2002 年 16 巻 p. 253-266
A multibody dynamics model of the humerus-shoulder complex system, driven by a musculoskeletal system, has been formulated based on an updated Lagrange approach, using the continuum mechanics of muscle with the evolutional constitutive law of Hatze’s model.
Japan’s population is rapidly aging; within the next 10 years, the elderly are expected to reach 25 percent of the total population. Assistive technology for recovery from disease and increasing medical expenses require more rational approaches to the bone-muscle system in limb-trunk motions, such as interactions between the thoracolumbar-spine system and the upper and lower limb system, which had been insufficiently analyzed.
This paper focuses on a theoretical model of a multiple bones-joints system, driven by muscle activations. First we formulated the continuum mechanics of skeletal muscle with the evolutional constitutive law of Hatze (1977). A joint muscle activation generates kinematics and dynamics. For example, activation includes (1) generating angular motion of linked systems, for a multibone and multijoint system; (2) constraint of muscle contraction due to neuro-activation generating a counter force applied to equilibrate the external joint torque; (3) a paired contraction of counter muscles in a joint, giving rise to increased joint stiffness; and others. We therefore formulated the evolutional constitutive law of a muscle model so that it includes independent variables for both motion and constraint forces, the sum of which determine the activation level. The muscle constitutive equations were first formulated using the link coordinate system of each muscle strip. Then they were assembled by coordinate transformations from those for each strip to a common global system.
A multi-body dynamics approach for a multiple bone-joint system driven by muscle activation was then formulated. The link element coordinates were defined for each bone, and positional vectors for the center of gravity of each bone, distance between adjacent joints, and muscle positional vector were formulated and transformed to the global coordinate system. Using the positional vectors, translational and rotational motions of individual elements, we formulated the kinetic energies of the elements and the potential energies stored in individual muscles and joint elements, expressed in incremental forms. The governing equations of motion for each link, and the dynamic equilibrium equation for each joint, based on the updated Lagrange method, were formulated and solved by prescribed constraint and applied load conditions, using the developed computer simulation system.
As an actual application to assistive technology problems, an elderly person’s stand-up motion, aided by humerus-shoulder forces for lifting one’s upper body weight was analyzed. The calculated results for activation dynamics were compared with those, obtained from an EMG measurement experiment. Satisfactory agreement between these was confirmed, verifying that the developed computer system can satisfactorily estimate activation dynamics of muscle, replacing the traditional EMG measurement approach.