Mechanical design and analytic solution for unfolding deformation of locomotive ferromagnetic robots
Graphical abstract
Schematic illustrations of (a) assembling, magnetizing and (b) locomotion mechanism of the free-standing 3D ferromagnetic robot.
Introduction
Untethered microrobots can be actuated by light [[1], [2]–3], chemical [[4], [5]–6], humidity [7,8], temperature [[9], [10]–11], magnetic field [[12], [13]–14] and other stimuli [[15], [16]–17], finding exciting biomedical applications such as biosensors, drug delivery machines and minimally invasive surgical tools [18]. Of all these wireless actuation methods, magnetic actuation holds greater potential to realize fast and precise manipulation, and safe penetration into most materials including biological tissues, enabling minimally invasive operations inside the body [19,20].
Recently, magnetically actuated soft-bodied robots are fabricated by embedding hard magnetic fillers into soft polymer matrices [18,[21], [22]–23], and magnetic programming of the soft composites can be achieved by template-assisted, lithographic or 3D printing approaches [24]. Compared with traditional rigid robots, the magnetic soft robots exhibit great merit of biocompatible stiffness, high mobility and fast transformations, thereby providing robots with multimodal locomotion, complex shape changes and more functions [21,22]. However, soft and compliant mechanical properties of the soft-bodied robots stem from high volume fraction of soft polymer matrix (i.e., low volume fraction of hard magnetic fillers), which obviously lead to magnetically weak composites that are unfavorable for actuation [25]. When the volume fraction of hard fillers increases, the aforementioned merit of soft composites would weaken, the robots would have limited mobility and require larger magnitudes of applied magnetic field. Moreover, the robots would be more vulnerable to material failure since the yield/fracture strain decreases with higher volume fraction of hard fillers. In this paper, we propose an innovative design of magnetic robots through theoretical modeling and finite element analysis (FEA). The robot takes the form of an arch-shaped ferromagnetic film assembled by the mechanics-guided 3D assembly technique, which can transform patterned planar precursors into deterministic and sophisticated 3D structures in the most advanced materials [26,27], thereby creating opportunities for high-performance magnetic robots. After the precursor has buckled into 3D shapes, a parylene coating is deposited to encapsulate and conserve the buckled ferromagnetic film. A mechanical torque is induced in the robot under external magnetic field [24], leading to unfolding and folding deformations, which provides the driving force for locomotion. Combining the merits of high-quality ferromagnetic materials and rapid assembly of diverse 3D structures, we demonstrate that precursors in straight sheets yield 3D robots allowing actuation at magnetic fields of ∼110 mT, which are comparable to those of the reported matrix-based soft-bodied robots. Moreover, the precursors in serpentine configurations could yield 3D robots operating at low magnetic fields down to 1 mT, which are reduced by two orders. The low actuation fields suggest that the proposed design method provides a new way to achieve compliant ferromagnetic robots, inspiring more high-performance magnetically actuated robots with various advanced functional materials and 3D structures via the well-established the mechanics-guided 3D assembly technique [28,29].
As the 3D ferromagnetic robots are proposed for the first time in this paper, none of the existing theoretical work has studied the unfolding deformation of buckled structures assembled by mechanics-guided 3D assembly under magnetic fields. Here, the theoretical modeling is inspired by some recent studies, which can be divided to three categories. The first category deals with the predictions of buckled configurations and maximum strains of structures upon compressive buckling [[30], [31], [32], [33]–34]. The second category involves investigation about the twisting deformations of slim ribbons in the serpentine structures [13,[35], [36], [37]–38]. The third category provides analytical analysis and predictions of deformed configurations of matrix-based ferromagnetic straight sheet under an applied magnetic field [21,[39], [40]–41].
This research aims to propose a new way to fabricate high-performance ferromagnetic robots through structural innovation and mechanical design, as an alternative to the existing soft-bodied robots through material innovation. Essential design guidelines are also offered for the proposed method regrading locomotion speed and device reliability. We hope these results could serve as a good benchmark for future research on this robot design.
Section snippets
Arch-shaped robots in the form of straight sheets
Compared with rigid body robot designs, compliant mechanisms provide a pathway for robots with advantages such as compliance, less parts and multimodal locomotion [42]. They could convert local input forces or torques into overall deformation and displacement through elastic deformations instead of interaction of rigid bodies [42]. Compliant mechanisms are widely implemented by use of soft polymer composites, as polymers could be stretched over large strains without plastic deformation [18,21].
Serpentine-shaped robots
In this section, we propose a novel walking robot in 3D serpentine configurations. By comparison with the magnetically actuated robots that use simple buckled straight sheets, the 3D serpentine configurations enable robots with much smaller actuation fields and much better locomotion performance, due to ultralow bending stiffnesses.
A 2D precursor of the serpentine configuration is shown in Fig. 4a, where L0, b, H and λ are the initial length, ribbon width, height and unit cell length,
Rational design and discussion
In this section, the springback of arch-shaped robots in straight ribbons and serpentine ribbons, with deposited parylene coating, would be carefully inspected upon releasing the two bonding sites, such that the desired shapes could be obtained. Also, the maximum strain in the brittle NdFeB layer would be examined to ensure device reliability. Furthermore, the performance of rational designs in both configurations with respect to unfolding deformation are compared to illustrate advantageous
Conclusion
In summary, this work presents an innovative design of arch-shaped ferromagnetic robots formed by mechanics-guided 3D assembly and a systematic study of its unfolding deformation under the applied magnetic field. The ferromagnetic robots in two different geometries are proposed for illustration, one in straight ribbons, the other in serpentine ribbons. Concise and approximate analytic solutions to evident unfolding lengths of both designs are obtained by combining theoretical studies and FEA,
CRediT authorship contribution statement
Zhengang Yan: Methodology, Formal analysis, Investigation, Writing – original draft, Writing – review & editing. Kaifa Wang: Formal analysis, Supervision, Funding acquisition, Writing – review & editing. Baolin Wang: Supervision, Funding acquisition, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This research was supported by the National Natural Science Foundation of China (Project Nos. 11972137, 11972133), Guangdong Basic and Applied Basic Research Foundation (Project No. 2019A1515011348). Z.Y. acknowledges support from the China Scholarship Council to study at Northwestern University during the period from September 2018 to September 2020.
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