Mechanical design and analytic solution for unfolding deformation of locomotive ferromagnetic robots

Highlights

• A compliant and high-performance robot design is developed by utilizing mechanics-guided three-dimensional (3D) assembly technique.

• The robot would unfold and fold periodically under cyclic magnetic fields, driving the robot in a desired direction.

• To illustrate the versatile applicability of this approach, robots in two different representative geometries are presented.

• A scaling law for the straight design and an approximate analytic solution for the serpentine design are provided.

Abstract

Magnetically actuated robots are attracting much interest due to the advantages of fast response, remote manipulation and enabling operations in enclosed spaces. Recent advances in fabricating ferromagnetic polymeric matrices embedded with hard magnetic fillers provide routes to multimodal locomotion for soft-bodied robots. One limitation of these matrix-based robot designs is that it requires low volume fraction of hard magnetic fillers to achieve soft and compliant robot body such that moderate magnetic fields are sufficient for actuation. However, low volume fraction of functional magnetic fillers leads to magnetically weak soft robots that are difficult to actuate. Here, we propose a compliant and high-performance robot design operating at magnetic fields down to 1 mT by utilizing a high-quality ferromagnetic film and mechanics-guided three-dimensional (3D) assembly technique. A parylene coating is deposited to keep the assembled arch shape, allowing releasing and actuating the structure as a freestanding robot. The robot would unfold and fold periodically under cyclic magnetic fields, driving the robot in a desired direction. To illustrate the versatile applicability of this approach, robots in two different representative geometries are presented, one in traditional straight configuration and the other in serpentine configuration. Through theoretical analysis and finite element analysis, fundamental results are offered for the proposed robot design, including concise solutions to the unfolding deformation, the effects of coating thickness on spring back, the maximum strain in the hard ferromagnetic film and a comparison of unfolding deformation of both designs. The results clearly show the effect of geometry/material parameters, external magnetic field and prestrain in assembly process, providing essential design guidelines to compliant and fast-moving magnetic robots via the proposed method.

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.