Kinematic Coupling – Toolchanger 1/3

Kinematic Coupler are widely used in the Industry to align Motor parts, Injection Molds or in optical instruments. A kinematic coupling aims to join two separable parts precisely and repeatable to one another.

That’s why this part is so crucial for a tool-changer, it ensures that on every pick the tool locks in the same place.
There are different geometries and systems, all based on the same premise; they restrict movement with precisely defined points, lines or surfaces of contact.
If done right it can achieve sub µ repeatability accuracy, but that’s not even necessary for a 3D Printer tool-changer. The results of my recent blog post show that with the Maxwell System and printed ASA parts the deviation is around 6µ, not visible in the line pattern of printed parts.


My first prototypes had three matching cones. To make it short, don´t do it like that! The cylinder creates an infinite amount of contact points, which results in a heavily over-defined geometry. The result is lousy precision, alignment problems and in the worst case even jams. The goal of Kinematic coupling is to create just as much contact points to restrict motion in six degrees. In this example, it´s especially bad because both sides feature cones, with three cones and three spheres it would be better, but still not great.


Maxwell System

For the next iteration, I gathered some papers and Information about kinematic coupling design guidelines and luckily found several useful links (below the post).

Based on the gained knowledge I designed the next iteration as a Maxwell coupling system. It features three spheres and three grooves which results in precisely 6 restrictions of motion. It worked very well right out the box and is still in use currently. I made a repetition test to benchmark the accuracy and the result was that there is around 6 Micron deviation.

Kelvin Coupling

The tool changer of my Printer is an unusual case. Because the passive cooler also adds a restriction there is one too many. I only realized it when a user pointed it out to me in a 3D printer forum. So now the Maxwell system won´t do it anymore. Good for me that in 1868 Lord Kelvin invented the Kelvin Kinematic Coupling. It looks a bit crazier but restricts the movement in six degrees of motion just as the maxwell system. Instead of restricting it 2+2+2 like the Maxwell system, it does it 3+2+1.

With the Kelvin coupling, I can remove one sphere which saves space and this time I got six restrictions.



Further Optimizations & Design Guidelines


The arrangement is an essential factor to achieve high precision and stability. The most couplings you see are based on an isosceles triangle with a 120° angle between the coupling points and the centroid. This arrangement should be ideal and is an absolute no brainer, but it may be the case that restriction force you to design very flat or high couplings. So for instance, if you want to do a very high coupling, the centroid needs to move down, or likewise up when a wide coupling is intended. By moving the centroid up/down, you can reach 120° between the centroid and the coupling point, even with flat or high couplings.



The surfaces of the coupler shouldn’t ever touch, so it’s necessary to leave some clearance, depending on the accuracy of your tools.


It´s possible to cut the spheres and V groves close to the contact points. Don´t forget to leave clearance!


Whether you use balls, ellipsoids, or barrel shapes doesn’t matter in terms of restrictions. With ellipsoids, the base area is slightly larger, which is why they are more stable, especially with FDM printing. I guess best practice is to use the shape which can be constructed and produced most efficient.



Quasi Kinematic Coupling

Kinematic couplings are ideally suited for precise positioning, but because of the six tiny contact surfaces, they are not sturdy. One Solution would be to add bigger magnets which pull the parts together with more force. But the Magnets already are pretty strong, and at some point, my printer won´t be strong enough to decouple. The solution to this problem is a quasi Kinematic Coupling which doesn´t mate at a defined point but a defined line — doing so it slightly overconstrains the Coupling and adds stability. I made tiny groves, barely visible, and it enhanced the stability very well.



Hardness & Surface finish

The harder and smoother a surface is, the better for a kinematic coupler. That’s why ABS, and FDM printing in general, is not the best choice in this regard; however, it works well enough. But of course, it can get better! E3D is using hardened metal rods and spheres mounted on a laser cut Aluminium sheets, which is indeed excellent! However, it makes the coupling bulky, and there are too many parts and assembly involved for my taste. So the next step will be an SLA printed coupler. SLA printer came a long way and are getting affordable. Besides that, there are some tough resins out which are not as brittle as they were. The problem is that parts printed with these tough resins cost a fortune when ordered on 3D-Hubs, so I need to wait until my own SLA printer arrives to do it.



If you stick to the standard kinematic couplers are very easy to do. And because they are so versatile, I will use it for other things like molds or camera equipment too!

However this is a very condensed collection of Information i gathered, and I’m not an engineer. If there are any factual flaws, don’t hesitate to contact me!







  • 24/05/2019


    This is good stuff. I will be following it!

  • 10/07/2019

    Bill Murray

    Thanks for the great info. I’ll be using this as I design ways to align jigs for positioning/limiting application of adhesive to specific areas of material (just for fun, and for ease of locating)

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