Joshua Merz



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As robots approach smaller scales, they lose multiple actuation and directed locomotion. The locomotion at the nanoscale requires a non-reciprocal motion to generate a net trust and independent movement at Low Reynolds numbers (the Scallop theorem). Current fabrication techniques generate single-particle nanorobots with limited actuation. Developing nanorobots with multiple-actuation is necessary to advance different technological applications, such as drug delivery and minimally invasive surgery. On the other hand, to produce predictable locomotion at Low Reynolds Numbers, we use Brownian Dynamics simulations to model a simplified nanorobot composed of three permanently magnetized particles. Further, the particles are connected with a spring, which is quantified by the Rauss Bead-Spring model. We consider three-link nanorobot shapes varying in the size of the leftmost particle (and consequently that particle’s magnetic moment) to break the symmetry of their movement and overcome the Scallop theorem. The three-link nanorobot is exposed to a time-varying magnetic field and analyzed under multiple particle-field interaction parameters. We analyze the simulation results by quantifying the probability distribution of the final center-of-mass position of the three-link nanorobot across 10,000 time steps. We compare different conditions with different shapes and particle-field interaction parameters. Simulation results show that symmetric nanorobots show no locomotion. However, as the asymmetry of the nanorobot increases and as the particle-field interaction parameter increases, the nanorobot experiences a significant locomotion. Results show the relevance of assembling asymmetric magnetic particle nanorobots to overcome the Scallop theorem and generate net locomotion in the nanorobots. In the future, we will explore other particle shapes to promote different actuation and locomotion.


Research and Creative Experience for Undergraduates (RCEU)


Chemical and Materials Engineering

College Name

College of Engineering


Isaac Torres-Díaz

Publication Date


Document Type


Nanorobot Locomotion by Breaking the Scallop Theorem



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