Meeting Abstract
Flexures and ligaments are the two predominant morphologies of articular joints in animals. Flexural joints use a soft elastic flexure that is contained entirely within the articular space, and constrains or permits rotations based on the cross-sectional geometry of the flexure. Ligamentous joints are formed by bands of ligaments at the periphery instead of an internal elastic member. Rotations that stretch the ligaments are constrained, and other rotations are free. Flexural joints help in passive posture maintenance and elastic energy storage, but are found only in small animals like insects. We show that this transition in joint morphology is driven by a severe restriction on the range of rotation and strength of muscle-driven flexural joints. A longer flexure can rotate by larger angles before the adjoining segments come in contact and prevent rotation. Slender flexures are however prone to elastic buckling unless the ratio of the thickness to the length is greater than a material dependent critical value. Therefore, to prevent buckling, longer flexures have to be thicker and the one with maximal range of rotation is as wide as the adjoining segment. The bending stiffness of a flexure is proportional to the cube of its thickness, but muscle cross-sectional area and strength are proportional only to the square of the segment diameter. This allometry limits the feasible range of rotation for biological tissues to less than 1 rad, and the joint can no longer support external forces. Distal adhesive pads are therefore necessary to exert forces or lift loads when using a flexure. This is consistent with the observation that animals with flexures have distal adhesive pads, and are smaller than a few millimeters. The length-scale of a millimeter, at which adhesion becomes ineffective, therefore governs the transition from flexures to ligaments. Funding: HFSP RGY0091.
