Inspiring Learning: Assessment of Friction in a Real-World Model Using the Moving Frame Method in Dynamics
This project conducts research in energy dissipation. It also demonstrates the power of the new Moving Frame Method (MFM) in dynamics to inspire undergraduate students to embark on research in engineering. The MFM is founded on Lie Group Theory to model rotations of objects, Cartan’s moving frames to model the change of a frame in terms of the frame, and a new notation from the discipline of geometrical physics. The MFM presents a consistent notation for single bodies, linked systems and robotics. This work demonstrates that this new method is accessible by undergraduate students. The MFM structures the equations of motion on the Special Euclidean Group and the Principle of Virtual work. A restriction on the virtual angular velocities to enable variational methods empowers the method. This work implements an explicit fourth order Runge-Kutta numerical integration scheme. It assesses the change in mechanical energy. In addition, this work researches the energy losses due to friction in a system of linked rigid bodies. This research also builds the physical hardware and compares the theory and experiment using 3D visualization. The authors built the structure to observe the actual motion and approximate the energy loss functions. This project demonstrates the power of WebGL to supplement analyses with visualization.