Jerry commented yesterday, "Does anyone see a roller inductor in the making???"
That's most likely well beyond my 3D skillset, and making the reliable moving contacts would be a real challenge.
But a continuously variable inductance is a real plus in impedance matching networks.
And for some configurations that have a single LC pair that produces a match, it's essential.
The "Differential T" is one of those.
Always wanted to make one with more QRP-friendly dimensions than the big MFJ version.
Linking two common variable caps with 3D printed gears to make them act as a differential should not be hard.
And, recall that it's possible to change the effective inductance of a coil by introducing material into the interior of the winding.
If it's ferromagnetic, like iron powder or ferrite, the inductance increases. If is non-ferrous, like brass or aluminum, the inductance decreases.
Think of the PTO (permeability tuned oscillator) devices that have been popular, like TenTec's rigs and Steve Weber's MMR40 transceiver.
So I have an experiment under way to try to create a "PTI" (permeability tuned Inductor).
I'm 3D printing a coil form with an inner cylinder that will hold a length of 3/8" diameter aluminum rod, able to slide in and out of the coil.
Alternatively a ferrite rod, or an iron powder "rod" made by stacking several toroid cores. We'll see what kind of inductance range is achievable. It will also be necessary to investigate the losses. I seem to recall an article quite a few years back that implied the non-ferrous insert acted like shorted turns and did not impact the Q.
In fact I'm almost certain there was an article in one of the ham mags a ways back about an antenna matcher that used this very principle.
I like to invite folks who are so inclined and have the tools to join in this experimentation - we might come up with a nifty doodad.