About chain sag,

How to you get your 3% figure?

I have worked on chain sag modeling using the catenary mathematical equations and I get figures based on actual sled weight (11.6 kg) and chain density (0,14 kg/m).

I must say that my malsow has 3501mm between shafts and 617 mm above workspace top.

I have not yet checked the experimental measurements compared to the model. (1.5mm seems low.) But the model predicts a balanced catenary with less than 2mm adjustements on one chain in the lower corners. ( The other chain then actually quite straight under tension).

… But that is still a work in progress. I would share if someone cares to play with (free open source software) octave math tool. Anyway I will put all that in my branch’s firmware documentation folder when it is clean enough.

For modeled figures, see image here-under. (0,0 is the uper left workspace corner. (100,50) if the lowr right corner. (matrix size is 100 columns spaning 2400 mm, 50 rows spanning 1200mm). Red color is chain additional length direction (mm). Note that bottom right corner is all left chain correction, and bottom left corner is all right chain correction. Any sled position verticaly near under a shaft has low chain sag for that chain. So chain sag correction zones are somewhat mutually exclusive.

Note: Calculated using a catenary differential equation with sled weight and chain weight distribution.

**UPDATE 2018-11-17**

So I reviewed the octave simulation with the standard Maslow frame size. Here I compare the simple triangular kinematics without any chain sag compensation, and apply a forward kinematics including a true catenary equation to find the “achieved” XY position. I then compute the sled distance from the XY target due to sag.

Note: to keep things simple: no beam flex, no chain stretch, chain length is ideal, no chordal effect, etc. Just sag and accurate sprocket triangle calculations with exact tangent point locations.

The model suggests a 3mm error in bottom corners.

I was curious to see the error caused by a chain sag correction based on the parabola estimation. So I computed the parabola estimation used in the maslow firmware and substracted it from the catenary sag estimation. Once the correciton factor tuned to match catenary at the bottom corners (7.6), the difference is quite small over the workspace:

That suggests the parabola chain sag estimation can do a good job if it is tuned right.

**End of UPDATE**