Update: Kinematic Coupling

This week, I got a chance to get on the CNC router in the Makerworkshop to build the three-groove coupling with magnetic preload that I had designed and mocked up with soft materials.

The fabrication process went smoothly and I was very satisfied with the product. The “snap” provided by the magnets used for preload is particularly satisfying. I often find myself toying with this coupling, and can see myself keeping this around as a conversation piece for a long time to come.

Testing

Magnetic Kinematic Coupling Test from Shien Yang Lee on Vimeo.

As before, I tested the angular repeatability of this coupling using my trusty laser pointer. One issue I ran into was the difficulty of rigidly fixturing a disc-shaped object in my apartment where I had minimal tools. I ended up attaching the bottom disc (with the grooves) to my desk using three strips of gaffer tape spaced 60° apart, taking advantage of the tape’s flexibility to place the disc under quasi-exact constraint. This is possible because the tape is virtually incapable of applying any lateral or compressive forces due to its flexibility.

Over 8 cycles, I obtained a group of points all lying within 2 mm of each other on a wall 2.9 m away. This suggests an angular error of only 0.04° — a 15-fold improvement over the melon-and-cardboard mock-up! I think at least part of this error can be attributed to the imperfect fixturing — impact loads when the balls engage the grooves may have caused the fixed disc to move slightly. The actual angular error is probably even lower!

Three-Groove Kinematic Coupling Fabrication

My original plan was to machine my coupling from plywood and glue in steel contact elements. Unfortunately, the CNC router in the Makerworkshop is down for repairs. Inspired by Prof. Slocum’s demonstration using bagels and fruits, I decided to make a version of my design using soft materials. I thought this would be sufficient to help me build intuition. I had already acquired all the materials and generated toolpaths for the original plywood and steel design, so I plan to also produce that once the machine is back up. A performance comparison between my soft materials mockup and the final version would be interesting.

Melon Coupling Fabrication

I had a perfectly ripe honeydew melon I was looking forward to eat, and decided to borrow a small part of it to build my mockup. I cut the melon into 2 circular discs and punched holes in one of them, placing each hole on a vertex of an equilateral triangle. I then “transferred punch” those holes onto the other disc using a chopstick, thereby laying out the positions of the matching vee grooves. Cutting the vee grooves was a good chance for me to practice my knife skills.

I had hoped to glue the bearing balls to the melon disc over the holes. I had even whipped up a batch of starch-based glue to try this (gelatinizing cornstarch is a popular cooking technique in Chinese cuisine!). Unfortunately, the moist surface of the melon didn’t take well to adhesives, and I had to fall back on making the top half of the coupling from cardboard, to which I glued the steel balls.

Repeatability Testing

Melon Kinematic Coupling Repeatability Test from Shien Yang Lee on Vimeo (CC-BY-SA 4.0)

I tested the cardboard-melon coupling for angular repeatability using a laser pointer projecting onto a wall 59-inches away. The maximum spread over 5 engage-disengage cycles was 5/8″. Converting this sine error to an angular error using simple trigonometry, we find that the coupling is repeatable to within 0.607°. Extremely impressive for a coupling made out of ripe (so soft!) melon and cardboard with minimal measuring. I think this demonstrates how robust the concept of exact constraint design is against fabrication and material inconsistencies.

Melon coupling repeatability test calculation

Machined Plywood + Steel Coupling

Update: See the fabrication and testing of my revised (non-melon) kinematic coupling here.

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.