Choosing s sensor that can measure precise milimeters in linear motion for automatic wood saw measurements and cutting

Give me an example for sensors please

You don't need explict sensors. You use closed loop systems with e.g. glassscale or encoders.

For open loop steppers you could use some micro switches and rely on the resolution of the steppers to get better than 1mm

If there is a motor-gear box backlash problem, the mechanics of measuring the wood vs carriage vs sensors might be an issue.

Do you have pics of your system?

What part of your machine moves, the saw blade or the board? How much force is required to move the blade through the board (or vise versa)?
I've seen similar machines that used simple rack & pinions with incremental rotary encoders.

Based on my personal experience and not marketing the accuracy is more like 5mm and that’s generous. It can measure a millimeter but if you take ten measurements the will all be different.

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