In recent years, the development of bionic robots has gained significant attention due to their potential in various applications such as search and rescue, exploration, and industrial inspection. Among these, bionic quadruped robots are particularly notable for their ability to mimic the locomotion of four-legged animals, combining static and dynamic stability for efficient movement across complex terrains. However, traditional designs often face challenges like multiple actuators, high energy consumption, and complex control systems. To address these issues, we propose a novel leg structure for a bionic robot driven by a single hydraulic cylinder. This design reduces the number of drives, simplifies control, and enhances energy efficiency while maintaining robust performance. In this article, we present the structural design, kinematic modeling, and simulation analysis of this bionic robot leg, emphasizing its potential for widespread adoption.
The inspiration for our bionic robot leg comes from the skeletal structure of quadruped animals, such as dogs, which exhibit efficient and adaptive locomotion. By analyzing the biomechanics of these animals, we identified key joints like the shoulder and elbow, which are typically actuated separately in conventional robots. Our approach integrates these joints into a single-degree-of-freedom mechanism driven by a hydraulic cylinder, reducing mechanical complexity. The leg consists of several linkages, including a thigh, shank, and connecting rods, arranged to replicate the lifting and extending motions observed in biological systems. This bionic design not only improves agility but also minimizes inertia by distributing mass more effectively, a common issue in electric motor-driven systems where actuators are concentrated at joints.
To quantify the mobility of our bionic robot leg, we calculated its degrees of freedom using the planar mobility formula, as the mechanism operates primarily in a two-dimensional plane. The formula is given by:
$$ F = 3n – 2p_L – p_H – F_0 – F_v $$
where \( n \) is the number of moving links, \( p_L \) is the number of lower pairs (revolute or prismatic joints), \( p_H \) is the number of higher pairs, \( F_0 \) represents local degrees of freedom, and \( F_v \) denotes redundant constraints. For our bionic robot leg, we have 7 moving links and 10 lower pairs, with no higher pairs, local freedoms, or redundant constraints. Substituting these values:
$$ F = 3 \times 7 – 2 \times 10 = 1 $$
This confirms that the leg has a single degree of freedom, simplifying control and actuation. The hydraulic cylinder’s linear motion is translated into coordinated joint movements through a linkage system, enabling the bionic robot to perform tasks like walking and climbing with minimal input. This efficiency is crucial for applications where energy conservation is paramount, such as long-duration missions in remote environments.
Kinematic analysis is essential for understanding the motion characteristics of the bionic robot leg. We employed the Denavit-Hartenberg (D-H) parameter method to establish a coordinate system for each link, facilitating the derivation of forward and inverse kinematics. The D-H parameters define the relationship between consecutive links using four variables: link length \( a_i \), link twist \( \alpha_i \), joint offset \( d_i \), and joint angle \( \theta_i \). For our bionic robot leg, the D-H parameters are summarized in the following table:
| Link | \( a_i \) (mm) | \( \alpha_i \) (rad) | \( d_i \) (mm) | \( \theta_i \) (rad) |
|---|---|---|---|---|
| 1 | 450 | 0 | 0 | \( \theta_1 \) |
| 2 | 380 | 0 | 0 | \( \theta_2 \) |
The homogeneous transformation matrix between links \( i-1 \) and \( i \) is given by:
$$ T_i^{i-1} = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_i & \sin\theta_i \sin\alpha_i & a_i \cos\theta_i \\
\sin\theta_i & \cos\theta_i \cos\alpha_i & -\cos\theta_i \sin\alpha_i & a_i \sin\theta_i \\
0 & \sin\alpha_i & \cos\alpha_i & d_i \\
0 & 0 & 0 & 1
\end{bmatrix} $$
For our bionic robot leg, the overall transformation from the base to the end-effector (foot) is computed by multiplying individual matrices. The position of the foot in the base coordinate system is derived as:
$$ P = \begin{bmatrix}
x \\ y \\ z
\end{bmatrix} = \begin{bmatrix}
a_1 \cos\theta_1 + a_2 \cos(\theta_1 + \theta_2) \\
a_1 \sin\theta_1 + a_2 \sin(\theta_1 + \theta_2) \\
0
\end{bmatrix} $$
This equation represents the forward kinematics, allowing us to determine the foot position based on joint angles. For velocity analysis, we compute the Jacobian matrix \( J \), which relates joint velocities to end-effector velocity. The velocity vector \( \dot{P} \) is:
$$ \dot{P} = J \dot{\theta} $$
where \( \dot{\theta} = [\dot{\theta}_1, \dot{\theta}_2]^T \). The Jacobian for our bionic robot leg is:
$$ J = \begin{bmatrix}
-a_1 \sin\theta_1 – a_2 \sin(\theta_1 + \theta_2) & -a_2 \sin(\theta_1 + \theta_2) \\
a_1 \cos\theta_1 + a_2 \cos(\theta_1 + \theta_2) & a_2 \cos(\theta_1 + \theta_2)
\end{bmatrix} $$
Thus, the foot velocity components are:
$$ \dot{x} = -[a_1 \sin\theta_1 + a_2 \sin(\theta_1 + \theta_2)] \dot{\theta}_1 – a_2 \sin(\theta_1 + \theta_2) \dot{\theta}_2 $$
$$ \dot{y} = [a_1 \cos\theta_1 + a_2 \cos(\theta_1 + \theta_2)] \dot{\theta}_1 + a_2 \cos(\theta_1 + \theta_2) \dot{\theta}_2 $$
These kinematic equations are vital for motion planning and control of the bionic robot, ensuring smooth and stable gait patterns. Additionally, we derived the relationship between the hydraulic cylinder’s extension and the joint angles to integrate actuation into the model. Using geometric analysis, the cylinder length \( \Delta L \) is related to the joint angle \( \theta_1 \) by:
$$ \Delta L = \sqrt{L_1^2 + L_2^2 – 2L_1 L_2 \cos(\theta_1 + \phi)} $$
where \( L_1 \) and \( L_2 \) are link lengths, and \( \phi \) is a constant angle. Similarly, for the thigh and shank angles, we apply the law of cosines to find:
$$ \theta_2 = \cos^{-1}\left( \frac{L_3^2 + L_4^2 – \Delta L^2}{2L_3 L_4} \right) $$
These inverse kinematic relations enable precise control of the bionic robot leg by mapping hydraulic cylinder movements to desired foot trajectories.
To validate the design and kinematic model of our bionic robot leg, we conducted dynamic simulations using ADAMS software. The leg model was built in SolidWorks and imported into ADAMS, where constraints and drives were applied. The hydraulic cylinder was modeled with a translational motion drive, and forces were added to simulate a load of 250 N on the leg, representing typical operating conditions for a bionic robot in real-world scenarios. The simulation involved multiple gait cycles to assess consistency and performance. Key parameters, such as link lengths, were based on biological proportions from canine anatomy, as shown in the following table:
| Component | Length (mm) |
|---|---|
| Thigh | 450 |
| Shank | 380 |
| Frame | 300 |
| Connecting Rod 1 | 315 |
| Connecting Rod 2 | 330 |
The simulation results demonstrated that the bionic robot leg follows a biologically inspired motion sequence: starting from a fully extended position, lifting to a maximum height, and then extending downward. Over three cycles, the foot trajectory showed a maximum lift of 0.150 m from the lowest point, with velocity profiles indicating smooth transitions. For instance, at 0.66 s, the foot reached a reverse velocity of -91.87 mm/s, and at 3.04 s, it achieved a forward velocity of 159.06 mm/s. The torque at the thigh joint peaked at 4.46 N·m when the foot was at its highest position, minimizing when fully extended. This correlation between torque and position optimizes energy use in the bionic robot, highlighting the efficiency of the single hydraulic drive system.
Furthermore, we analyzed the foot displacement and velocity over time to verify gait stability. The curves revealed periodic patterns with minimal oscillations, confirming that the bionic robot leg maintains consistent performance across cycles. The following equation summarizes the foot position as a function of time, derived from simulation data:
$$ y(t) = A \sin(\omega t + \phi) + y_0 $$
where \( A \) is the amplitude, \( \omega \) is the angular frequency, and \( y_0 \) is the offset. This harmonic motion aligns with natural walking dynamics, reinforcing the bionic aspect of our design. The integration of kinematics and dynamics in simulation provides a comprehensive validation tool for future enhancements of bionic robot systems.
In conclusion, our work on the bionic robot leg structure demonstrates a significant advancement in quadruped robotics. By leveraging a single hydraulic cylinder and a linkage-based design, we achieved a simple, efficient, and controllable mechanism that mimics biological locomotion. The kinematic analysis using D-H parameters and Jacobian matrices provides a solid foundation for motion planning, while ADAMS simulations confirm the leg’s ability to perform stable gaits under load. This bionic robot design not only addresses common issues like high energy consumption and complex control but also opens avenues for applications in challenging environments. Future work will focus on optimizing material selection for lightweight construction and integrating sensory feedback for adaptive control, further enhancing the capabilities of bionic robots in real-world scenarios.
The potential of bionic robots extends beyond locomotion to include collaborative tasks in healthcare and disaster response. As we continue to refine this technology, the principles outlined here will serve as a benchmark for developing more agile and resilient robotic systems. The success of this bionic robot leg underscores the importance of biomimicry in engineering, paving the way for next-generation robots that seamlessly interact with their surroundings.