TITLE:
Constant Power Model in Arm Rotation—A New Approach to Hill’s Equation
AUTHORS:
Ahti Rahikainen, Mikko Virmavirta
KEYWORDS:
Arm Movement, Force-Velocity Relationship, Muscle Power, Hill’s Equation
JOURNAL NAME:
World Journal of Mechanics,
Vol.4 No.6,
June
27,
2014
ABSTRACT: The
purpose of this study was to further develop the constant power model of a
previous study and to provide the final solution of Hill’s force-velocity
equation. Forearm and whole arm rotations of three different subjects were
performed downwards (elbow and shoulder extension) and upwards (elbow and
shoulder flexion) with maximum velocity. These arm rotations were recorded with
a special camera system and the theoretically derived model of constant maximum
power was fitted to the experimentally measured data. The moment of inertia of
the arm sectors was calculated using immersion technique for determining
accurate values of friction coefficients of elbow and whole arm rotations. The
experiments of the present study verified the conclusions of a previous study
in which theoretically derived equation with constant maximum power was in
agreement with experimentally measured results. The results of the present
study were compared with the mechanics of Hill’s model and a further
development 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) the state of low speed, maximal acceleration without external load
which applies to the hypothesis of constant moment; 2) the state of high speed,
maximal power without external load which applies to the hypothesis of constant
power and 3) the state of maximal power with external load which applies to
Hill’s equation. This is a new approach to Hill’s equation.