Three Groove Kinematic Coupling Design

Concept Selection

One of the tasks for the course this week is to design and build a three groove kinematic coupling. You can read more about kinematic couplings here, but they are primarily used to repeatably position objects relative to each other. I don’t yet have a specific application in mind for this coupling, apart from a vague notion that I would like to eventually use it to fixture some sort of camera in a future project. Therefore, I will be building my coupling to a 2.5″ coupling circle diameter — a reasonable size to accommodate most hand-held cameras.

In the interest of controlling cost, I have chosen to use plywood for the top and bottom plates of the coupling. To select the material for ball and groove contact elements, I estimated the Hertzian contact stresses resulting from anticipated loads (from a ~1 kg camera) using Prof. Slocum’s design spreadsheet and found that a wood-on-wood interface would have been feasible. However, I ultimately decided to use steel for the contact elements in order to avoid potential issues that may result from material and geometric irregularities found in biological materials. Additionally, gluing in steel balls and dowel pins would be easier and faster than machining them out of wood, which would require either a time-consuming workholding setup or a CNC machine.

Analysis

I adapted the template spreadsheet to predict the stiffness and error motions specific to my design. You can view the full spreadsheet here. Some of the key insights from this analysis are:

  • With a preload of 1.48 N per ball, as would be the best case scenario with the 3 lb max.-pull magnets I am intending to use, and a 2-kg object (reasonably large SLR or medium format camera) on the coupling, the maximal lateral force it can tolerate is approximately 13 N when applied in line with a vee groove. Lateral loads above this threshold would cause the coupling to come unseated.
  • An RMS stiffness of 62 N/micron. This means that the Z-position should be capable of achieving sub-micron repeatability in the face of minor variations in the preload or weight of the upper piece of the coupling. This is important as it would facilitate interchangeability of the part being fixtured.

Detailed Design and CAD

After convincing myself of the feasibility of my design, I built a solid model to check that I haven’t made any mistakes in my geometric calculations and to generate toolpaths for the CNC router I plan to use to machine the plywood boards that will receive the steel contact elements. I also decided to use a pair of neodymium magnets inset into the plywood plates to provide a more consistent preload for the coupling. These magnets will be glued into circular pockets positioned at the center of each half of the coupling. My CAD models can be downloaded here.

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