Constant Power Model in Arm Rotation—A New Approach to Hill’s Equation

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.

Modeling the Force-Velocity Relationship in Arm Movement

Modeling the force-velocity dependence of a muscle-tendon unit has been one of the most interesting objectives in the field of muscle mechanics. The so-called Hill’s equation [1,2] is widely used to describe the force-velocity relationship of muscle fibers. Hill’s equation was based on the laboratory measurements of muscle fibers and its application to the practical measurements in muscle mechanics has been problematic. Therefore, the purpose of this study was to develop a new explicit calculation method to determine the force-velocity relationship, and test its function in experimental measurements. The model was based on the motion analysis of arm movements. Experiments on forearm rotations and whole arm rotations were performed downwards and upwards at maximum velocity. According to the present theory the movement proceeds as follows: start of motion, movement proceeds at constant maximum rotational moment (Hypothesis 1), movement proceeds at constant maximum power (Hypothesis 2), and stopping of motion. Theoretically derived equation, in which the motion proceeds at constant maximum power, fitted well the experimentally measured results. The constant maximum rotational moment hypothesis did not seem to fit the measured results and therefore a new equation which would better fit the measured results is needed for this hypothesis.