Dynamical Modeling of the Grand Piano Action

The grand piano action is modeled as a set of four rigid bodies using Kane’s method. Computerized symbol manipulation is utilized to streamline the formulation of the equations of motion so that several models can be considered, each of increasing detail. Various methods for checking the dynamical model thus derived are explored. A computer animation driven by simulation of the equations of motion is compared to a high-speed video recording of the piano action moving under a known force at the key. For quantitative evaluation, the velocities and angular velocities of each of the bodies are extracted from the video recording by means of digitization techniques. The aspects of the model of particular interest for emulation by a controlled system, namely, the mechanical impedance at the key and the velocity with which the hammer strikes the string, can be studied in the equations of motion and compared to empirical data.