Supplemental text, tables and figures from How pigeons couple three-dimensional elbow and wrist motion to morph their wings

Birds change the shape and area of their wings to an exceptional degree, surpassing insects, bats and aircraft in their ability to morph their wings for a variety of tasks. This morphing is governed by a musculoskeletal system, which couples elbow and wrist motion. Since the discovery of this effect in 1839, the planar ‘drawing parallels’ mechanism has been used to explain the coupling. Remarkably, this mechanism has never been corroborated from quantitative motion data. Therefore, we measured how the wing skeleton of a pigeon (<i>Columba livia</i>) moves during morphing. Despite earlier planar assumptions, we found that the skeletal motion paths are highly three-dimensional and do not lie in the anatomical plane, ruling out the ‘drawing parallels’ mechanism. Furthermore, μCT scans in seven consecutive poses show how the two wrist bones contribute to morphing, particularly the sliding ulnare. From these data, we infer the joint types for all six bones that form the wing morphing mechanism and corroborate the most parsimonious mechanism based on least-squares error minimization. Remarkably, the algorithm shows that all optimal four-bar mechanisms either lock, unable to track the highly three-dimensional bone motion paths, or require the radius and ulna to cross for accuracy, which is anatomically unrealistic. In contrast, the algorithm finds that a six-bar mechanism recreates the measured motion accurately with a parallel radius and ulna and a sliding ulnare. This revises our mechanistic understanding of how birds morph their wings, and offers quantitative inspiration for engineering morphing wings.