Modeling Muscle Mechanics of Arm and Leg Movement

The first purpose of this study was to develop a constant power model of arm rotations and to provide a new solution for Hill’s force – velocity equation. Elbow and shoulder extensions/flexions with maximum velocity were recorded in the sagittal plane with a special camera system in which one film frame contained a series of subject images and the paths of the marker lights were seen as dashed light lines. Additional experiments were analyzed using the Vicon motion analysis system with 8 cameras, which enabled the use higher frame rates (300 Hz). The theoretically derived model of constant maximum power was fitted to the experimentally measured data. The moments of inertia of the arm sectors, needed for determining accurate values of friction coefficients of elbow and whole arm rotations, were calculated using the immersion technique. The experiments of the present study verified that the theoretically derived equation with constant maximum power was in agreement with the experimentally measured results.

The results of the present study were compared with the mechanics of Hill’s model and a further developed version of Hill’s force–velocity relationship was derived: Hill’s model was transformed into a constant maximum power model consisting of three different components of power. It was concluded that there are three different states of motion: 1) a state of low speed, maximal acceleration without external load, which applies to the hypothesis of constant moment, 2) a state of high speed, maximal power without external load, which applies to the hypothesis of constant power and 3) a state of maximal power with external load, which applies to Hill’s equation. This is a new approach to Hill’s equation.

The second model of the present study was based on the oscillatory movement of vertical jumping as the body center of mass moves first downwards and then upwards during ground contact. This path can be presented as a mathematical model of the leg movement. In the present study the model of leg movement without leg pushing force was constructed first and then the pushing force was added to the model. Equations (representing damped/strengthening and sine-formed oscillatory motion) were derived for the path of the body center of mass in jumping on one leg and on two legs and they fitted the experimental results. The equation of strengthening oscillatory motion also matched the measured paths of motion in counter movement jump (CMJ) starting from zero velocity and the pushing phase in shot put. It was hypothesized that the vertical displacement-time curve may become a strengthening oscillatory motion as exertion of leg force increases. In shot put the displacement of the body center of mass (CoM) was obtained from previously measured shot displacements. Velocities and forces acting at the CoM were calculated and the total ground reaction force was derived.

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City (for University):
University of Jyväskylä