(Georgia Institute of Technology, 2010-07-07)
Eicholtz, Matthew R.
The dynamics of rigid body motion are dependent on the inertial properties of the body - that is, the mass and moment of inertia. For complex systems, it may be necessary to derive these results empirically. Such is the case for manual wheelchairs, which can be modeled as a rigid body frame connected to four wheels. While 3D modeling software is capable of estimating inertial parameters, modeling inaccuracies and ill-defined material properties may introduce significant errors in this estimation technique and necessitate experimental measurements. To that end, this thesis discusses the design of a device called the iMachine that empirically determines the mass, location of the center of mass, and moment of inertia about the vertical (yaw) axis passing through the center of mass of the wheelchair.
The iMachine is a spring-loaded rotating platform that freely oscillates about an axis passing through its center due to an initial angular velocity. The mass and location of the center of mass can be determined using a static analysis of a triangular configuration of load cells. An optical encoder records the dynamic angular displacement of the platform, and the natural frequency of free vibration is calculated using several techniques. Finally, the moment of inertia is determined from the natural frequency of the system.
In this thesis, test results are presented for the calibration of the load cells and spring rate. In addition, objects with known mass properties were tested and comparisons are made between the analytical and empirical inertia results. In general, the mass measurement of the test object had greater than 99% accuracy. The average relative error for the x and y-coordinates of the center of mass was 0.891% and 1.99%, respectively. For the moment of inertia, a relationship was established between relative error and the ratio of the test object inertia to the inertia of the system. The results suggest that 95% accuracy can be achieved if the test object accounts for at least 25% of the total inertia of the system. Finally, the moment of inertia of a manual wheelchair is determined using the device (I = 1.213 kg-m²), and conclusions are made regarding the reliability and validity of results. The results of this project will feed into energy calculations for the Anatomical Model Propulsion System (AMPS), a wheelchair-propelling robot used to measure the mechanical efficiency of manual wheelchairs.