Modeling friction in robotic systems using the moving frame method in dynamics

Abstract

This paper reports on the new moving frame method in dynamics that has proven to excite students and reduce student attrition. It applies the moving frame method to the analysis of a two-body system. The moving frame method is founded on Lie Group Theory to model rotations of bodies, 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. However, we have distilled these mathematical tools to matrix multiplications. The moving frame method presents a consistent notation for single bodies, linked systems, and robotics and from 2D problems and 3D problems. This paper demonstrates that this new method makes advanced 3D dynamics accessible to undergraduate students and inspires them to engage in learning beyond expectations. In this paper, we use the Principle of Virtual work to extract the equations of motion. While others have applied pieces and aspects of these mathematical tools, the notation presented here integrates them; it is accessible, programmable, and simple. Most importantly, this paper presents a restricted variation of the angular velocity to use in Hamilton’s Principle to extract the equations of motion. In addition, this project inspired students to research the energy losses due to friction in a system of linked rigid bodies. This project also builds the physical hardware and compares the theory and experiment using 3D visualization. This project demonstrates the power of Web Graphics Library to supplement analyses with visualization, so students can see the discipline of dynamics in action. It is imperative to study this student project while viewing the 3D animations, perhaps on cell phones.