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Consider the attached model, which belongs to http://www.peeron.com/scans/8841-1
I'm having trouble building the arch thing, which appears in step 12 of the instructions.

In the main model, I have the pieces set before final rotation and translation. The yellow and green pins should match each other. Given that the height (yellow-black or green-black) is 180 units and that the desired displacement (yellow-yellow or green-green) is 50 units, the rotation angle (around the black pins) should be asin(50/180)=16.13°. When I apply that, I get the assembled arch at the back of the model, and the problem is the teeth in the angle pieces (4273a) do not interlock properly.

Of course, since there are 16 teeth in each piece, the angle should be a multiple of 360/16=22.5°. But the result when I use this angle is in the back2.ldr submodel, and as you can see there's not enough space at the top of the arch.

So, am I doing something wrong? Is some dimension not correctly modeled in the LDraw parts? Or maybe the physical model relies on some flexibility of the plastic? Things would be easier if the horizontal offset were 70 instead of 50, since asin(70/180)=22.89°, much closer to 22.5°.
When you have the parts, nothing beats a real life experiment Wink
Yes, the arch is heavily stressed!
[Image: stress001.jpg]
Are those 8-unit long axles?
Oomph, sorry! no, these were 10L axles! with 8L axles stress is lower, but still doesn't fit this width. It requires two more studs base width to fit.
OK, so my calculations were correct, and so are the LDraw parts. Thanks for trying, most of my LEGO pieces are stored in a box somewhere.
Seeing this, J.C. Tchang created Lsynth parameters for bent axles. See it here (in French).
Good, I was thinking about the same solution myself.

But what to do when the pieces involved are not so easily bent?

Consider the attached simple model, which corresponds to the top right inset in http://www.peeron.com/scans/8855-1/7. I think everything is correct, yet the holes in red pieces don't match the holes in yellow one. What would be the recommended solution? Move the red part 1 unit anyway, even if it causes an overlap? Apply some skew (0.025 in the z,z component of the matrix) to it?

Also, the diagonal bricks in steps 6 and 9 of the same instructions do not fix exactly, as far as I could compute, so I just scaled their length slightly above or below 1, which is hardly noticeable visually. Do you think this is a good solution?
Are we sure the blue LDraw part is correctly modeled? To me, the part of it that's over the technic axle looks too thick.

Edit: looking at the pictures of the part on Peeron, I no longer think the LDraw part is too thick.
The top inset model fits fine in real world, but I was not able to find what could be wrong, probably very small inaccuracies everywhere that happen to add up in this particular model. I would indeed make all parts slightly collide to compensate.
Diagonal bricks don't fit exactly IRL... your solution may be the right one!
It seems to me that there are two "hack" solutions: move the parts around so that some overlap, or apply a non-uniform scale factor to one or more of the parts (squeeze it). I have attached two modified versions of your test model that do just that.

The "overlap" one has both the gray technic locking bushing and the blue technic toggle connector positioned such that their locking portions protrude into the adjacent red pieces.

The "squeeze" one scales the technic locking bushing by 0.9 in the Y axis. This isn't too visible when viewing the model, but it allows everything else to line up (after adjusting its location, which I also did). Note that this solution causes LDView to spit out a warning about the part being transformed non-uniformly, but, in my opinion, looks better.