Design

I designed a Kinematic Coupling for attaching large (3 lbs) quick-discharging batteries to a satellite testbed in the Space Systems Lab. The batteries need to be taken on and off the testbed for charging (so that tests can be run efficiently switching in different sets of batteries); however, the testbed is mounted on a spherical air bearing and for reasons relating to control, the center of mass of the system cannot be more than 10 microns from the center of rotation. It also takes a long time to run the code and adjust the system to rebalance the air bearing each time. This means that the batteries must be mounted to precisely the same location each time they are put back on the testbed. One very repeatable method for doing this is with a Kinematic Coupling.

 Find links to my full write-up and results, part drawings, my solid model and the equations / code used for my predictions here:

• Full write-up and results
• Solid model
• Part drawings
• Equations and code for analysis

For ease of manufacturing, I decided to go for a three ball / three groove design for my Kinematic Coupling as shown in Figure 1.

Figure 1: Solid model of Kinematic Coupling three-ball, three-groove design.

The main design considerations were:

• Avoidance of material contacts that are fretting or galling (because over time the wear will impact the repeatability).
• The contact pressure must be greater than one and a half times the smallest ultimate yield strength of the materials in contact.
• The contact point of the ball to the groove must be at least twice the diameter of the contact ellipse from the groove’s edge to be certain to avoid fractures forming at the edge  (St. Venant).
• The midpoints of the lines connecting the balls must intersect.
• Place the balls widely to reduce problems with tipping.

Manufacturing

I used an OMAX waterjet to cut out the main top and bottom parts out of ½” aluminium stock and then I programmed the mill to cut out the 90 degree V-grooves with a countersink end tool. The machined parts are shown in Figure 2.

Figure 2: (a) The top of the Kinematic Coupling to be connected to the battery. (b) The bottom of the Kinematic Coupling to be fixed to the testbed.

I assembled the Kinematic Coupling using a bolt with a split-lock washer through the center to provide a known preload as shown in Figure 3.

Figure 3: Fully assembled Kinematic Coupling.

Testing

The angular repeatability and accuracy of my Kinematic Coupling was measured by mounting a laser pen on top of the coupling and by removing and replacing the top part multiple times. The angular stiffness was measured with the same laser pen setup and by applying a force with a spring scale. I attempted to measure the z-axis repeatability of my coupling with a clamp stand to hold the dial indicator and the coupling bolted to the optical bench; however, with the dial indicator I had available, the repeatability was below the resolution (0.001”) of the instrument so it was not possible to calculate this value. I also attempted to measure the stiffness in the z direction by applying weights to the balls but with the weights I had available, I was unable to see any deflection with the dial indicator I had available. The angular test setup is shown in Figure 4.

Figure 4: Test setup for measuring angular stiffness, repeatability and accuracy.

Results and Analysis

Table 1 gives a breakdown of the measured results from testing and the predictions I made using the analysis and equations in my design code. The equations used were based on Hertzian  point contact stresses. An appendix for the actual testing results can be found at the end of my complete write-up document.

Table 1: Summary of predictions and testing results and how they compare for my Kinematic Coupling.

Conclusions

My Kinematic Coupling performed very close to how I predicted it would and very well in terms of repeatability, accuracy and stiffness, making it an appropriate choice for precisely fixing batteries to the satellite testbed.