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Deformable linear objects (DLOs), such as rods, cables, and ropes, play important roles in daily life. However, manipulation of DLOs is challenging as large geometrically nonlinear deformations may occur during the manipulation process. This problem is made even more difficult as the different deformation modes (e.g., stretching, bending, and twisting) may result in elastic instabilities during manipulation. In this paper, we formulate a physics-guided data-driven method to solve a challenging manipulation task—accurately deploying a DLO (an elastic rod) onto a rigid substrate along various prescribed patterns. Our framework combines machine learning, scaling analysis, and physical simulations to develop a physics-based neural controller for deployment. We explore the complex interplay between the gravitational and elastic energies of the manipulated DLO and obtain a control method for DLO deployment that is robust against friction and material properties. Out of the numerous geometrical and material properties of the rod and substrate, we show that only three non-dimensional parameters are needed to describe the deployment process with physical analysis. Therefore, the essence of the controlling law for the manipulation task can be constructed with a low-dimensional model, drastically increasing the computation speed. The effectiveness of our optimal control scheme is shown through a comprehensive robotic case study comparing against a heuristic control method for deploying rods for a wide variety of patterns. In addition to this, we also showcase the practicality of our control scheme by having a robot accomplish challenging high-level tasks such as mimicking human handwriting, cable placement, and tying knots. 

The fisherman’s knot, renowned for its strength and reliability, finds applications in engineering and medicine. However, a comprehensive understanding of its mechanics remains limited in scientific literature. In this paper, we present a systematic study of the tightening behavior of the fisherman’s knot through a combined approach of tabletop experiments and discrete elastic rods simulations. Our experimental setup involves gradually applying tension to the two ends of the fisherman’s knot until it fractures. We observed a correlation between the knot’s material properties and its behavior during tightening, leading up to fracture. The tightening process of the fisherman’s knot exhibits distinct “sliding” or “stretching” motions, influenced by factors such as friction and elastic stiffness. Furthermore, the failure modes of the knot (material fracture and topological failure) are determined by an interplay between elastic stiffness, friction, and initial conditions. This study sheds light on the underlying mechanics of the fisherman’s knot and provides insight into its behavior during the tightening process, contributing to the broader understanding of the mechanics of knots in practical applications.

 

Abstract When an overhand knot tied in an elastic rod is tightened, it can undergo a sudden change in shape through snap buckling. In this article, we use a combination of discrete differential geometry (DDG)-based simulations and tabletop experiments to explore the onset of buckling as a function of knot topology, rod geometry, and friction. In our setup, two open ends of an overhand knot are slowly pulled apart, which leads to snap buckling in the knot loop. We call this phenomenon “inversion” since the loop appears to move dramatically from one side of the knot to the other. This inversion occurs due to the coupling of elastic energy between the braid (the portion of the knot in self-contact) and the loop (the portion of the knot with two ends connected to the braid). A numerical framework is implemented that combines discrete elastic rods with a constraint-based method for frictional contact to explore inversion in overhand knots. The numerical simulation robustly captures inversion in the knot and is found to be in good agreement with experimental results. In order to gain physical insight into the inversion process, we also develop a simplified model of the knot that does not require simulation of self-contact, which allows us to visualize the bifurcation that results in snap buckling. 

Changing the surface properties (i.e., roughness or friction) can be instrumental for many applications but can be a complex and resource-intensive process. In this paper, we demonstrate a novel process of controlling the friction of a continuous rod by delivering inorganic microparticles. A standardized continuous particle transfer protocol has been developed in our laboratory for depositing particles from a liquid carrier system (LCS) to the cylindrical rod substrate. The particle transfer process can produce controllable and tunable surface properties. Polymeric binder is used to deliver the particles as asperities over the rod substrate and by controlling their size, shape, and distribution, the coefficient of friction of the rod is determined. Tabletop experiments are designed and performed to measure the friction coefficient following the Capstan equation. The entrained particles on the substrate will create size- and shape-based asperities, which will alter the surface morphology toward the desired direction. Both oblique and direct quantitative measurements are performed at different particles and binder concentrations. A systematic variation in the friction coefficient is observed and reported in the result section. It is observed from the capstan experiment that adding only 1% irregular shaped particles in the suspension changes the friction coefficient of the rods by almost 115%. The proposed friction control technique is a simple scale-up, low-cost, low-waste, and low-energy manufacturing method for controlling the surface morphology.

 

Abstract Flagella and cilia are slender structures that serve important functionalities in the microscopic world through their locomotion induced by fluid and structure interaction. With recent developments in microscopy, fabrication, biology, and modeling capability, robots inspired by the locomotion of these organelles in low Reynolds number flow have been manufactured and tested on the micro-and macro-scale, ranging from medical in vivo microbots, microfluidics to macro prototypes. We present a collection of modeling theories, control principles, and fabrication methods for flagellated and ciliary robots. 

Abstract The mechanical response of a knot tied in elastic rods strongly depends on the frictional force due to rod–rod contact. The behavior of a knot can be qualitatively different based on the frictional coefficient of the elastic rod. Systematic variation of friction during rod–rod contact is a crucial component of any experimental design to uncover the underlying ingredients behind the mechanics of knots. In this paper, we demonstrate a novel process of controlling the friction of a continuous rod by adhering non-spherical inorganic micro-particles. Polymeric binder is used to deliver the particles as asperities over the rod substrate and by controlling their size and distribution the coefficient of friction of the rod is determined. In parallel, numerical simulations with the discrete elastic rods algorithm are used to reproduce the experimental observations. Tabletop experiments are performed where overhand knots with a variety of unknotting numbers are pulled tight. The force–extension curve of these experiments shows that the proposed process can successfully tune the friction between rods.