• Name: "Mechanical Computing Systems Using Only Links and Rotary Joints"
(Submitted on 10 Jan 2018)
by Ralph C. Merkle, Robert A. Freitas Jr., Tad Hogg, Thomas E. Moore, Matthew S. Moses, James Ryley

https://arxiv.org/abs/1801.03534

(There was a preceding report: http://www.imm.org/Reports/rep046.pdf)

Essential points:
+) extreme simplicity, only two elements, links and and 2D rotary joints
+) (as the paper says): "All parts of the system can remain permanently connected and yet still provide all necessary combinatorial and sequential logic"

It is not mentioned in the paper like this but I think the idea (Fig.3) can be interpreted a bit more abstractly as such:
The locks provide a singular mutual dead center point where one gets an additional "singular DOF".
(Does "singular DOF" make sense? I mean a point where two DOFs cross and one can switch between the two systems. There might be a relationship to holonomic constraints: https://en.wikipedia.org/wiki/Holonomic_constraints ? Or not.)
This one additional "singular DOF" allows for temporally decoupling the downstream logic from the upstream logic without actually detaching parts (which would likely cause vibrations), and thus allows for:
1) "repeated buffer power refresh in a pipeline by clocking" and
2) "(reversible) latch memory" in sequential logic. (referring low density memory, not particularly to to high density memory like Fig.16)

3D printing demo models (as suggested in the paper - Fig.22) would be cool, but even pretty simple things (beyond the depicted 3D modeled test part) like a basic one bit full adder (Fig.6) are already pretty darn big in their maximally compressed form (which, I take, is depicted in Fig.6).
Btw: Even basic universal gates NOR or NAND (NAND Fig.5 is double sized combo with negated logic I think) are already composite structures in this "calculus".
Naively composing these composites (e.g. to the aforementioned full-adder) without a then following simplification step makes the results even bigger. (It's an uncompressed form).

Making models by cutting links form bottle plastic (HDPE / PET) with scissor and hole puncher may be viable and cheap.

Some side-notes / observations:+) IIRC Nanosystems mentions that dissipation from sliding rotation scales worse than dissipation from sliding translation. But I think this is still much better than rod logic.
+) Friction force and thus dissipation too (dissipated_energy = force * path * friction_coeff) is in first approximation independent of area (at least on the macroscale). So if force is kept constant (not pressure as in the usual case!!) then a bigger superlubricating bearing should perform not much worse than a single sigma bond bearing. Shouldn't it? I'm oversimplifying. I definitely need to more thoroughly re-read the paper "Evaluating the Friction of Rotary Joints in Molecular Machines" Ref[11]
https://arxiv.org/abs/1701.08202.
+) IMO the single-sigma-bond-bearings partially destroy the benefit of radiation hardness which the massive links provide (mentioned in intro section 5.1).
That needs to be quantized.
+) The current design (Fig.24) with its stark size mismatch between bearings and links feels rather prone to overtones, ringing, sidewards wiggling, ... .
I could be wrong there.
+) Maybe the two preceding points are just a matter of optimization focus:
Minimal dissipation (design as presented - cost in radiation hardness and size)
Maximal radiation hardness (bigger bearings - cost in dissipation and size)
+) Flex logic (Fig.23) seems even better for the nanoscale but bad for 3D printed models with quickly wearing high dissipation plastics.
+) I'm a bit puzzled why they've chosen pushing instead of pulling. (Well it doesn't really matter much.)
+) The transmission lines move in a reciprocative manner (just like in rod logic) ... (Had to add "reciprocative". I totally love that word.)
+) Related mechanism: https://en.wikipedia.org/wiki/Whippletree_(mechanism)
+) Bonus for mentioning Konrad Zuse and his Z1

I still haven't read all the way through the paper.
So there's a chance I've missed some important points that I would like to point out especially.