The Euclidean hinge constraint in articulated motions

This paper derives what we term the Euclidean hinge constraint for projective reconstruction of objects displaying articulated motion. A Euclidean hinge is defined here to be an articulation axis with the proviso that any plane perpendicular to the articulation axis in link 1 has a coincident plane which is perpendicular to the articulation axis in link 2, and that these planes remain coincident under articulated motion. This constraint permits the independent projective reconstructions of two adjacent articulated links to be placed in a common frame. The constraint may be expressed mathematically by considering what we define as circular parallax. Additionally, the existence of a Euclidean hinge permits the projective frame to be brought nearer to a Euclidean frame for the reconstructed object