My PhD is entitled "Non-smooth model of the grand piano action". It was part of a collaboration between:

> Laboratoire de mécanique des Solides (LMS), École Polytechnique
> Laboratoire d'Intégration des Systèmes et des Technologies (CEA LIST), CEA

under the supervision of:

> Supervisor: Xavier Boutillon (LMS)
> Co-supervisors: Xavier Merlhiot (CEA LIST), José Lozada (CEA LIST)

 You can download my thesis (in English) and my final presentation (in French, to be opened with Acrobat Reader 9+).

phd piano action anders thorin non-smooth dynamics multibody nonsmooth        

          phd defense soutenance these piano dynamique non-régulière

Motivations for the study of the piano action

My thesis was part of a project with two main objectives:

> improve the touch of digital keyboards + adjustable touch

Keyboard manufacturers improve the quality of their touch by imitating the actual piano action - which is very complex, see below. The result is very arguable for most of them, to such an extent that some include an actual complete mechanism, while the production of sound is totally electronic. The resulting weight, size, cost, sensitivity to relative humidity, etc. are close to that of a piano - just because of the touch!


2-dof: Arguable touch

6-dof: Includes of a real piano action

Also, even if such keyboards offer sounds such as organs or harpsichords, they do not offer the corresponding touch.

The solution which is being studied at the LMS and CEA-LIST consist of a haptic device involving magneto-rheological fluid, whose properties can be changed with a very short response time (smaller than the characteristic time of the human perception). This solution opens doors to three major improvements: realistic feedback, simple technology and opportunity to program other dynamical behaviours.

          Haptic device designed by José Lozada (2007) [LMS, CEA-LIST]


> improve the understanding of the controllability of a mechanical device by a human (haptics)

      The piano action allows pianists to control the velocity of the hammer when it impacts the strings with very high accuracy and repeatability (control of date of impact ~ 1ms, relative error on the angular velocity ~ 2% [Principeaud and Boutillon 2008]). We believe this accuracy is mainly due to the reaction force of the key on the pianist's fingers. Building a haptic device capable of simulating and reproducing the behaviour corresponding to an accurate model of the grand piano action would make hundreds of relevant experiments possible, in order to better understand controllability of material interfaces by humans.

Functioning of the piano action

Animation of the piano action:

Slow motion of a piano keystroke:

Slow motion of a forte keystroke:

First contribution of my PhD

We raised a simple point, but that we think essential: a good model of the piano action should predict a good force in response to a input position of the key. This work led to a publication.

  • Second contribution of my PhD

    This one is more technical. Using numerical methods for non-smooth dynamical systems, implemented in xde, we managed to simulate the reaction force of the key on the finger in response to imposed positions, for piano and forte dynamical levels. The piano is the hardest to simulate, because it is the finest, and the hardest to control for a pianist (vast literature).