I finally did it. Since I am going to be getting my kit pretty soon, I wanted to check whether I wanted to use steel for the top beam on my frame. In my mind, this question is not related to rigidity, but the dimensional stability of the wood. I did some math to check how substantially the wood would shrink in the longitudinal direction (along the grain). I spent a short amount of time looking up rough numbers on the internet, and I did some rough math in Excel. I calculated that a 10 foot top beam would shrink or grow by ~2.3 mm in length at the extremes in ambient air humidity, from 20% to 80%. I did the calculations really quickly, and nothing is precise. I would like to get feedback to see if I mis-calculated anything. Below is the excel sheet I created. It is very rough, so I hope it is not too hard to follow. I can answer questions, or clean it up if necessary.

now do the math for dimensional shrinkage of steel over temperature ranges

the last time we discussed this we found that wood moved a bit less over typical
ranges of humidity than steel did over typical ranges of temperature IIRC
k

That’s surprising to me if true. The research I’ve done is that for a 100 degree F change in temperature, 10-foot piece of steel will expand about 1/16 of an inch but wood, with a change from say, 50% relative humidity to 95% relative humidity, will expand (lengthwise) about 1/8-inch. There’s also longitudinal expansion of wood due to temperature change that would add a little more, but it’s actually not as much as steel. Wood, however, suffers more from “radial” and “tangential” shrinkage/swelling due to changes in humidity. I would think how much that would affect the top beam depends upon whether the change is uniform. If the motors move forward or back or up or down the same amount, it won’t make much difference.

My opinion is that unistrut will generally work the best, but I guess if you live in a climate with relatively stable relative humidity, but widely varying temperatures, then maybe wood would be about the same or possibly better. If you are adventurous, you could add a heating strip inside the Unistrut channel and bring it to a consistent temperature everytime you cut… then it will be perfectly stable no matter what the outside temperature is

If the steel beam shrinks proportionally to the steel chains the result will be the machine cutting at slightly smaller scales. If the wood beam shrinks in a way that is not proportional to the steel chains, the result will be the machine cutting with a skew (lines will be curved). This difference is clear to me, and is a positive for steel. Because the chains shrink with temperature, you actually want the steel beam to shrink in unison. If the steel beam did not shrink proportional to the steel chains, temperature variations would cause the machine to cut with a skew (lines are curved).

1/16th of an inch over a 100 degree temperature change does not appear to be much to me. if you calibrate the machine at an average temperature, then the swing will be no more than 1/32 of an inch. If you recalibrate every season change, the temperature effects should be insignificant.

another way to look at it is a 2 mm change in the distance between the motors. Depending on how accurate you are with your measurements, I would say that that dimension is pretty close to the margin of error for the motor distance measurement.

And I agree with @madgrizzle that an average change will be nearly insignificant, and I would say that for most users even a 50 degree swing is unlikely between two adjacent seasons. Calibrate in the spring and/or fall and you should be good. Alternately, keep it in a semi-conditioned space to limit the thermal variation.

I agree that 1/32 inch not being too significant. I was thinking about accuracy at the top-center of the working area. I believe 1/32 inch of top-beam length translates to about 5/32 inch of vertical inaccuracy at the top-center location.

Yeah. The way I see it is: if I use a wood top-beam, I may have to re-calibrate every season. I may not use the machine very often, maybe once per season. If I have to re-calibrate once per season, I may have to re-calibrate every time I use the machine. That is unacceptable for me. That is why I am in favor of a steel top-beam.

As an aside, keep in mind that (at least for triangular kinematics), non-linear functions are used for some portions of the calculations. So if the entire frame shrank by a given percentage, the resulting cut pattern would still be skewed.

I planned for and used a piece of 10’ unistrut mainly for ease of construction. since I was making a wall mounted frame, I wanted to have the critical component (the top beam) be as hassle free as possible. No worrying about warping, or selecting a prime piece of wood, or contending with twist or other imperfections. Just level it out and I knew that I had a 10 foot top beam ready to go.

I think that, even though the equations are nonlinear, they still result in a linear scaling with respect to scaling. Imagine scaling a triangle up or down; even though the equation to calculate the angles are nonlinear, they do not change.

I am pretty sure a proportional scaling of the chains and top-beam maintains linearity in the cuts, except for the chain-sag compensation. Think about the Pythagorean equation a scalar multiplier can be applied to all three lengths, and the scalar cancels out.

I agree, but keep in mind then what you would need to worry about would be identical shrinkage in the chain, motor distance, and vertical offset from the bit to the motors. This would seem to make me think that the entire work area would need to shrink, at least in the vertical dimension, to maintain this relationship.

Chain sag is not a big component, but I think it would be upset by this.

Of course, the only way to really know would be to test it!

Right. I am pretty sure this is what would happen. Imagine the triangle being made by the two chains and the top beam. The vertical distance from the chain intersection and the top beam (y distance) will scale proportional to the other three lengths.

I was thinking about using something similar, however I am undecided on whether or not I want to go with a top beam that is longer than 10’. It seems like the biggest issue with the current machine is the ability to cut the lower corners. A longer top beam would fix that.