Three-Dimensional Kinematic Modelling of the Human Shoulder Complex—Part II: Mathematical Modelling and Solution Via Optimization

[+] Author and Article Information
S. T. Tümer

Mechanical Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia

A. E. Engin

Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio 43210

J Biomech Eng 111(2), 113-121 (May 01, 1989) (9 pages) doi:10.1115/1.3118775 History: Received June 23, 1988; Online June 12, 2009


In this paper, individual joint sinus cones associated with the sternoclavicular, claviscapular, and glenohumeral joints of the three-dimensional kinematic model introduced in Part I for the human shoulder complex are quantitatively determined. First, mathematical description of the humerus orientation with respect to torso is given in terms of eight joint variables. Since the system is a kinematically redundant one, solution for the joint variables satisfying a prescribed humerus orientation is possible only if additional requirements are imposed; and the “minimum joint motion” criterion is introduced for this purpose. Two methods, namely the Lagrange multipliers and flexible tolerance methods, are formulated and tested for the optimization problem. The statistical in-vivo data base for the circumductory motion of the upper arm is employed to determine a set of joint variables via optimization, which are then utilized to establish the sizes and orientations of the elliptical cones for the individual joint sinuses. The results are discussed and compared with those given on the basis of measurements made on cadaveric specimens.

Copyright © 1989 by ASME
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