A 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 behavior of the model was compared to the behavior of an experimental grand piano action and found to be very accurate for high force blows, and reasonably accurate for low force blows.
Issue Section:
Research Papers
Topics:
Friction,
Hammers,
String,
Jacks (Lifting equipment),
Rotation,
Dynamic models,
Springs,
Levers,
Testing
1.
Pfeiffer
, W.
, 1955, The Piano Key and Whippen
, Verlag Das Musikinstrument
, Frankfurt, English translation in 1965 by J. Engelhardt.2.
Matveev
, P. A.
, and Rymskij-Korsakov
, A. M.
, 1937, Sbornik
.3.
Oledzki
, A.
, 1972, “Dynamics of Piano Mechanisms
,” Mech. Mach. Theory
0094-114X, 7
, pp.373
–385
.4.
Topper
, T.
, and Wills
, B.
, 1987, “The Computer Simulation of Piano Mechanisms
,” Int. J. Model. Simulat.
0228-6203, 7
, pp. 135
–139
.5.
Gillespie
, B.
, and Cutkosky
, M.
, 1992, “Dynamic Modeling of the Grand Piano Action
,” Proc. International Computer Music Conference
, San Jose, CA, USA, Oct. 14–18, pp. 77
–80
.6.
Gillespie
, B.
, 1996, “Haptic Display of Systems with Changing Kinematic Constraints: The Virtual Piano Action
,” Ph.D. thesis, Stanford University.7.
Van den Berghe
, G.
, De Moor
, B.
, and Minten
, W.
, 1995, “Modeling a Grand Piano Key Action
,” Comput. Music J.
0148-9267, 19
, pp. 15
–22
.8.
Hayashi
, T.
, Yamane
, M.
, and Mori
, H.
, 1999, “Behavior of Piano-action in a Grand Piano. I. Analysis of the Motion of the Hammer Prior to String Contact
,” J. Acoust. Soc. Am.
0001-4966, 105
, pp. 3534
–3544
.9.
Gilardi
, G.
, and Sharf
, I.
, 2002, “Literature Survey of Contact Dynamics Modelling
,” Mech. Mach. Theory
0094-114X, 37
, pp. 1213
–1239
.10.
Hirschkorn
, M.
, 2004, “Dynamic Model of a Piano Action Mechanism
,” MASc thesis, University of Waterloo, Canada.11.
Hirschkorn
, M.
, McPhee
, J.
, and Birkett
, S.
, 2005, “Dynamic Modelling and Experimental Testing of a Piano Action Mechanism
,” Proceedings of ASME/IDETC Conference
, ASME, New York.12.
Schmitke
, C.
, and McPhee
, J.
, 2005, “Forming Equivalent Subsystem Components to Facilitate the Modelling of Mechatronic Multibody Systems
,” Multibody Syst. Dyn.
, 1384-5640in press.13.
Dunlop
, J.
, 1983, “On the Compression Characteristics of Fibre Masses
,” J. Text. Inst.
0040-5000, 74
, pp. 92
–97
.14.
Stamm
, W.
, 2004, “Compressional Behaviour of Felts
,” Diploma thesis, University of Karlsruhe, Germany.15.
Hunt
, K.
, and Crossley
, F.
, 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact
,” ASME J. Appl. Mech.
0021-8936, 42
, pp. 440
–445
.16.
Cull
, S.
, and Tucker
, R.
, 1999, “On the Modelling of Coulomb Friction
,” J. Phys. A
0305-4470, 32
, pp. 2103
–2113
.17.
Anonymous, 1992,
Steinway and Sons Technical Reference Guide
, Steinway and Sons
, NY.Copyright © 2006
by American Society of Mechanical Engineers
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