Rotational Stability Demonstrator

Rotational motion is a fundamental concept in many engineering systems, including spacecraft attitude control, robotics, and rotating machinery. However, several aspects of three-dimensional rigid-body rotation are difficult to fully understand using only equations or simulations. One important concept is intermediate-axis instability, in which a rigid body rotating about its intermediate principal moment of inertia becomes unstable and exhibits growing oscillations, or wobbling motion. Because this behavior is difficult to visualize, students often struggle to connect theory with real physical motion. This project addresses the need for a hands-on device that allows users to directly observe how mass distribution influences rotational stability. To address this challenge, a low-cost, fully mechanical three-ring gimbal system was developed to enable controlled three-dimensional rotation. Each ring provides one rotational degree of freedom, allowing the test object to rotate freely about three orthogonal axes. Analytical modeling and MATLAB simulations of Euler's equations were used to evaluate how inertia properties influence stability and to verify that the selected geometry produces unstable rotation about the intermediate axis while maintaining stable motion about the minimum and maximum axes. The final design consists of an aluminum base plate with two vertical T-slot support towers holding three concentric rings made of Polyethylene Terephthalate Glycol (PETG). The rings are connected using sealed ball bearings and stainless steel shoulder screws to achieve low friction and maintain alignment. Design improvements included removing unnecessary brackets, directly mounting towers to the base plate, refining bearing sizes, and adding rubber feet to reduce vibration. The inner gimbal supports interchangeable payloads to study how mass distribution affects rotational stability. Experimental testing is in progress to evaluate performance and compare observed motion with analytical predictions. The system is expected to demonstrate stable rotation about the minimum and maximum axes and instability about the intermediate axis. Performance will be assessed based on rotation smoothness, duration before energy dissipation, and clarity of motion. This project provides an accessible tool for understanding three-dimensional rotational dynamics through physical demonstration.