Gymnastics - a new 2D model of the high bar including endpoint movement

Abstract

The 2D modelling of the high bar apparatus in men's gymnastics is re-examined. Parameter estimations are elaborated regarding two concerns, first, to establish measurement demands raised by parameter estimations, and secondly, to find the need for new parameter estimations as different high bars are investigated. This is further used to evaluate the sufficiency of the FIG (Federation Internationale de Gymnastique) requirement for a competition high bar. A model structure was developed and justified, using two different high bar set-ups. Static and kinematic measurements revealed substantially different stiffness, damping and inertia characteristics in the vertical and horizontal directions, caused by the spatial non-fixation of the endpoints of the horizontal bar, as they rest on vertical posts wired to the floor. Horizontally, endpoint movement was found to add another 30% to the movement measured from bar bending, while vertically, endpoint movement was hardly measurable at all. The two directions were therefore modelled differently. Horizontally, two serially connected damped linear springs were fitted to the measurement data, whereas vertically only one such spring was needed, demanding a total of nine stiffness, damping and effective mass parameters for the model. It is shown that only parameter ratios are needed to model the unforced bar oscillations, and that all nine parameters can be found from three parameter measurements, e.g. stiffness, and then curve fitting to high bar self oscillations in the two directions to find the remaining ones. Parameter variations seem significant between bars, and finally, the sufficiency of the FIG vertical stiffness requirement was found questionable.