Hello...
I wish to make "3D ruler" to measure dimension in 3D space.
The idea is to have 3 capstans with at least 10m of dynema fishing line.
Lines from all 3 capstans are joined in single knot. Now if position of capstan are known, and then I measure length of unwinded line I can calculate the XYZ coordinate of knot.
Is this viable method? What accuracy I can except due line sag, thermal expansion .....?
And there are challenges. How to measure line unwinded.

To use Allegro A2051 (mice chip)  already fail as line is to thin.

Use single drum with groves (like screw) and measure drum rotation with incremental encoder. The issue is that drum need to be pretty big to have at least 10m of line in single layer.

To use drum without groves and line laid like in fishing well but for measurement to have two drum capstan with incremental encoder. I'm worried in capstan that there will be slippage and additional inacuracy.
Another challenge is to keep lines tensioned with same tension all the time.

I think that can be done with DC motor feded with constant current (motor is near all the time in stall condition). I have done similar years ago with induction motor and VFD. But induction motor will be to big for that and VFD is expensive.

or to have motor spinning magnet and in drum is cooper plate and tension is generated with eddy currents induced. (like in old type of speedometer)
An idea / comment?
edit.
Motivation:
Few years ago I build campervan. In the build process the worst are measurements. In the van there are NO flat edge NO straight lines! And measuring that is just nightmare. A lot of cardboard templates and tape to make shape. I did try with 3D scan camera (cheap one) but accuracy was to coarse to be usable. If I have device described I can place each unit in floor of van and measure all the edges I need and even create all curvatures. Now I have similar project (not camper van) but lot bigger. So I want to have something handy to do the job.
For tension: just use a brushed motor, make the current ~ 1/10 or less of the rated max. current and use a small gear (1:10 or so) and you have a source of force (just like the forcefeedback joystics)
on measuring line length: use optic encoders (4096 steps/rev) or magnetic encoder (allegro) and you are fine.
Note that when you use amecanic like a fishing rods drum your lenth/rev decreases as the line is extended  but you can calculate that (aproximately) or use a bigger drum.
I don't understand exactly this...
If I take (grooved) drum big enough to have only one layer of line then length is predictible by rotation and little angle deflection if line wind on beginning or end of the drum. To have multiple layers on drum I think is out of question as I need precision. I need max 2mm real top 3mm error on 5m distance otherwise project is dummed.
To achieve that precision I will probably need some callibration points to calculate line sag when is long, and line stretch over temperature.
3mm on 5m will not work with this setup, regardless how much force you apply.
I think most string potentiometers use a rotary spring to maintain line tension.
Good luck!
This can be option but it will come bulky and tension is not constant.
FYI: Catenary  Wikipedia  just calculate what tension force you'll need and if that force is more than the rod can handle.
Thanks to give me correct item name.
I found online calculator to calculate catenary and got really good numbers.
for example 50g/m dynema rope 10m long under 3N tension will sag 2cm, but in total length will be only 0.11mm longer. So line stretch and temp expansion will play probably more. But seems that 2mm accuracy is plausible.
Yes, but the main weight of ~ 1kg will sit in the center of your construction  or do you plan to make 3 heavy endpionts with 3x esp32 + 3x battery + ... ?
Interesting project! What holds the object to be measured in place?
Build the device and let us know how well it performs.
Didn't know of existence of Draw wire encoders. Thus they have short wire up to 3m. Longer are just to expensive. Will try with cheap (600cpr) encoder and spring from 10m tape measure.
For usage the each unit will be placed in triangle shape as far as practical for usage. Probably will use magnets to hold in metalic plates. Then distance of placement need to be known. Probably will use some of ESP modules, to capture data from encoders (all 3 wired to same ESP) and send results via WiFi to smartphone as display. Thus don't know if encoder cables can be extended let say to 5m each.
just edited 1st post and added motivation why.
when you can place the unit on the floor then tyou can place all stuff needed inside the center knot. there would also be no deflection (cable flat on the ground). You'd just need to do the trigonometry for the anchor points, as the cables will most likely not run through common center (or you'd need a sane construction to make that happen).
It's not all in the floor.
Need to measure in walls and ceiling too. But yes all can be done with 3 units layd on floor.
Ok. One point remains unsolved: you do not know the angle of the 3 lines, so you cannot get the absolute position in one go. You'd have to take at least 2 measurements with the center knot significantly moved (e.g. 1m). Idealy you'd fix the endpoints, then move the center around, and your program would calculate the 2d positions of the 3 endpoints while tating constant measurements and error compensation. Should give you a good reading after all.
Didn't check kinematics yet but I'm pretty sure that if I know position of 3 start points (planar) then I can calculate point in 3D space knowing length of line. If this is not true then I don't know how on the earth delta 3D printers works. They can reach any point in 3D space with changing 3 positions. I know of I go behind "encoders" plane then I need to manually say that I'm in other side. But that is near impossible as line need to go around base plate to other side
One point in 2D needs 2 coordinates  whatever they may be. You have 3 points, but only 3 coordinates. You need to take at least one more static measurement so that you get 3 more coordinates (different from the ones before  if you don't want to deal with singulatities). Delta printers use polar coordinates  R and Alpha in 2D, cathesian use X and Y in 2D. You measure just R, but not Alpha, so you need to come up with a plan.
I'm little bit confused. The math is not my stong side at all. But if I image the following scheme seems that is doable.
A,B,C are measuring units.
X is unknown point in space
The distance AB, BC, AC are predetermined when probes are placed.
Knowing AB, BC, AC the ABC plane is known and also the angles (probably not needed at all)
Distances AX, BX, CX are measured by device.
Now we have triangles AXC, CXB, BXA and ABC, with all known length. In my 1st view seems that there are enough information to do calculation. The only issue seems to be if X is under plane defined by ABC. I'm sure that I will need help there but at least it seems doable.
For many decades such measurements have used a single wrap around a spindle of know circumference and count the turns/partial turns to get the length of line fed out. You can do the same.