Content uploaded by Bart L.R. De Moor
Author content
All content in this area was uploaded by Bart L.R. De Moor on Feb 17, 2016
Content may be subject to copyright.
Modeling a Grand Piano Key Action
... A complete model is given in [Van den Berghe et al., 1995], where the jack and the repetition lever are fixed to the whippen. This model cannot account for changing kinematic constraints. ...
... The key and the hammer are modelled, neglecting friction, but the escapement is not considered. In 1995, Van den Berghe et al. Van den Berghe et al. [1995] considered a 3-DOF model where the whippen-lever-jack assembly is rigid. The escapement is therefore not modelled either. ...
The grand piano action aims at propelling the hammer up to the strings. 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. This controllability is believed to be due to the dynamic behaviour of the piano action. 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. The sound following the impact of the hammer on the strings is not analysed. In the last fifteen years, various models of the piano action including several degrees of freedom, friction and intermittent contacts, have been proposed. Our approach differs from existing work in that it is based on a new viewpoint for model validation and simulation. 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. Velocity discontinuities, occurring during the descent of the key, raise numerical issues which are analysed. They are overcome by non-smooth numerical methods that have been implemented in the computer program XDE. The results of the simulation are presented and compared to experimental measurements. For both piano and forte keystrokes, most of the irregularities in the measured force are reflected in the simulated force. The kinematics of the bodies is also correctly predicted. Eventually, a sensitivity analysis of the dynamic behaviour to the model's parameters is proposed.
... The key and the hammer are modelled, neglecting friction, but the escapement is not considered. In 1995, Van den Berghe et al. [11] considered a 3-DOF model where the whippen-lever-jack assembly is rigid. The escapement is therefore not modelled either. ...
... His second set (paper's Figure 19) presents key and hammer motions in response to a force applied to a 2-DOF model. Van den Berghe [11] presents a 3-DOF model. Again, the resulting key's and hammer's motions in response to a force look very similar to measurements. ...
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. Surprisingly, simple as well as sophisticated models seem to yield very valuable simulations when compared
to measurements. 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. The model, purposely chosen as obviously too simple to be predictive of the dynamics of the grand piano
action, appears either as very good or as very bad, depending on which physical quantities are used as the input and output. We discuss the sensitivity of the simulation results to the initial conditions and to noise and the sensitivity of the experimental/simulation comparisons to the chosen
dynamical model. It is shown that force-driven simulations with position comparisons, as they are proposed in the literature, do not validate the dynamical models of the piano action. It is suggested that these models be validated with position-driven simulations and force comparisons.
... It has been modeled using Kane's method [1]. A reduced order model was also used in the design of a virtual piano action [2] and to improve the performance of digital pianos [3]. The hammer shank has been modeled as a Timoshenko beam, and the pianistic touch was shown to affect the tone [4]. ...
The modern piano has remained largely unchanged since the 1800s. The currently used piano and its tonal system evolved through science and engineering advancements; its current form has subtle and obvious implications to Western music, such as its equal-tempered tonality. The modern piano is a popular instrument, but it has several obvious limitations, including frequent maintenance , heavy/cumbersome weight, a painstaking fabrication process, and an expensive price. It also has a more subtle shortcoming: the modern piano was designed as an equal-tempered instrument. Temperament refers to the tuning scheme used for a musical instrument. On an equal-tempered instrument, the interval between adjacent notes is approximately equal. From an ethnomusical perspective, many pieces played on the modern piano are distorted in this equal temperament (e.g., J.S. Bach's Well-Tempered Clavier). To remedy several of these shortcomings , two directions are explored. First, a 3D printed grand piano action is presented, which the authors believe is the first of its kind, using a carbon fiber reinforced thermoplastic. By lowering the difficulty of the fabrication process and the frequency of maintenance requirements, the cost of the piano could be significantly reduced. Second, a novel self-tuning controller is presented, which the authors believe is the first frequency controller that could be easily implemented on a high-tension piano. This frequency controller uses a Red Pitaya, Hall Effect sensor, and stepper motor to modify the frequency of a monochord, which is demonstrated by an experiment. The tuning assembly design of the monochord could be implemented on a high-tension piano. The presented technology could be utilized to advance the modern piano, increasing its versatility and decreasing its cost.
... Common key stroke recognition works with two measurement points and the delay between them with every stroke. Van den Berghe describes such a system in [17] and mentions the unsatisfying possibilities to create differentiated key strokes on electric pianos. Also our MIDI grand piano works with simple key sensors for attack recognition. ...
Finger force, acceleration and position are fundamental in playing music instruments. Measuring these parameters is a technical challenge and precise position and acceleration measurement of single fingers is particularly demanding. We present a sensor setup for multi modal measurements of force, position and acceleration in piano playing. We capture outputs from the upper extremity contributing to the total force output seen at the fingers. To precisely characterize fingers' positions and acceleration we use wearable sensors. A 6-axes (3-force and 3-torque axes) force sensor precisely captures contributions from hand, wrist and arm. A finger's acceleration sensor and a MIDI grand piano complete the measuring setup. The acceleration and position sensor is fixed to the dorsal aspect of the last finger phalanx. The 6-axes sensor is adjustable to fit individual hand positions and constitutes a basis setup that can be easily expanded to account for diverse measurement needs. An existing software tool was adapted to visualize the sensor data and to synchronize it to the MIDI out. With this basis setup we seek to estimate the isolated force output of finger effectors and to show coherences of finger position, force and attack. To proof the setup, a few pilot measurements were carried out.
... However, as with previous models, the parameters could not be derived successfully through physical measurement and these had to be adjusted arbitrarily to achieve a realistic response. Van den Berghe et al. [8] applied Newton-Euler equations in constructing a complex bond graph model of grand piano action dynamics with component bodies represented by macros interacting through dampers and springs. ...
The theoretical framework for constructing a fully mechanistic multibody dynamic model of a vertical piano action is described, and its general validity is established. Equations of motion are derived symbolically using a graph-theoretic formulation. Model fidelity is increased by introducing several novel features: (i) a new contact model for representing the compression of the felt-lined interfaces between interacting parts, capable of capturing the intermittent loading and unloading of these contacts occurring through the key stroke, as well as providing smooth transitions between these states; (ii) models for two important components that are unique to the vertical action, the bridle strap and the butt spring; (iii) a sophisticated key pivot model that captures both the rotational motion and the vertical translation of the key as it can lift off the balance rail under some conditions; (iv) flexible beam models for backcheck wire and hammer shank so as to predict observed vibrations in the response accurately; and (v) coupling of the mechanism model to a flexible stiff string model for realistic hammer impact. For simulation, parameters were obtained by experimental testing and measurement of a physical prototype vertical action. Techniques are described for the virtual regulation of the model to ensure that initial conditions and pseudostatic response accurately represent the precise configuration and desired relationships between the parts during the key stroke. Two input force profiles were used for simulations, a forte pressed (hard) and piano pressed touch (soft), typical of those measured at the key surface when activated by a pianist. Simulated response to these quite different inputs is described, and compared to experimental observations obtained from a physical prototype.
... Van den Berghe et al [7] created a model in 1995 with parameters based on physical properties of the action. In a later attempt to improve the computational efficiency of the model, a simplified model was created, which was then 'trained' to match experimental results. ...
A new model for a grand piano action is proposed in this paper. The multibody dynamic model treats each of the five main action components (key, whippen, jack, repetition lever, and hammer) as a rigid body, and 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 experiments on individual action components, allowing the model to be used as a prototyping tool for actions that have not yet been designed or built. The behaviour of the model was compared to the behaviour of an experimental grand piano action and found to be very accurate for high force blows, and reasonably accurate for low force blows.
... Van den Berghe, De Moor, and Minten [1] applied Newton-Euler equations in dynamic modeling of a grand piano action in which each body of the mechanism was modeled by a macro. They constructed their system by placing dampers and springs between each body and utilized bond graphs to simulate it. ...
The dynamic behavior of a vertical piano action mechanism is studied using a simulation model and compared qualitatively to observations obtained by high-speed imaging of a real action. The simulated response of all components is obtained for two different prescribed input force profiles applied at the key front. These inputs represent in simplified form the general shape of a typical force input by a pianist measured at the key surface for a strong (forte) strike, or two key strikes in rapid succession. The graph-theoretic multibody model constructed represents the components and their interactions. Explicit contact edges provide forces generated between two bodies as a function of their kinematic states, using a special contact model to represent the compression of felt lined interfaces that can separate during the key stroke. Masses and geometrical parameters of the action were measured by importing scanned images from a real action into CAD software. The highly nonlinear system of five ordinary differential equations of motion was derived symbolically and solved by a numerical stiff solver in Maple. The effects of two components not present in the horizontal grand piano action, the bridle strap and hammer butt spring, were examined using simulations. The butt spring is seen to serve an important function in assisting the return of the hammer to its rest position on key release. The model will be useful in future studies to compare vertical actions to horizontal grand piano actions, as these are known to exhibit quite different playing characteristics.
The behavior of the highly dynamic mechanical transmission between the key and the strings of pianos remains insufficiently understood. Called action, this mechanism is essential for the instrument playability and touch. Upright and grand piano actions, although based on similar principles, present quite different behaviors. This work outlines two models, one for each action, that have been carried out using a similar multibody approach with equivalent modeling hypotheses. The models take all the moving bodies into account as well as the intermittent contacts geometry and specific force laws. In addition, experimental validation with high-speed camera have been successfully achieved. Simulations of the models allow, among others, to estimate the maximal playing frequency, to discover the bridle strap and butt spring usefulness in the upright piano, to illustrate the fast repetition capability at a halfway keystroke in the grand piano action and to virtually adjust its settings. These results help in understanding the actions functioning and capabilities, and should contribute to a useful tool for piano makers, showing the interest of the multibody modeling approach for demystifying piano actions behavior and performances.
Piano performers perceive differences when playing digital and acoustic pianos, but little is known about the elements of the differences. It is essential to clarify them in order to assess the consequences of using digital pianos as acoustic piano replacements in both performance and education situations.
Models with impact or dry friction, yielding discontinuous velocities or accelerations, have motivated research for appropriate numerical methods in the community of non-smooth dynamics. In this work, we apply such methods on the grand piano action. This multibody system has two properties of interest in terms of modelling and simulation: it is extremely sensitive to small misadjustments, and its functioning strongly relies on dry friction and stick–slip transitions—known to be crucial for the touch of the pianist. Using numerical methods of non-smooth contact dynamics, the non-smooth character of dry friction was conserved, in contrast to classical approaches based on regularization which additionally impose the somewhat arbitrary choice of a regularizing parameter. The use of such numerical method resulted in computations about a few hundred times faster than those reported in recent literature. For the first time, the presented predictions of the piano action’s simulations are forces (in particular, the reaction force of the key on the pianist’s finger), instead of displacements which filter out most of the dynamical subtleties of the mechanism. The comparisons between measured and simulated forces in response to a given motion are successful, which constitutes an excellent validation of the model, from the dynamical and the haptic points of view. Altogether, numerical methods for non-smooth contact dynamics applied to a non-smooth model of the piano action proved to be both accurate and efficient, opening doors to industrial and haptic applications of sensitive multibody systems for which dry friction is essential.
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. 1. INTRODUCTION Pianos are judged not only on the basis of their tone, but also feel or 'touch'. The 'dynamics' of the multi-body piano action determine the 'touch' or force history which one feels at the keyboard in response to a given gesture input. Behind these 'dynamics' lie the mechanical properties of the piano action, which are governed by the principles of newtonian mechanics. With tools from the field of applied mechanics, we can build dynamical models whose behaviors approximate those of the piano action. Use of good engineering approximations can be expected to lead to models which are not overly complex, yet descriptive enough to capture the salient properties. Once such a dynamical model has been devised and proven, a few interesting applications are possible. First, the model allows the testing of piano action (or similar keyboard) designs without having to build prototypes. Secondly, piano simulators can be created. The possibility of synthesis by electronic instruments of not just the sound but also the touch-response of a piano is now within reach. Touch response can be emulated by a keyboard which in fact lacks a piano action but has instead actuators or programmable passive devices and an accompanying control system. A few designs have already been prototyped (Cadoz 1990, Baker 1988).
This article describes an experimental study of the timing in the grand piano action. The function of the action is described by timetables for the motions of the moving parts. Important timing properties included are the relation between key bottom contact and hammer–string contact, the interval of free hammer motion before the impact on the string, and the hammer–string contact duration. The influence of the regulation and dynamic level on these timing properties is analyzed. The results of the measurements are discussed, with a focus on the implications for piano playing, regulation, and design.
Active Touch Keyboard United States Patent No. 4,899,631. Cadoz, C. et al. 1990A Modular Feedback Keyboard Design
- R Baker
Baker, R. 1988. Active Touch Keyboard. United States Patent No. 4,899,631. Cadoz, C. et al. 1990. "A Modular Feedback Keyboard Design." Computer Music Journal 14(2):47-51.
The Fuga Series of Intelligent Imagers Available from IMEC v.z.w
- B Dierckx
Dierckx, B. 1992. The Fuga Series of Intelligent Imagers. Available from IMEC v.z.w, Kapeldreef 75, B-3001 Leuven, Belgium.
Structure in Dynamic System Models. Why a Bond Graph is More Informative than its Equations
- D C Karnopp
Karnopp, D. C. 1989. "Structure in Dynamic System Models. Why a Bond Graph is More Informative than its Equations." IMACS Transactions on Scientific Computation 88(3):15-18.
System Dynamics : a Unified ApproachVibration and Sound Radiation of a Piano SoundboardModeling a Concert Grand Action
- D C Karnopp
- R C Rosenberg Wiley
- H Suzuki
Karnopp, D. C., and R. C. Rosenberg. 1975. System Dynamics : a Unified Approach. New York: Wiley. Suzuki, H. 1986. "Vibration and Sound Radiation of a Piano Soundboard." Journal of the Acoustical Society of America 80:1573-1582. System Build. 1993. Reference Manual. Integrated Systems Inc., 2500 Mission College Blvd., Santa Clara, California, USA. Van den Berghe, G. 1992. "Modeling a Concert Grand Action." Master of Science Thesis. ESAT, Katholieke Universiteit Leuven, Kard. Mercierlaan 94, B-3001
Piano Key Action Models for Electric Pianos The IEEE 1994 Student Paper Book
- Leuven
- Belgium
- Van
- G Berghe
Leuven, Belgium. Van den Berghe, G. 1993. "Piano Key Action Models for Electric Pianos." The IEEE 1994 Student Paper Book. New York: IEEE Press.