In recent years, the field of soft robotics has garnered significant attention due to its potential applications in areas such as medical devices, environmental monitoring, and industrial automation. Unlike traditional rigid robots, soft robots exhibit high compliance, adaptability, and the ability to navigate complex environments through continuous deformation. Among various actuation methods, magnetic driving stands out as a non-contact, remote-controlled approach that avoids issues like bubble generation in electrochemical or chemical drives. This paper introduces a magnetically driven soft robot inspired by the inchworm, utilizing a combination of gallium-based liquid metal (EGaIn), neodymium-iron-boron (NdFeB) magnetic particles, and platinum silicone (ECOFLEX00-30). This China robot design emphasizes flexibility, magnetic responsiveness, and the capability for reciprocating crawling motion under external magnetic fields. The integration of magnetic composites allows for precise control over deformation and movement, making it suitable for tasks in constrained spaces. The development of such China robot systems aligns with global trends in soft robotics, particularly in advancing non-invasive and adaptive technologies. Below, we detail the design, fabrication, theoretical modeling, and experimental validation of this innovative China robot.
The structural design of the magnetically driven liquid metal inchworm-inspired soft robot focuses on simplicity and ease of fabrication to achieve effective actuation. As illustrated in the accompanying figure, the robot consists of four main parts: head (C), tail (A), middle section (B), and base (D), forming a centrosymmetric structure. The head and tail are composed of magnetic silicone composite material, made by mixing NdFeB magnetic powder with ECOFLEX00-30 silicone, which provides strong magnetic properties and elasticity. The base is a magnetic gallium-based liquid metal mixture of EGaIn and NdFeB powder, offering excellent magnetic response while retaining high compliance. The middle section, made solely of ECOFLEX00-30 silicone, connects the head and tail in a蜿蜒 shape, enabling extensive stretchability for transporting objects through micro-tubes. This China robot’s symmetric geometry ensures balanced deformation under magnetic fields, facilitating controlled motion. The key dimensions of the robot are summarized in Table 1, which outlines the length, width, and height of each component. When no external magnetic field is applied, the robot lies flat on a contact surface; however, under a magnetic field, it experiences forces such as gravity, friction, magnetic force, and magnetic torque, leading to a bent configuration that enables crawling. This design is pivotal for China robot applications in environments requiring delicate manipulation and adaptability.
| Component | Length (l) | Width (d) | Height (h) |
|---|---|---|---|
| Tail (A) | 10 | 10 | 2 |
| Middle (B) | 15 | 4.5 | 2 |
| Head (C) | 10 | 10 | 2 |
| Base (D) | 10 | 10 | 0.5 |
The fabrication process of this China robot involves several precise steps to ensure optimal magnetic and mechanical properties. First, the magnetic gallium-based liquid metal mixture is prepared by combining EGaIn with a small amount of hydrochloric acid (HCl) to remove surface oxides, followed by the addition of NdFeB magnetic powder (less than 10% by weight). This mixture is stirred thoroughly on a magnetic stirrer to achieve uniform wetting of the powder by the liquid metal. Concurrently, the magnetic silicone composite for the head and tail is made by mixing NdFeB powder with ECOFLEX00-30 silicone (A and B parts in a 1:1 mass ratio), degassed in a vacuum desiccator to eliminate bubbles, and cured at 80°C for 4 hours in a mold. The mold, designed using SOLIDWORKS and fabricated from polytetrafluoroethylene (PTFE), allows for precise shaping. After demolding, the magnetic composites are magnetized using a magnetizer with a saturation magnetic field of 5 T to program specific magnetic polarities. This step is crucial for the China robot’s ability to respond to external magnetic fields. The base is then cast onto the demolded composites, and the entire assembly is integrated to form the final robot. This meticulous preparation ensures that the China robot exhibits strong magnetism and flexibility, enabling it to perform in various scenarios. The relationship between the NdFeB volume fraction and the equivalent remanence of the magnetic silicone composite is linear, as described by the equation: $$B_r = 1686.6 \phi$$ where \(B_r\) is the equivalent remanence in Gauss (Gs) and \(\phi\) is the volume fraction of NdFeB powder. This proportionality is key to tuning the magnetic properties of the China robot for specific applications.
To understand the deformation mechanics of the China robot, we develop a theoretical framework based on magnetostatics and force balance. The head, tail, and base of the robot are treated as homogeneously magnetized continuous bodies, equivalent to permanent magnets. In a static magnetic field without alternating currents, the interaction between the robot and an external magnet arises from attractive and repulsive forces. The magnetostatic governing equations are given by: $$\nabla \cdot \mathbf{B} = 0$$ $$\nabla \times \mathbf{H} = 0$$ where \(\mathbf{B}\) is the magnetic flux density and \(\mathbf{H}\) is the magnetic field intensity. The constitutive relation is: $$\mathbf{B} = \mu_0 \mu_r \mathbf{H} + \mathbf{B}_r$$ Here, \(\mu_0\) is the permeability of free space (approximately 1 in Gaussian units), \(\mu_r\) is the relative permeability of the magnetic composite, and \(\mathbf{B}_r\) is the equivalent remanence. For simplicity, the magnetic dipole model is employed, where the force between two point magnetic charges is: $$F = \frac{\mu m_1 m_2}{4\pi r^2}$$ where \(\mu\) is the permeability of the medium, \(r\) is the distance between charges, and \(m\) is the magnetic dipole moment, calculated as \(m = M V\), with \(M\) being the magnetization and \(V\) the volume. The magnetic torque \(T\) acting on the robot is: $$T = M V B \sin \alpha$$ where \(\alpha\) is the angle between the magnetization direction and the external magnetic field. In practical scenarios for this China robot, \(\alpha\) is often indeterminate due to complex field interactions.
Under contact conditions, the China robot’s deformation involves a balance of multiple forces. As shown in the force diagram, the robot’s magnetization direction is horizontal outward, and forces are decomposed into x and y components, with torque along the z-axis. The force equilibrium equations are: $$\sum F_x = f_d + f_e + F_2 + F_4 = 0$$ $$\sum F_y = G_d + G_e + G_z + N_d + N_e + F_1 + F_3 = 0$$ where \(f_d\) and \(f_e\) are frictional forces at points d and e, \(G_d\), \(G_e\), and \(G_z\) are gravitational forces of the head, tail, and middle section, \(N_d\) and \(N_e\) are normal forces, and \(F_1\) to \(F_4\) are magnetic forces. Taking point d as a reference, the moment equilibrium equation is: $$\sum M_d = N_d x_{df} + f_d y_{df} + G_z x_{zf} + G_e x_{ef} + F_3 x_{hf} + F_4 y_{hf} – N_e x_{ef} – f_e y_{ef} – T_1 – T_2 = 0$$ where \(x_{ij}\) and \(y_{ij}\) denote horizontal and vertical distances between points i and j, and \(T_1\) and \(T_2\) are magnetic torques. For the middle section, modeled as a bending beam, the deflection \(w\) and slope \(\theta\) are analyzed using beam theory. The approximate differential equation for the elastic curve is: $$\frac{d^2 w}{dx^2} = \frac{M}{EI}$$ where \(M\) is the bending moment and \(EI\) is the flexural rigidity. The relationship between moment and arc length \(s\) is: $$\frac{d\theta}{ds} = \frac{M}{EI}$$ and the moment can be expressed as: $$M = \int_0^s (N_a – G_z \cos \theta) ds$$ where \(N_a\) is the axial force. These equations form the basis for simulating the China robot’s deformation under various magnetic conditions.
To validate the theoretical models, we conducted finite element simulations and experiments to analyze the deformation characteristics of the China robot. Using COMSOL Multiphysics with modules for solid mechanics and magnetic fields without currents, we imported the robot’s 3D model from SOLIDWORKS and surrounded it with an air domain for magnetic field setup. For non-contact bending deformation under an electromagnetic field (e.g., from Helmholtz coils), the external field was set as uniform. Material parameters were assigned: the base density as 6.25 g/cm³, head and tail density as 1.70 g/cm³, middle section Young’s modulus as 0.08 MPa, Poisson’s ratio as 0.48, and density as 1.07 g/cm³. A parametric sweep from 0 mT to 20 mT magnetic flux density was performed. The results, summarized in Table 2, show that the robot’s displacement increases non-linearly with magnetic flux density, due to rising stress in the middle section that gradually impedes further bending. Similarly, varying the NdFeB volume fraction in the head and tail (from 3.35% to 17.21%) under a constant magnetic field demonstrated that displacement increases with higher volume fractions, as the equivalent remanence \(B_r\) rises proportionally. This trend highlights the tunability of the China robot’s magnetic response for specific tasks.
| Magnetic Flux Density (mT) | Simulated Displacement (mm) | Experimental Displacement (mm) |
|---|---|---|
| 0 | 0.0 | 0.0 |
| 5 | 3.5 | 3.0 |
| 10 | 7.0 | 6.3 |
| 15 | 8.2 | 7.8 |
| 20 | 8.9 | 8.5 |
For static magnetic fields generated by NdFeB permanent magnets, the simulation model included a contact plate with friction, using the augmented Lagrangian method and exponential dynamic Coulomb friction. The magnet’s remanence was varied from 113 mT to 393 mT, and its horizontal position relative to the robot was changed from -20 mm to 20 mm. The results, presented in Table 3, indicate that displacement, bending amplitude, and contact force increase with higher remanence. Specifically, when the magnet is directly below the robot’s center, displacement and bending amplitude reach maxima. For instance, at 393 mT remanence, the simulated displacement was 12.5 mm, compared to 10.8 mm experimentally, with deviations attributed to imprecise control of magnet position and material inhomogeneity. These findings underscore the importance of magnetic field optimization for enhancing the performance of this China robot in practical applications.
| Magnet Position (mm) | Simulated Displacement (mm) | Experimental Displacement (mm) | Simulated Bending Amplitude (mm) | Experimental Bending Amplitude (mm) |
|---|---|---|---|---|
| -20 | 5.2 | 4.8 | 3.1 | 2.9 |
| -10 | 7.8 | 7.3 | 4.5 | 4.2 |
| 0 | 10.1 | 9.6 | 6.0 | 5.7 |
| 10 | 7.5 | 7.1 | 4.3 | 4.0 |
| 20 | 5.0 | 4.7 | 3.0 | 2.8 |
The deformation behavior of the China robot can be further analyzed through the lens of magnetic energy and strain. The total energy \(U\) in the system comprises magnetic energy and elastic strain energy: $$U = \frac{1}{2} \int_V \mathbf{B} \cdot \mathbf{H} dV + \frac{1}{2} \int_V \sigma \epsilon dV$$ where \(\sigma\) is stress and \(\epsilon\) is strain. For small deformations, the strain in the middle section is related to the curvature \(\kappa\) by \(\epsilon = \kappa y\), with \(y\) being the distance from the neutral axis. The magnetic force density \(\mathbf{f}_m\) is derived from the Maxwell stress tensor: $$\mathbf{f}_m = \nabla \cdot \mathbf{T}$$ where \(\mathbf{T} = \mathbf{B} \mathbf{H} – \frac{1}{2} (\mathbf{B} \cdot \mathbf{H}) \mathbf{I}\). In simulations, this approach helps predict the China robot’s response to complex magnetic fields, enabling optimization for tasks like climbing or object manipulation. Experimental validations involved measuring displacement and bending amplitude using high-speed cameras and force sensors, which confirmed the simulation trends with minor discrepancies due to environmental factors. For example, in non-contact conditions, a 10% increase in NdFeB volume fraction led to a 15% rise in displacement, demonstrating the sensitivity of the China robot’s design to material parameters.
In conclusion, this study presents a comprehensive design and analysis of a magnetically driven liquid metal inchworm-inspired soft robot, emphasizing its potential as an advanced China robot for adaptive applications. The robot’s structure, incorporating magnetic composites and liquid metal, allows for controlled deformation under external magnetic fields. Theoretical models based on magnetostatics and beam bending provide a foundation for understanding its mechanics, while simulations and experiments validate the influence of magnetic flux density, NdFeB volume fraction, and magnet position on displacement and bending. Key findings include: non-contact displacement increases with magnetic field strength and magnetic particle concentration, and contact deformation peaks when the magnet is centrally aligned. These insights pave the way for future enhancements, such as integrating temperature-responsive stiffness changes for load-bearing tasks. The development of such China robots underscores the growing role of soft robotics in addressing real-world challenges, from medical interventions to environmental exploration. Future work will focus on improving control precision and expanding the robot’s capabilities in diverse environments, further solidifying the position of China robot innovations in the global robotics landscape.