Principles of use of tensile J-curve materials in antagonistic arrangements

Natural ligaments are soft connective tissues that provide high stretchability for dexterous flexibility but switch to high stiffness to protect the musculoskeletal system from excessive deformation. These two functions cannot be independently tuned in conventional engineering materials with linear or hyperelasticity. Biological materials achieve this tailored behavior through a highly nonlinear tensile response characterized by a J-shaped curve, featuring an extended “toe region” of low force up to intermediate strains followed by an inflection, called the “heel region” which marks the onset of nonlinear stiffening. Here, we aim to study the characteristics of J-curves to establish principles for their use in robotic mechanisms. We define and measure the J-curve features responsible for protectiveness and mobility, describe the effective stiffness and the level of nonlinearity as a function of pre-stretch, and elucidate how the J-curve decouples flexibility from damage protection. Experimental measurements reveal the performance advantages of twisted and coiled elastomeric J-curve materials in engineered antagonistic arrangements and highlight their unique design space compared with linear elastic systems. Furthermore, we present a conceptual analysis of exploiting J-curve materials in energy-efficient running as an outlook toward their use in bioinspired robots.