Martin Hirschkorn  BSc PEng MASc Masters of Applied Science Graduate Motion Research Group Systems Design Engineering Email: Please contact someone else in the group.

Thesis Abstract:

While many industries rely heavily on careful modelling and analysis to test new designs, musical instrument makers typically rely instead on experienced craftspeople. As a result, basic piano technology has remained quite static for decades.

In other industries, there are many tools available to simulate and analyse the various components. This has allowed the industries to quickly and efficiently test new designs.

While some attempts have been made to model the behaviour of the grand piano action (the mechanism that translates a key press into a hammer striking a string), most researchers have reduced the system to a simple model with little relation to a real action. While such models are useful for certain applications, they are not appropriate as design tools for piano makers, since the model parameters have little physical meaning and must be calibrated from the behaviour of a real action.

A new model for a piano action is proposed in this thesis. The model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body. The action model also incorporates a contact model to determine the normal and friction forces at 13 locations between each of the contacting bodies. All parameters in the model are directly measured from the physical properties of individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been built.

To test whether the model can accurately predict the behaviour of a piano action, an experimental apparatus was built. Based around a keyboard from a Boston grand piano, the apparatus uses an electric motor to actuate the key, a load cell to measure applied force, and optical encoders and a high speed video camera to measure the positions of the bodies. The apparatus was found to produce highly repeatable, reliable measurements of the action.

The behaviour of the action model was compared to the measurements from the experimental apparatus for several types of blows from a pianist. It was found that the model could very accurately predict the behaviour of the action for high force blows. When the forces were lower, the behaviour of the action model was still quite reasonable, but some discrepancy from the experimental results could be seen.

Areas of Study:

• Mechanics of Musical Instruments
• Kinematics and Dynamics of Multibody Systems
• Analysis and Design of Mechanisms and Machinery
• Computational Methods for Analysis and Design
• Contact Mechanics

Publications and Presentations:

• M. Hirschkorn, S. Birkett, J. McPhee, Kinematic Model of a Piano Action Mechanism, presented at the 19th Canadian Congress of Applied Mechanics, June 2003, Calgary, Canada

• M. Hirschkorn, Dynamic Model of a Piano Action Mechanism, MASc Thesis, Department of Systems Design Engineering, University of Waterloo, Canada, September 2004

• M. Hirschkorn, J. McPhee, S. Birkett, Dynamic Modelling and Experimental Testing of a Piano Action Mechanism, presented at the ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, September 2005, Long Beach, USA

• M. Hirschkorn, J. McPhee, S. Birkett, Dynamic Modelling and Experimental Testing of a Piano Action Mechanism, Journal of Computational and Nonlinear Dynamics, January 2006, Volume 1, Issue 1, pp. 47-55

Other Cool Stuff:

The Motion Research Group has been using a high-speed digital video camera for various experiments. While the primary application for the camera in this project is to take video and measurements of a piano action, there are many other fascinating things that can be captured, such as paper clips and water droplets.

All videos are encoded in the XviD format. The videos are © 2003 - 2005, but if you want to use them, let us know and we'll happily let you, as long as you give us credit.

The first video relates directly to this project. It shows a single blow struck on a real grand piano action. The video demonstrates how this reasonably complicated mechanism works, but also shows some of the effects that are particularly difficult to model, such as the flexibility of the wooden components and compressibility of the felt.

A single strike of a grand piano action (2.1 MB) Captured at 1000 fps. Played at 20 fps.

This set of videos was made just to test some interesting phenomena that cannot be easily seen with the naked eye or normal photographic techniques.

A paper clip dropped on a desk (1.1 MB) Captured at 1000 fps. Played at 20 fps.
A few water droplets splashing (1.4 MB) Captured at 1000 fps. Played at 15 fps.
One drop colliding with another (1.1 MB) Captured at 1000 fps. Played at 15 fps.
A soap bubble falling and popping (0.4 MB) Captured at 2000 fps. Played at 15 fps.
Two soap bubbles falling and popping (0.5 MB) Captured at 2000 fps. Played at 15 fps.
A balloon popping (0.3 MB) Captured at 2000 fps. Played at 5 fps.

The next series of videos shows several different liquids dropped under the same conditions. Due to the differences in viscosity and surface tension, the effects are quite different.

Water dropped on a horizontal surface (7.1 MB) Captured at 2000 fps. Played at 25 fps.
Soap and water solution dropped on a horizontal surface (2.3 MB) Captured at 2000 fps. Played at 25 fps.
Ethanol dropped on a horizontal surface (4.1 MB) Captured at 2000 fps. Played at 25 fps.
Oil dropped on a horizontal surface (2.2 MB) Captured at 2000 fps. Played at 25 fps.

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