4019866

## 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 (Hill 1938 and 1970) 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. This study continues the development of earlier study (Rahikainen 2004). Methods: Herein the force-velocity relationship has been given as an equation of motion. 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 force, movement proceeds at constant maximum power, stopping of motion. The measurements of arm movements were performed by a special motion camera system which represents the movement as a series of object images. Between these images the paths of the mark light attached to the moving object can be seen as a broken light-line. Results: Theoretically derived equation, in which the motion proceeds at a constant maximum power (hypothesis), fitted well the experimentally measured results. The values of friction coefficient C and power and friction coefficient ratio P/C were obtained within the curve fitting, whole arm rotation downwards C = 2.83 kg m / s2, P/C =360 1/s2, whole arm rotation upwards C = 2.83 kg m / s2, P/C =250 1/s2 and forearm rotation downwards C = 2.38 kg m / s2 and P/C =285 1/s2. The constant maximum force hypothesis did not seem to fit the measured results. Conclusions: A further development of Hills forcevelocity relationship was derived, in which Hills model was transformed into a certain kind of a constant maximum power model. The results of the present study were compared with the mechanics of Hills model. For the constant maximum force hypothesis a different kind of equation was suggested which would better fit the measured results.