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Equations that clarify the mechanical relationships between various parameter values and the velocity of the distal endpoint of a two-segment kinetic chain modeling the human arm were developed and analyzed. In particular, a single equation was presented that relates the distal endpoint velocity to the system’s angular momentum (as an indicator of muscular torque input), the ratio of the distal segment’s angular velocity to that of the proximal segment (the flail ratio), and the angle between the two segments (the configuration angle). These three system variables were analyzed to examine which values are best for creating a large value for the velocity of the distal endpoint. In addition, a sensitivity analysis was conducted to determine whether the relationships between the system values and the distal endpoint velocity were consistent for varying segment parameters. The relationships found were consistent for the various segment parameters. For any given values of the flail ratio and the configuration angle, the larger the value of the system angular momentum, the larger the value of the distal endpoint velocity. For any given values of the system angular momentum and the configuration angle, the larger the flail ratio, the larger the value of the distal endpoint velocity. For given values of the system angular momentum and the flail ratio, the optimal configuration angle that maximizes the distal endpoint velocity depends on the flail ratio value. While it may be impossible to generate simultaneously the combination of optimal parameter values determined, the knowledge of the relationships of these parameters with each other and with the distal endpoint velocity will aid in the search for an attainable optimal compromise.
Michele LeBlanc is now with the Natural Science Division at Pepperdine University, Malibu, CA 90263-4321; Jesús Dapena is with the Dept. of Kinesiology at Indiana University, Bloomington, IN 47405.