Kinematic Model of a Piano Action Mechanism

摘要

A modem piano action is a complex mechanism of wood, metal, and cloth (felt and leather) components that transfer forces applied by a pianist into a hammer motion that excites the string. In practice, an action must have an escapement system to allow the hammer to be free of the mechanism during the period of impact with the string, preventing blocking and the damping effect that this causes. In addition, a system to catch the hammer and allow rapid repetition is usually included. These two complexities may be disregarded when considering just the basic operation of the mechanism, which in essence is simply a system of three levers in series providing a rapid acceleration of the hammer from a small motion of the key. Due to the difficulties arising from the non-linearities in the piano action dynamics, theoretical investigations initially focused on the kinematics [1]. More recent work has been able to incorporate some dynamic effects [2, 3]; in these models however, component parts are treated as rigid bodies, to simplify the mathematical representation, and action response is related only to the motion of these components in response to ideal, fnctionless, mechanical linkages. Experimental investigations of action behaviour have been quite comprehensive [4, 5, 6,7]. Despite the importance of dynamic effects, useful results can be obtained from a study of the kinematics alone [8]. This article presents a kinematic model of the (simplified) modern piano action and illustrates how non-trivial conclusions may be derived.