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.

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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.

Many techniques have been developed for analyzing and evaluating mechanical systems for the purpose of improving design and control, such as the operational space formulation. It has been been shown to be a useful tool when working with robotic manipulators, but has not been extended to consider rovers. Rovers are fundamentally different due to the wheel-ground contact, that does not exist for fixed-base systems. In this paper, several different aspects of the operations space formulation, inertial properties, control, multi-arm systems, redundancy, and unactuated coordinates are investigated in the context of rovers. By considering a different interpretation of the operational space of a rover, several sets of generalized coordinates were chosen to represent the movement of two example rovers. Simulations were performed to demonstrate how these choices of generalized coordinates can be used to analyze various characteristics of the rovers and can improve the behavior for certain maneuvers, such as wheel walking.