compressed by screws, ensuring reliable static sealing. The motor shaft seal is achieved using a triple-stage O-ring gland, effectively balancing sealing performance with minimizing frictional losses. This modular and robust sealing strategy is crucial for the practical operation of the bionic robot in underwater environments.
2. Kinematic Analysis and Design of the Non-Quick-Return Mechanism
A stable, symmetrical traveling wave is essential for smooth and efficient propulsion in a bionic robot. The quick-return characteristic, common in some crank-rocker linkages, causes the rocker to swing faster in one direction than the other. This asymmetry can introduce vibrations and reduce the quality of the generated wave. Therefore, we designed a special crank-rocker linkage with no quick-return property.
2.1 Geometric Condition for Eliminating Quick-Return
The quick-return characteristic is quantified by the time ratio or advance-to-return ratio, which is determined by the extreme position angle (θ) of the rocker. When the rocker’s two extreme positions are symmetric about the frame line, the crank angles required for the forward and return strokes are equal, resulting in a time ratio of 1 and no quick-return effect. This occurs when the coupler and crank are collinear in both extreme positions.
Consider the crank-rocker mechanism ABCD as shown in the kinematic diagram, where link AD (length a) is the crank, link AB (length d) is the frame, link DC (length b) is the coupler, and link BC (length c) is the rocker. Let the rocker swing through an angle 2θ. In the symmetric, non-quick-return configuration, when the rocker is at its extremes (positions BC and BC’), points A, D, C and A, D’, C’ are collinear, respectively.
From the geometry of the extreme positions, the stroke of the rocker tip (C to C’) is given by:
$$ CC’ = AC – AC’ = (a + b) – (b – a) = 2a $$
This stroke must also equal the vertical projection difference of the rocker: $$ CC’ = 2e = 2c \sin\theta $$, where e = c sinθ. Therefore, the primary condition is:
$$ a = e = c \sin\theta \quad \text{(1)} $$
Applying the law of cosines in triangle ABC (when the crank and coupler are extended, AC = a+b):
$$ d^2 = (a + b)^2 + c^2 – 2(a + b)c \cos\gamma \quad \text{(2)} $$
Where γ is the acute angle between the coupler and the rocker at this extreme. Noting from the right triangle that $$ \cos\gamma = \frac{e}{c} = \frac{a}{c} $$, we substitute into (2):
$$ d^2 = (a + b)^2 + c^2 – 2(a + b)c \cdot \frac{a}{c} = (a + b)^2 + c^2 – 2a(a + b) $$
Simplifying this equation leads to the fundamental dimensional relationship for a non-quick-return crank-rocker:
$$ a^2 + d^2 = b^2 + c^2 \quad \text{(3)} $$
In summary, the necessary conditions for a non-quick-return crank-rocker mechanism are:
- Equation (3) must be satisfied.
- The shortest link must be the crank (Grashof condition for a crank-rocker).
- The sum of the shortest and longest links must be less than or equal to the sum of the other two links (Grashof’s Law for full rotatability).
2.2 Dimensional Synthesis
We aimed for a rocker swing angle (2θ) of approximately 60° (θ=30°) to provide a substantial fin amplitude without exceeding typical material strain limits. From Equation (1), $$ a = c \sin30° = 0.5c $$. For compactness and mechanical feasibility, we selected c = 30 mm, yielding a = 15 mm.
Using the geometry, the horizontal projection h of the rocker at its midpoint is $$ h = c \cos\theta = 30 \cos30° ≈ 25.98 mm $$. The frame length d can be derived from the right triangle formed in one extreme position: $$ d = \sqrt{h^2 + (b – a)^2} $$. However, we must also satisfy Equation (3). Substituting a=15 and c=30 into (3) gives: $$ 15^2 + d^2 = b^2 + 30^2 $$, or $$ d^2 = b^2 + 675 $$.
We chose b = 50 mm as a reasonable coupler length. This gives: $$ d^2 = 50^2 + 675 = 3175 $$, so d ≈ 56.35 mm. This set of dimensions (a=15, b=50, c=30, d≈56.4) satisfies all the conditions and was adopted for the bionic robot’s propulsion units. The maximum pressure angle (α_max), a critical metric for force transmission quality, occurs at the rocker’s extreme and equals θ:
$$ \alpha_{\text{max}} = \theta = 30° $$
This value is well below the typical allowable limit of 50°, indicating good kinematic performance for this bionic robot mechanism.
2.3 Motion Simulation Validation
To verify the non-quick-return property of the designed linkage, a kinematic simulation was performed using SolidWorks Motion. A model of the mechanism was assembled, and a constant-speed rotary motor (8 RPM) was applied to the crank. The linear velocity of the rocker tip (point C) was plotted over a full cycle. The resulting velocity-time curve, as shown conceptually, was nearly sinusoidal and symmetric about the time axis. The magnitudes of the peak velocities during the forward and return strokes were virtually identical, confirming the absence of a quick-return effect. This symmetric motion profile is crucial for the bionic robot to generate a stable and efficient traveling wave for propulsion.
3. Prototype Development and Experimental Performance
3.1 Prototype Assembly
A functional prototype of the bionic underwater robot was fabricated to validate the design. The structural components, including the propulsion linkage parts, vertebral segments, and hulls, were manufactured using Nylon 12 (PA12) via Selective Laser Sintering (SLS) 3D printing. This material offers an excellent strength-to-weight ratio and good water resistance. The electronic components (DC motor, servo, control board, battery) were integrated into the sealed modules. Finally, a 1 mm-thick silicone sheet was attached to the array of rocker arms to form the continuous undulatory fin. The completed prototype is highly compact and lightweight, with a total mass of approximately 750 g and overall dimensions of 64.5 cm (L) × 16.8 cm (W) × 10.6 cm (H).
3.2 Underwater Motion Testing and Performance Analysis
The bionic robot’s forward swimming performance was evaluated in a static water tank (2.6 m long, 0.6 m deep). The robot was positioned at one end and commanded to swim at full speed (motor driven at 60 RPM) to the opposite end. Its motion was tracked, and the displacement over time was recorded to calculate velocity.
The robot covered the 2.6 m distance in approximately 10.2 seconds, resulting in an average forward speed (V_avg) of:
$$ V_{\text{avg}} = \frac{\text{Distance}}{\text{Time}} = \frac{2.6 \text{ m}}{10.2 \text{ s}} \approx 0.255 \text{ m/s} = 25.5 \text{ cm/s} $$
Analysis of the velocity profile indicated a steady increase in speed after initial acceleration, reaching a maximum velocity (V_max) of about 0.30 m/s (30 cm/s) during the latter part of the traversal. This performance is competitive, especially considering the robot’s small size and simple single-motor drive.
To benchmark our bionic robot, Table 2 compares its key performance metrics with other recently reported bio-inspired underwater robots from the literature. The comparison highlights the favorable trade-off achieved by our design in terms of speed relative to size and mechanical complexity.
| Bionic Inspiration | Propulsion Mode | Year | Reported Average Speed (cm/s) | Key Characteristics |
|---|---|---|---|---|
| Squid | Jet Propulsion | 2020 | 2.8 | Soft body, pulsed jet |
| Shark | Caudal Fin Oscillation | 2020 | 14.5 | Two-joint, pressure-driven soft tail |
| Ray | Pectoral Fin Flapping | 2022 | 7.3 | Wide pectoral fins, flapping motion |
| Jellyfish | Bell Pulsation | 2023 | 9.16 | Cam-driven, contractive bell |
| Flatworm (This Work) | Lateral Fin Undulation (MPF) | 2023 | 25.5 | Non-quick-return crank-rocker, flexible spine, compact |
Furthermore, preliminary tests in a natural, low-current water environment demonstrated the bionic robot’s capability for stable locomotion and basic directional control via spine bending. The undulatory fin produced minimal visible turbulence and very low acoustic noise, aligning with the desired stealth and low-disturbance characteristics for a surveillance or monitoring bionic robot.
4. Conclusion and Future Perspectives
This paper presented the comprehensive development of a novel bionic underwater robot inspired by the flatworm’s MPF swimming mode. The core contribution is the design and implementation of a propulsion system based on an array of non-quick-return crank-rocker mechanisms. Through theoretical kinematic analysis, we derived and applied the precise dimensional conditions ($$ a^2 + d^2 = b^2 + c^2 $$) required to eliminate quick-return, ensuring symmetric rocker oscillation. This mechanism, combined with a 60° inter-unit phase shift, effectively generates a stable traveling wave along a flexible fin membrane.
The integration of a cable-driven, flexible vertebral column adds a layer of maneuverability, allowing the bionic robot to modulate its posture. The prototype, constructed with lightweight 3D-printed components, validates the design’s feasibility. Experimental results confirm successful underwater locomotion with a competitive average speed of 25.5 cm/s, demonstrating that the proposed mechanical architecture achieves a favorable balance of performance, simplicity, and compactness for a bionic robot.
Future work will focus on several advanced aspects to elevate the capabilities of this bionic robot platform. Firstly, a detailed dynamic and hydrodynamic analysis is necessary. This involves developing a coupled fluid-structure interaction (FSI) model to understand the thrust generation mechanics of the undulating fin more precisely, accounting for both active driving and passive elastic deformation. Computational Fluid Dynamics (CFD) simulations will be instrumental in optimizing fin shape, undulation frequency, and amplitude for peak efficiency. Secondly, enhancing autonomy is crucial. Integrating embedded sensors (inertial measurement units, depth sensors, cameras) and implementing closed-loop control algorithms will enable autonomous navigation, obstacle avoidance, and station-keeping. Finally, exploring the use of advanced smart materials, such as shape memory alloys or dielectric elastomer actuators, for the fin membrane could lead to even more compact, silent, and energy-efficient versions of this bionic robot, pushing the boundaries of what is possible in underwater biomimetic systems.