• biorobotics
• modeling
• nonlinear
• nonlinear structures
• robotics
• structures

Structures capable of exhibiting controlled, nonlinear elastic displacements enable complex morphing patterns and multistable behaviors that could never be achieved with traditional rigid mechanisms. The incomplete controllability and the degree of uncertainty of the spatial configuration are the main shortcomings of structures employing such nonlinear elements. Accurate modeling and simulations, together with experimental validation, are essential preliminaries to the design of functional nonlinear elastic structures. This work takes as a reference a ribbon-based nonlinear structure with a rich set of equilibrium configurations. It is composed of several thin elastic strips bound to a rigid rod. Spatial reconfiguration of the bundle of strips is obtained imposing a rigid rotation and/or a vertical translation at one extremity.First, we provide a numerical characterization of the stability of the relevant equilibrium configurations as a function of the imposed kinematic boundary condition. Second, based on existing mathematical models and a custom-built finite elements model, we prove that the mentioned configurations can be obtained analytically and numerically by modeling the strips as elastic rods. We verify the consistency of the finite element model by acquiring three-dimensional scans of the actual configuration at different points in the reconfiguration paths and compute the surface-to-surface distance error.
Moving to possible applications, we present and characterize a device exploiting the rich variety of equilibrium shapes of our ribbon structures, with possible applications in the tissue sampling from biliary duct strictures. We reproduce some results in the state-of-the-art of deployable tools for such biopsy procedures and numerically compare their performance to the ones of our device. Finally, we present the concept of an SMA-actuated earthworm-like crawling robot, with the possible application as a tool for pipe inspection, based on a linear array of bundles of nonlinear elastic strips.
Through this work, we have seen the main analytical and numerical approaches to the modeling of nonlinear elastic ribbon structures and to the study of their stability. We applied these concepts to a specific structure, trying to remain as general as possible in the tractation, to provide the reader with the instruments to generalize it to other nonlinear elastic, ribbon-based structures.
We have shown how controlled, large deformations at a low energy cost lead to structures that efficiently and smartly solve engineering problems. Sometimes, as in pop-up tents and foldable sunshades, the exploitation of these large deformations and the points of stability in the configurations. The design of multiple minima in the elastic energy allows for multistable behavior of the structure, making it switch among stable configurations in the space of parameters. It addresses the downsides of undetermined kinematics that typically affect such structures.
We have discussed some concepts of nonlinear elastic, ribbon-based structures that may find application in the biomedical field. We have seen how axial buckling leads to a three-fold radial expansion of metal blades inside the bile duct. We have shown how reconfiguration of nonlinear elastic Ni-Ti blades can increase their stiffness of orders of magnitude.
We have finally discussed the advantages in terms of mechanical intelligence that nonlinear deformations bring into the field of soft robotics. The use of flexible appendages relieves the central control units from the burden of controlling the pose at the points of contact with the environment.
From the modeling perspective, the next steps are to generalize the behavior for all the values in the space of the parameters and for different ratios of the geometrical quantities. A further step in this direction is to consider different degrees of freedom at the boundary regions of the strips, possibly generating new peculiar and stable configurations.
As concerns the applications, we have presented some speculative proof-of-concept designs. A significantly more robust experimental validation has to be carried out, first in a lab environment, on-field after. An accurate and reiterated choice of the geometry, materials, and functional design features has to lead either to the optimal design or to its overthrow.