Remotely actuated programmable self-folding origami strings using magnetic induction heating

Transforming planar structures into volumetric objects typically requires manual folding processes, akin to origami. However, manual intervention at sub-centimeter scales is impractical. Instead, folding is achieved using volume-changing smart materials that respond to physical or chemical stimuli, be it with direct contact such as hydration, pH, or remotely e.g., light or magnetism. The complexity of small-scale structures often restricts the variety of smart materials used and the number of folding sequences. In this study, we propose a method to sequentially self-fold millimeter scale origami using magnetic induction heating at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>150</mml:mn></mml:math> kHz and 3.2 mT. Additionally, we introduce a method for designing self-folding overhand knots and predicting the folding sequence using the magneto-thermal model we developed. This methodology is demonstrated to sequentially self-fold by optimizing the surface, placement, and geometry of metal workpieces, and is validated through the self-folding of various structures, including a 380 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>m</mml:mi> <mml:mi>m</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:math> croissant, a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>321</mml:mn></mml:math> mm² box, a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>447</mml:mn></mml:math> mm² bio-mimetic Mimosa pudica leaf, and an overhand knot covering <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>524</mml:mn></mml:math> mm². Our work shows significant potential for miniature self-folding origami robots owing to the novel sequential folding approach and the ability to achieve remote and tetherless self-folding within constrained environments.