Simulation of Codmanʹs paradox reveals a general law of motion

Codmanʹs paradox refers to a specific pattern of motion at the shoulder joint. It asked how a mysterious axial rotation about the longitudinal axis of the arm occurred during two or three sequential arm rotations that did not involve rotation about the long-axis. The objective of this paper was to find how the mysterious axial rotation occurred in the Codmanʹs paradox. First, Codmanʹs paradox and Codmanʹs rotation were defined in general situations that involved arm rotations about orthogonal axes starting from the neutral attitude as well as rotations about non-orthogonal axes and starting from non-neutral attitudes. Then a general law of motion was proposed to answer the question of the Codmanʹs paradox, which is stated as when the long-axis of the arm performs a closed-loop motion by three sequential rotations defined as Codmanʹs rotation, it produces an equivalent axial rotation angle about the long-axis. The equivalent axial rotation angle equals the angle of swing—the second rotation in the three sequential long-axis rotations. Validity of the proposed law of motion is demonstrated by computer simulation of various Codmanʹs rotations. Clinical relevance of the proposed law of motion is also discussed in the paper.