Spent some time in CAD trying to flesh out exactly what I want. I think I'm going to add more 4x4s to the middle, so I get an absolute tank like
@zippyslug31 . That also provides nice sections for drawers and a cabinet.
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Before I critique anything, let me say that this finished product is something that I'd be very happy to have. My heirs would inherit it, because it would serve very well.
I may be getting ahead of myself with those though... For starters, I'm just going to focus on the frame, fancy bits can be added later.
Nothing wrong with getting ahead of yourself, so long as you know you're doing it. It's a good way to end up going down a rabbit hole if it gets away from you, but it also helps you future proof a little too, if you're gonna need hinges somewhere, or one of those drawers is going to have to hold a particular piece that's fifteen and seven eighths of an inch wide, and you need a finger under it to lift it...
A couple things I'm not sure about. For the top, I could just add several more horizontal braces like so (they aren't perfectly lined up in the drawing right now). And they will definitely go under the lathe mounting bolts ala
@MrCrankyface
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Those supports are under no obligation to be symetrical. So long as the maximum span between any two doesn't exceed any design strength (or on a small bench, no gap is big enough to make you loose that warm fuzzy feeling like "this'll hold anything...). You can add all the extras that you want, and I agree with you, one should "land" directly under every mounting point that your lathe has.
Alternatively,
@silence dogood suggested a beam to go under the lathe, which I have seen before. Maybe something like this, if I just threw another 4x4 directly under where the lathe should be, with some extra 2x4s on the side to provide a mount for the bolts? Kind of like it now that I drew it up, just creating a lot more cuts to make
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I'm not so sure that the beam is going to gain you a whole bunch, if any, in this way and configuration. It will be a tremendous gain in one sense, but a tremendous structural loss to "split" all the cross supports.
One other thought from this last drawing- Just thoughts, and they're somewhat contradictory to each other... As it's built right now, if you could put a pure vertical load on that, you're probably in the range of supporting somethinig in the low/mid to high/mid twenty thousand pound range. Hold a tape measure up to some (any) available cabinets, drawers, whatever you can find. I believe (I don't know, and why I'm suggesting you check), I believe those center four by fours are going to cost you a lot of access. WAY more than the nominal or actual dimensions would imply. Of course, they also give the impression of the bench being built like a brick (out)house too.
On the other hand, those extra four by fours do add more (presumably glued) joints, which goes towards geometrical stability. Vibrations, racking, movement in directions other than vertical. Which I think is far more at issue here than a brute strength pure vertical load.
More I think about it, the more I don't think this thing needs to roll around. Taking your suggestion to make the bottom level with the legs, it could have a huge contact with the ground and I'm sure feel ridiculously sturdy... Problem is my garage is very sloped. I think the back will need to be ~1/2" higher than the front to be even where I want to place this thing. And I'd rather not try to build that in, for fear of getting it wrong and having to shim anyway, and also so it's still usable in my next garage which will hopefully be reasonably level.
So I don't know... Maybe I'll just throw the casters on anyway, see how well they do
Huge contact with the ground, especially on imperfect floors, is that it hits EVERY high spot, but none of the low spots. If it's built too strong to "flex" into a solidly planted position, it'll rock. I'd personally prefer if it hit at all four corners only. Eight "corners" with the extra center "legs" could be doable too, but leveling gets complicated, and I suspect your lathe is only bolting at two ends, with no middle supports? If so, that makes microadjusting the center of the bench pretty irrelevant.
If you're considering giving up on wheels, consider this- Make sure that some feature is added, OR some existing feature is suitable, such that you can actually get under it enough to jack this thing up, even if it's incrementally by the millimeter, have a plan. You're in the range where it's light enough that you and a few buddies could probably drag it around, and that "might" be the most prudent approach, but leave a plan. Or better yet, a "way out", when you need to (or just want to) drag it around yourself. If you put four wood pads on the outside legs (like your guy in the video did to mount his casters), then you'd have on average, 12mm of space under nearly the entire perimeter of that bench. You could get a prybar in that easily. That's something tangible and solid that you or anyone helping you can bank on and work with at any time, when plan A, (arguably the better plan) doesn't work out.