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Applied Bionics and Biomechanics
Volume 4, Issue 1, Pages 19-29

Estimating Shoulder-Complex Mobility

Bertrand Tondu

LESIA, Département de Génie Electrique, Institut National de Sciences Appliquées, Campus Universitaire de Rangueil, 31077 Toulouse, France

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Modeling shoulder motions is essential in understanding upper-limb dynamic behavior. However, the mobility of the shoulder complex—in terms of degrees of freedom (DOFs)—is seldom quantified. In this paper we propose applying the theory of mechanisms and, especially, the powerful Grübler–Kutzbach formula to estimate it. This approach requires a rigorous kinematic analysis. So we suggest basing it on a bone schematisation derived from an extension of Dempster’s historical notation associated to mechanical interpretation of the physiological joints involved. In so doing, the proposed shoulder complex mobility leads to justifying a nine-DOF serial-chain upper-limb mode, which extends the classical seven-DOF arm–foream–wrist model and completing it by adding a clavicle-like link with a two-DOF mobility.