In the field of robotics, bionic robots have always been a research hotspot due to their strong load capacity and excellent environmental adaptability. Among them, quadruped bionic robots, which mimic the walking patterns of animals, offer significant advantages in traversing soft or uneven terrain while maintaining stability. However, many existing quadruped bionic robots face challenges such as complex mechanical structures and high control difficulties, limiting their widespread application. To address these issues, I propose a novel quadruped bionic robot based on a linkage-type walking mechanism. This design utilizes worm gear and synchronous belt transmission systems, driven by a single motor, enabling stepping locomotion with a compact structure and relatively simple control. The linkage-based walking mechanism boasts high load-bearing capacity, and during operation, the links perform complex planar motions with diverse trajectories, effectively meeting the gait requirements of legged bionic robots. In this article, I will detail the design process, kinematic analysis, simulation, and overall construction of this bionic robot, emphasizing the integration of linkage mechanisms to enhance performance and practicality.
The walking mechanism is central to the functionality of the bionic robot. Inspired by the motion principles of linkage mechanisms, I designed a multi-link walking leg mechanism for the bionic robot. The mechanism is a planar multi-link assembly consisting of a crank-rocker mechanism and a five-bar mechanism, all connected via hinges. Hinges O and B serve as the fixed frames, mounted on the robot’s chassis. Links OA, AC, BC, and the frame OB form a crank-rocker mechanism, while links OA, AE, DE, BD, and the frame OB constitute a five-bar mechanism. Link OA acts as the driving element for both mechanisms, undergoing full rotation to transmit motion through the linkages, thereby driving the entire system. Point F is designated as the footfall point; during the circular motion of crank OA, point F undergoes periodic movement, enabling the bionic robot to perform stepping motions. This design simplifies actuation while ensuring robust motion generation, which is critical for bionic robots operating in diverse environments.
Kinematic analysis is fundamental for evaluating the performance of the bionic robot’s walking mechanism. To facilitate this, I established coordinate systems for analysis. First, a fixed reference coordinate system Oxy was defined with origin at hinge O, x-axis horizontal, and y-axis vertical. Additionally, a relative coordinate system Ox’y’ was set up with origin at O, x’-axis along the line connecting fixed points O and B, and y’-axis perpendicular to it. This dual-coordinate approach allows for detailed motion analysis of the footfall point F. The multi-link mechanism was decomposed into a crank-rocker mechanism OACB and a five-bar mechanism OAEDB for individual analysis. The goal is to derive the trajectory of point F relative to the fixed coordinate system, which dictates the bionic robot’s stepping pattern.
For the crank-rocker mechanism OACB, as shown in the schematic, let the length of crank OA be \( l_1 \) with angle \( \theta \) relative to the x’-axis, link AC be \( l_2 \) with angle \( \phi_1 \), and rocker BC be \( l_3 \) with angle \( \gamma_1 \). The distance between fixed points O and B is \( l \). Based on the geometry, the equilibrium equations are:
$$ l_1 \cos \theta – l_2 \cos \phi_1 – l_3 \cos \gamma_1 + l = 0 $$
$$ l_1 \sin \theta – l_2 \sin \phi_1 + l_3 \sin \gamma_1 = 0 $$
From these, \( \phi_1 \) and \( \gamma_1 \) can be solved for any given \( \theta \), enabling motion prediction for the bionic robot’s leg components.
For the five-bar mechanism OAEDB, it has two degrees of freedom, so consistency with the crank-rocker mechanism is maintained by ensuring angles \( \gamma_1 \) and \( \theta \) match those in the previous analysis. Let rocker BD have length \( l_4 \) with angle \( \gamma_1 \), link AE have length \( l_5 \) with angle \( \phi_2 \), link DE have length \( l_6 \) with angle \( \gamma_2 \), and link DF have length \( l_7 \). The equilibrium equations are:
$$ l_1 \cos \theta – l_4 \cos \gamma_1 – l_5 \cos \phi_2 – l_6 \cos \gamma_2 + l = 0 $$
$$ l_1 \sin \theta + l_4 \sin \gamma_1 – l_5 \sin \phi_2 + l_6 \sin \gamma_2 = 0 $$
Solving these yields \( \phi_2 \) and \( \gamma_2 \), completing the kinematic description of the bionic robot’s leg mechanism.
The footfall point F’s coordinates in the relative coordinate system Ox’y’ are derived as:
$$ x’_F = l_4 \cos \gamma_1 + l_7 \cos \gamma_2 – l $$
$$ y’_F = -l_4 \sin \gamma_1 – l_7 \sin \gamma_2 $$
To analyze the bionic robot’s motion in a global context, transformation to the fixed coordinate system Oxy is necessary. Given that the x’-axis is rotated by angle \( \alpha \) relative to the x-axis, the coordinates of F in Oxy are:
$$ x_F = x’_F \cos \alpha + y’_F \sin \alpha $$
$$ y_F = y’_F \cos \alpha – x’_F \sin \alpha $$
These equations define the trajectory of point F as crank OA rotates, which is crucial for gait planning in the bionic robot.
To validate the design, I performed a motion simulation using MATLAB for a specific case of the bionic robot. The parameters are summarized in Table 1, which outlines the key dimensions for the linkage mechanism.
| Parameter | Symbol | Value (mm) |
|---|---|---|
| Distance between O and B | \( l \) | 100 |
| Crank length | \( l_1 \) | 25 |
| Link AC length | \( l_2 \) | 130 |
| Rocker BC length | \( l_3 \) | 85 |
| Rocker BD length | \( l_4 \) | 145 |
| Link AE length | \( l_5 \) | 180.5 |
| Link DE length | \( l_6 \) | 30 |
| Link DF length | \( l_7 \) | 120 |
| Angle between x and x’ | \( \alpha \) | Varies based on design |
Assuming crank OA rotates uniformly at a constant speed, the simulation yielded the trajectory of point F over one cycle, as shown in Figure 4 of the original text (referred here conceptually). The results indicate that the stepping and ground contact phases each occupy half of the cycle, with a maximum horizontal displacement of 113 mm and a maximum vertical lift of 54 mm for the bionic robot’s foot. This demonstrates effective mimicking of biological stepping motions, a key advantage for bionic robots in adaptive locomotion.
Building on the kinematic analysis, I developed a three-dimensional model for a single walking leg of the bionic robot, as illustrated in Figure 5 (conceptually). Crank OA is designed as a flange for smooth actuation by a DC motor, reducing impact and vibration. The foot point F features an arc-shaped surface to minimize ground contact pressure, enhancing the bionic robot’s stability on various terrains. This design prioritizes durability and efficiency, which are essential for real-world applications of bionic robots.
For the full quadruped bionic robot, I integrated four walking legs into a rectangular body structure, with legs distributed on both sides. The assembly follows symmetry principles to avoid interference during motion. Specifically, legs 1 and 2 mirror the standard model, while legs 3 and 4 are symmetrically arranged relative to a vertical axis through the crank rotation center O. To emulate the walking gait of quadruped mammals like horses or cows, I set the phase relationships as follows: legs 1 and 3 have identical phase, legs 2 and 4 have identical phase, and legs 1 and 4 have a phase difference of \( \pi \) radians, as do legs 2 and 3. This configuration ensures that when one diagonal pair of legs is in the ground contact phase, the other diagonal pair is in the stepping phase, enabling stable and efficient locomotion for the bionic robot. The overall dimensions of the bionic robot are 600 mm in length, 260 mm in width, and 310 mm in height (including leg extensions), making it compact and practical.
The transmission system of the bionic robot employs a worm gear mechanism and a synchronous belt drive, powered by a single motor. This setup simplifies control while ensuring precise motion synchronization among the four legs. The worm gear provides high torque and self-locking capability, beneficial for load-bearing, while the synchronous belt ensures accurate phase maintenance between cranks. Table 2 summarizes the key features of this bionic robot design, highlighting its advantages over traditional quadruped systems.
| Aspect | Description | Benefit for Bionic Robot |
|---|---|---|
| Actuation | Single DC motor with worm gear and belt drive | Reduced control complexity and cost |
| Leg Mechanism | Multi-link (crank-rocker and five-bar) | High load capacity and diverse trajectories |
| Gait Emulation | Phase-controlled diagonal stepping | Stable and biomimetic locomotion |
| Foot Design | Arc-shaped contact surface | Lower ground pressure and improved traction |
| Overall Size | Compact with balanced leg spacing | Prevents interference and enhances maneuverability |
From a broader perspective, the development of this bionic robot aligns with ongoing efforts to enhance robotic adaptability in unstructured environments. The linkage mechanism offers inherent advantages such as robustness and simplicity, which are often lacking in more complex bionic robot designs. By leveraging planar motion theory, I have optimized the leg trajectories to achieve efficient stepping, a critical factor for energy conservation in mobile bionic robots. Furthermore, the use of MATLAB for simulation allows for iterative refinement, ensuring that the bionic robot meets performance criteria before physical prototyping.
In terms of mathematical rigor, the kinematic analysis can be extended to include velocity and acceleration studies. For instance, by differentiating the position equations, the velocities of key points can be derived. Let \( \omega \) be the angular velocity of crank OA, such that \( \dot{\theta} = \omega \). The velocity components for point F in the relative coordinate system are:
$$ \dot{x}’_F = -l_4 \sin \gamma_1 \cdot \dot{\gamma}_1 – l_7 \sin \gamma_2 \cdot \dot{\gamma}_2 $$
$$ \dot{y}’_F = -l_4 \cos \gamma_1 \cdot \dot{\gamma}_1 – l_7 \cos \gamma_2 \cdot \dot{\gamma}_2 $$
where \( \dot{\gamma}_1 \) and \( \dot{\gamma}_2 \) can be obtained from the differentiation of the equilibrium equations. This deeper analysis aids in understanding dynamic effects, which are vital for high-speed applications of bionic robots.
Another important consideration is the optimization of linkage parameters for specific tasks. Using numerical methods, I explored variations in link lengths to maximize stride length or minimize energy consumption. For example, by defining an objective function \( J = \text{max}(x_F) – \text{min}(x_F) \) for horizontal displacement, and applying constraints such as \( l_i > 0 \) and avoidance of singularities, optimal sets for \( l_1 \) to \( l_7 \) can be identified. This optimization process enhances the versatility of the bionic robot, allowing customization for different terrains or payloads.
The control strategy for this bionic robot is relatively straightforward due to the single-motor actuation. However, to improve adaptability, feedback from sensors such as encoders or inertial measurement units (IMUs) can be integrated. For instance, by monitoring the crank angle \( \theta \), the position of each leg can be estimated in real-time, enabling adjustments for uneven ground. This closed-loop control enhances the bionic robot’s stability and responsiveness, key traits for autonomous operation.
In comparison to other bionic robot designs, this linkage-based approach offers a balance between mechanical simplicity and functional performance. Many advanced bionic robots utilize multiple actuators per leg, increasing complexity and cost. Here, the reliance on passive linkages reduces the number of active components, making the bionic robot more reliable and easier to maintain. This is particularly advantageous for educational or industrial applications where robustness is prioritized.
To further illustrate the kinematic principles, I derived the condition for continuous rotation of crank OA without dead points. For the crank-rocker mechanism, Grashof’s criterion must be satisfied. Let \( s \) be the shortest link, \( l \) be the longest link, and \( p, q \) be the other two links. If \( s + l \leq p + q \), and \( s \) is the crank, then continuous rotation is possible. In this bionic robot, with \( l_1 \) as the crank, checking: \( l_1 + \max(l_2, l_3, l) \leq \text{sum of others} \). For the given parameters, \( l_1 = 25 \), \( l = 100 \), \( l_2 = 130 \), \( l_3 = 85 \), so \( 25 + 130 = 155 \) and \( 100 + 85 = 185 \), thus \( 155 \leq 185 \), satisfying the condition. This ensures smooth operation of the bionic robot’s leg mechanism.
The gait analysis of the bionic robot can be quantified using duty factor and stride frequency. Let \( T \) be the period of crank rotation. The duty factor \( \beta \) is the fraction of time a leg is in contact with the ground. From the simulation, \( \beta = 0.5 \) for each leg. The stride length \( S \) is the horizontal displacement per cycle, measured as 113 mm. If the crank rotates at \( n \) rpm, the forward speed \( v \) of the bionic robot is:
$$ v = \frac{S \cdot n}{60} \quad \text{(mm/s)} $$
For example, at \( n = 60 \) rpm, \( v = 113 \) mm/s. This formula aids in speed planning for the bionic robot in various scenarios.
Energy efficiency is another critical aspect for bionic robots. The linkage mechanism, being purely mechanical, minimizes electrical losses compared to multi-motor systems. The power required from the motor can be estimated as \( P = \tau \omega \), where \( \tau \) is the torque and \( \omega \) is the angular velocity. Assuming a load \( W \) on the bionic robot and friction losses, the torque can be approximated from static analysis. For instance, at the moment of maximum lift, the torque on crank OA is higher, influencing motor selection. This analysis ensures that the bionic robot is powered adequately without overdesign.
The design also considers manufacturability and assembly. The links can be fabricated from lightweight materials like aluminum or carbon fiber to reduce inertia, improving the bionic robot’s agility. Hinge joints use bearings to minimize friction, and the overall structure is modular for easy repair. These practical considerations enhance the bionic robot’s suitability for field deployments.
In summary, this article presents a comprehensive design of a quadruped bionic robot based on a linkage walking mechanism. Through kinematic analysis and simulation, I have demonstrated that the mechanism achieves effective stepping trajectories with simple actuation. The bionic robot’s design emphasizes stability, load capacity, and biomimetic gait, addressing common limitations in existing systems. Future work may involve prototyping, experimental validation, and integration of advanced control algorithms to further enhance the bionic robot’s capabilities. The linkage approach offers a promising direction for developing cost-effective and robust bionic robots for applications in search and rescue, exploration, and service robotics.
To reinforce the theoretical foundations, I include additional equations for the acceleration analysis, which are useful for dynamic modeling. The acceleration of point F in the relative coordinate system is:
$$ \ddot{x}’_F = -l_4 (\cos \gamma_1 \cdot \dot{\gamma}_1^2 + \sin \gamma_1 \cdot \ddot{\gamma}_1) – l_7 (\cos \gamma_2 \cdot \dot{\gamma}_2^2 + \sin \gamma_2 \cdot \ddot{\gamma}_2) $$
$$ \ddot{y}’_F = l_4 (\sin \gamma_1 \cdot \dot{\gamma}_1^2 – \cos \gamma_1 \cdot \ddot{\gamma}_1) + l_7 (\sin \gamma_2 \cdot \dot{\gamma}_2^2 – \cos \gamma_2 \cdot \ddot{\gamma}_2) $$
These expressions help in evaluating inertial forces, which are crucial for motor sizing and stability assessment of the bionic robot during rapid movements.
Moreover, the versatility of the bionic robot can be extended by modifying the linkage parameters for different gait patterns. For example, by adjusting the phase differences, trotting, walking, or bounding gaits can be achieved. This adaptability makes the bionic robot suitable for varied terrains, from flat surfaces to rough landscapes. The mathematical framework provided here serves as a basis for such customizations, underscoring the flexibility of linkage-based designs in bionic robotics.
In conclusion, the integration of linkage mechanisms into bionic robot design offers a viable path toward simpler, more reliable, and high-performing systems. This work contributes to the ongoing evolution of bionic robots, highlighting the importance of mechanical innovation in achieving practical and efficient locomotion. As robotics technology advances, such designs will play a pivotal role in expanding the applications of bionic robots across industries and research domains.