Measuring the Mass Properties
To ensure any simulations of the platforms is representative of the experiment, it is important that the mass properties be correct. Generally, this step only needs to be completed when there is a significant weight change to the platform (for example, adding the robotic manipulator with a heavy gripper attachment). The mass properties that are required for an accurate simulation are:
- Spacecraft mass
- Spacecraft center of mass
- Phasespace LED positions relative to the center of mass
- Thruster locations relative to center of mass
- Spacecraft inertia
The measurement of mass and the center of mass can be performed using the three point method. This technique requires three scales in the following configuration:
A free-body diagram (FBD) for this configuration would take the form:
Where A, B, and C are the mass readings at each corner, W is the total of all three mass measurements, and D/E are distance measurements between the various scales, as shown in the free-body diagram. A visual representation of the measurements made in 2017 is shown below:
From the center of mass, it is also necessary to calculate the relative distance of the thrusters to the center of mass, as well as the positions of the LEDs relative to the center of mass. This can all be done in the latest GUI. From the main page of the GUI (in the Initialize Parameters tab), click on the "Open Mass Properties App" button:
This will open the Mass Properties Application. In this application, you simply need to enter the measurements you took using the three scales. The units for the measurements should be in [kg]. Once you have entered the mass of as measured by the scales, click on "Calculate Center of Gravity" to update all of the mass properties for the platforms. This button will also create a text file called "tracker_positions_phasespace" which contains the locations in X, Y, and Z of the LEDs for each platform, relative to their own COG. To get a visual representation of the COG and the LEDs, simply check the "Show Plots" button before clicking on the "Calculate Center of Gravity".
Measurement of the moment of inertia can be performed using a few different techniques. One simple method is to use the reaction wheel, with known inertia, torque, and RPM, to apply a torque to the spacecraft. The angular acceleration of the spacecraft and the known applied torque can then be used to calculate the inertia via the simple equation:
Another way of measuring the inertia is the bifilar pendulum (BP) technique. This method involves suspending the rigid body at two points approximately equidistant from the center of mass, applying a torque to induce oscillations, and then measuring the frequency of said oscillations:
A video demonstration of the technique is also available here. Once the frequency of the oscillations has been measured, the mass moment of inertia can be approximated as:
This can all be done automatically in the Mass Properties application. Simply enter the measurements you took for the D, L, and the frequency of oscillation and then click on the "Calculate Inertia using Bifilar Pendulum Technique" to update the parameters.
Note: If you want to override the calculations and simply enter a value for the mass and inertia, check the "Override Properties" box in the top right of the application "Summary of Salient Data" section:
