Mechanisms and Machinery

Mechanisms and machinery are two important classes of application of our research in multibody dynamics and design optimization.

A very interesting industrial application of our research is to the dynamics of a "piano action", the complex wood and felt mechanism that transforms the finger-driven key motion into the flight of a hammer that strikes a string.  The goal of this project is to create a mathematical model and computer simulation of the dynamics of a piano action.  This will allow a user to determine the response of an action by defining input conditions, geometric characteristics, and material properties. It will then be possible to determine how the action responds to different key presses, and how changes to the design will affect that response. The model, as well as related experimental studies, will also be used to investigate the extent to which an artist can physically control this response process when playing the piano.
The mathematical piano model is being created using the Graph-Theoretic Method (GTM). This project will expand on techniques currently available in GTM by incorporating more complex components, such as compressible felt and leather, and more difficult situations, such as flexible body impacts.

A more fundamental area of research is the mechanism "type synthesis" problem, which we are tackling by combining our analysis methods with genetic algorithms for optimization; the end result will be a theory and computer algorithm that determines the optimal mechanism topology (e.g. 4-bar vs. Watt II 6-bar) for a given design task.

Selected Publications:

• Y. Liu and J. McPhee, Automated Kinematic Synthesis of Planar Mechanisms with Revolute Joints, Mech.-Based Des. Struct. Mach., v.35, 405-445, 2007.
• J. Cain, D. Staley, G. Heppler and J. McPhee, Stability Analysis of a Dynamically Tuned Gyroscope, J. Guid. Cont. Dyn., v.29, 965-969, 2006.
• M. Hirschkorn, J. McPhee, and S. Birkett, Dynamic Modelling and Experimental Testing of a Piano Action Mechanism, ASME Journal of Computational and Nonlinear Dynamics, v.1, 47-55, 2006.
• Y. Liu and J. McPhee, Automated Type Synthesis of Planar Mechanisms using Numeric Optimization with Genetic Algorithms, to appear in ASME Journal of Mechanical Design, 2005.
  
• M. Hirschkorn, Dynamic Model of a Piano Action Mechanisms, a thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Applied Science in Systems Design Engineering, 2004.
  
• Y. Liu and J. McPhee, Type Synthesis of Planar Multibody Systems  using Topology as a Design Variable, Proceedings of 11th World Congress in Mechanism and Machine Science, Tianjin, China, August 18-21, 2003.
  
• M. Hirschkorn, S. Birkett, and J. McPhee, Kinematic Model of a Piano Action Mechanism, Proceedings of the 19th Canadian Congress of Applied Mechanics (CANCAM 2003), Calgary, Canada, June 1-6, 2003.
  
• J. McPhee, Expert Report on Quadco Equipment Inc. versus Timberjack Inc., File No. T-867-96 , Trial Division, Federal Court of Canada, September 2001.