5/16/2023 0 Comments Moving grand piano tie theactionThe model, purposely chosen as obviously too simple to be predictive of the dynamics of the grand pianoĪction, appears either as very good or as very bad, depending on which physical quantities are used as the input and output. We propose here a very simple model, with only 1-degree of freedom, and compare its outcome with force and motion measurements obtained by playing a real piano mechanism. Surprisingly, simple as well as sophisticated models seem to yield very valuable simulations when compared The kinematics and the dynamics of the piano action mechanism have been much studied in the last 50 years and fairly sophisticated models have been proposed in the last decade. Eventually, a sensitivity analysis of the dynamic behaviour to the model's parameters is proposed. The kinematics of the bodies is also correctly predicted. For both piano and forte keystrokes, most of the irregularities in the measured force are reflected in the simulated force. The results of the simulation are presented and compared to experimental measurements. They are overcome by non-smooth numerical methods that have been implemented in the computer program XDE. Velocity discontinuities, occurring during the descent of the key, raise numerical issues which are analysed. Indeed, using a in-depth study of a model with a single degree of freedom, it is shown that the simulation of a complete dynamic model must be driven with a displacement whilst, until now, only force driven simulations have been presented. Our approach differs from existing work in that it is based on a new viewpoint for model validation and simulation. In the last fifteen years, various models of the piano action including several degrees of freedom, friction and intermittent contacts, have been proposed. The sound following the impact of the hammer on the strings is not analysed. The present thesis proposes a simulation method of a complete model of the mechanism, which opens doors to improvements of the haptic rendering of digital keyboards. This controllability is believed to be due to the dynamic behaviour of the piano action. This mechanism provides the pianist with a high-controllability of the time of impact of the hammer with the strings and the hammer's velocity at the impact. The grand piano action aims at propelling the hammer up to the strings.
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