PUPS 4: Groove KC Model

1.

Please see  Update: Kinematic Coupling for my latest work on the groove KC model. In summary, I constructed an updated model from machined plywood and hardened steel contact elements (dowel pins and steel balls).

2.

Stiffness

This metric was the most challenging to measure. Without access to precise inspection equipment, I resorted to placing dead weights such as a 100-g bag of fasteners on the KC and attempting to measure deflection using a laser pointer. This yielded no perceptible motion at a distance of 2.9 m. I attribute this to two reasons:

  1. I placed the weight above the center of the coupling circle, which would have resulted in deflection along the vertical axis. To the first order, this is not expected to cause any rotational error — making our Abbe error-based measurement scheme moot.
  2. My design is predicted to have an RMS stiffness of 62 N/micron. Since my dead weight only applied a force of less than 1 N, the predicted deflection would be far too small to measure using my methods.

The Makerworkshop will be commissioning an Instron UTS in the coming weeks, and I plan to repeat this test using the machine once it comes online.

Repeatability

Please see Update: Kinematic Coupling for repeatability test results. In summary, I measured 0.04° of angular for my KC.

Accuracy

I designed the top and bottom faces of my KC to be 28.95 mm apart. The actual stack was measured to be 29.0 mm thick. I was impressed by how close I got, considering that the plywood rounds were machined on a less-than-stiff CNC router with a relatively worn-out sacrificial bed. In any case, we know the three-groove KC is quite robust against small inaccuracies and this is borne out in the repeatability test results.

3.

I am yet to quantify this, but I believe the actual apparent stiffness of my KC would be significantly lower than the value predicted by the spreadsheet. The original spreadsheet predictions only considered the interface materials. In my case, I predict that the majority of the deflection would come from the plywood support structure instead of the hardened steel contact elements. If I had to make KC’s for my table, I would update the spreadsheet to account for the plate bending that occurs within the coupling circle when the coupling is centrally loaded.

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