Stretchable origami robotic arm with omnidirectional bending and twisting

Significance The octopus quickly reconfigures its arms to perform highly integrated tasks, such as swimming, walking, and preying. Inspired by such a soft-bodied cephalopod biosystem, we engineer compliant origami robotic arms to achieve multimodal deformations that integrate stretching, folding, omnidirectional bending, and twisting for functions such as grasping and lifting objects by means of precise magnetic actuation. The remote magnetic field control allows distributed actuation of the multiple degree-of-freedom robotic system for complex motions to achieve the aforementioned shape-changing capabilities and functionalities. Origami robotic arms with untethered control are applicable to biomedical devices and morphing mechanisms in environments with limited access.


Materials and Methods 1. Sample Fabrication
A. Kresling Pattern. The Kresling units used in the main text have the same geometry but two different sizes as shown in Fig. S1A & B. For the demonstrations of 12-unit and 18-unit robotic arms used in Fig.   4 & 5, the unit size is 75% of the units used in Fig. 1-3. Both units are fabricated using Tant origami paper (0.14 mm thick) with an 80 W CO2 laser cutter (Orion Motor Tech, China). The small-scale robotic arms use a different Kresling geometry (Fig. S1C) with a comparable cross-section dimension to an endotracheal intubation tube (Fig. S16). The small-scale units are fabricated using polypropylene film

Magnetic Properties of Magnetic Plates
The magnetic properties of the magnetic materials are measured using a 7400A vibrating sample magnetometer (Lake Shore Cryotronics, Inc., USA). The magnetic moments of 4 mm×4 mm×1 mm samples are measured. Corresponding remanent magnetic moment densities (Mr) are calculated by dividing the magnetic moment by the sample volume. The Mr of the 20 vol% and the 40 vol% magnetic materials are 112.1 kA m -1 and 227.5 kA m -1 , respectively.

Mechanical Characterizations of the Kresling Unit
A. Folding and Deploying Behaviors. The force-displacement curves of the Kresling unit's folding and deploying processes are measured using a universal testing machine (3344, Instron, Inc., USA). The experimental setup is shown in Fig. S2A and B. Cyclic tension-compression tests are performed to characterize the mechanical properties of fabricated Kresling units as shown in Fig. S2C. The mechanical performance is stable after around 300 cycles. The exhibited hysteresis in the folding-deploying plot comes from energy dissipation, due to the contact and friction between Kresling panels during deploying and folding (1). All fabricated Kresling units are cyclically loaded 300 times for a stable behavior before being used in magnetic actuation in this work. The torque-displacement curve at stable state is derived from the force-displacement curve and displacement-rotation angle relation. See (2) for more details about the measurement and derivation. where Mr is the remanent magnetic moment density 227.5 kA m -1 , V is the volume of the magnetic plate 0.88 cm 3 , θBM is the angle between magnetic field and the magnetization direction, θ is the unit's bending angle.

Magnetic Actuation Setup
All demonstrations are performed using a 3D Helmholtz coil system shown in Fig. S4. Three pairs of standard Helmholtz coils are configured orthogonally to each other. The coils can generate 2.96 mT A -1 , 2.97 mT A -1 , and 2.90 mT A -1 uniform magnetic fields within a space of 160 mm by 120 mm by 80 mm (X-axis, Y-axis, and Z-axis), respectively. The magnetic field direction and intensity can be manipulated by controlling the currents in the three pairs of coils.

Coordinate Transformations
For the magnetic actuation of the four-unit robotic arm, both global and local coordinate systems are used to realize bending and deploying. The global XYZ coordinate system is based on the 3D coils and the local xyz coordinate system is fixed at the top unit. To generate the magnetic field with specific direction and intensity in the 3D space, the magnetic field vector B can be decomposed to three axes of the global coordinate system and expressed as: where BX, BY, and BZ are the magnetic fields generated by the pair of coils in the X-axis, Y-axis, and Zaxis, respectively. B can also be decomposed to three axes of the local coordinate system and expressed as: where Bx, By, and Bz are the magnetic fields in the x-axis, y-axis, and z-axis of the local xyz coordinate system, respectively. Considering the magnetic field in 3D space is uniform, the transformation between the global XYZ and local xyz coordinate systems requires only rotation and can thus be expressed as: where Q is the transformation matrix between two coordinate systems. The designed four-unit robotic arm can bend toward any direction (denoted by γ) in the XY-plane with a bending angle of θ (Fig. S11). The transformation matrix Q can be expressed as: To realize stretching after the robotic arm's bending deformation, a magnetic field in the xy-plane of the local coordinate system should be applied to induce deployment. Then BX, BY, and BZ can be calculated from the bending deformation (γ and θ) of the robotic arm and the required deploying magnetic field Bx, By, and Bz. The reference currents are calculated and sent to the controller of the 3D Helmholtz coils.  (Fig. 1), two-unit assemblies (Fig. 2), and four-unit robotic arm (Fig.  3). Unit pictured in (B) is designed for arms including the 12-unit (Fig. 4) and 18-unit (Fig. 5) octopuslike robotic arms. Unit pictured in (C) is designed for the small-scale arms (Fig. S16-S18).               Prototype of a small-scale eight-unit robotic arm with a comparable cross-section dimension to an endotracheal intubation tube. The aim of this design is to provide well-controlled motion at the tip of medical tubes and catheters to guide the difficult navigation and positioning process during intubation (3), upper endoscopy (4), or catheterization (5) and to achieve object manipulation capability. Scale bars: 10 mm.