Double-spiral: a bioinspired pre-programmable compliant joint with multiple degrees of freedom

Abstract

Geometry and material are two key factors that determine the functionality of mechanical elements under a specific boundary condition. Optimum combinations of these factors fulfil desired mechanical behaviour. By exploring biological systems, we find widespread spiral-shaped mechanical elements with various combinations of geometries and material properties functioning under different boundary conditions and load cases. Although these spirals work towards a wide range of goals, some of them are used as nature's solution to compactify highly extensible prolonged structures. Characterizing the principles underlying the functionality of these structures, here we profited from the coiling–uncoiling behaviour and easy adjustability of logarithmic spirals to design a pre-programmable compliant joint. Using the finite-element method, we developed a simple model of the joint and investigated the influence of design variables on its geometry and mechanical behaviour. Our results show that the design variables give us a great possibility to tune the response of the joint and reach a high level of passive control on its behaviour. Using 3D printing and mechanical testing, we replicated the numerical simulations and illustrated the application of the joint in practice. The simplicity, pre-programmability and predictable response of our double-spiral design suggest that it provides an efficient solution for a wide range of engineering applications, such as articulated robotic systems and modular metamaterials.

Double‐Spirals Offer the Development of Preprogrammable Modular Metastructures

“…The force–displacement diagrams illustrate the nonlinear behavior of the metastructure, related to the specific phases of the deformation of double‐spirals under different loading scenarios (i.e., initial clearance, unrolling, and unfolding). [ 42 ] The tension and rotation of the metastructure in two different directions occur with an inversion of anisotropy. In tension, 0.5‐N force is enough to unroll double‐spiral 1 horizontally and reach the high‐stiffness unfolding phase (around 60‐mm displacement).…”

“…The compression of the double‐spirals starts with a low‐stiffness deformation phase, which arises from the free space between their coils, and continues with a gradual increase in the stiffness, which results from the contact between the coils. [ 42 ] The different compressive behaviors of the metastructure in x , y , and z directions are mainly caused by the different free space available between the coils of the double‐spirals and their thicknesses, which can be simply adjusted by changing the values of the design variables.…”

“…Following the method adopted by Jafarpour et al, [ 42 ] we used the equation of logarithmic spirals in the polar coordinate system (Equation ()) to plot spiral curves using the programming software MATLAB (MathWorks).…”

“…Adjustable design, multiple degrees of freedom, high extensibility, and reversible nonlinear deformability are properties of the double‐spirals that make them particularly interesting for the development of deformable structures. [ 42 ] We expect that preprogrammable double‐spiral modules will enable us to control the mechanical properties of a metastructure in different directions in a passive‐automatic way.…”

“…Adjustable design, multiple degrees of freedom, high extensibility, and reversible nonlinear deformability are properties of the double-spirals that make them particularly interesting for the development of deformable structures. [42] We expect that preprogrammable double-spiral modules will enable us to control the mechanical properties of a metastructure in different directions in a passive-automatic way.Using the finite-element method (FEM), we simulate the mechanical behavior of a four-module metastructure under different loading scenarios. We also manufacture two modular metastructures using 3D printing and illustrate their performance in practice.…”