Can you attach Windows zipped folder rather than rar file (I don't have an rar extractor on my machine)?

First let me say that I am on SW2014 so I unfortunately can't open your files. However I will try to reproduce it based off of the attached images.

I have worked on a couple designs almost exactly like this so I will try to share the method I came up with. I started by acknowledging that if I could get the upper half of the system to align in such a way that the gear on the left and the gear on the right are positioned with a tooth or root perfectly horizontal then the entire system will be symmetrical and so the bottom half with align as well. And so I determined that if I start on the right side of the large left gear and trace a path around the chain of gears and ending when I meet the centerline while I'm along the right gear, then that total distance should be a multiple of half of the linear gear pitch (arc length between teeth). So if you position the left gear such that a tooth is sticking out horizontally to the right, then if that total distance were an even multiple of the linear pitch then you'd end right tin the middle of a tooth or a root on the right gear (whether it is on a tooth or a root depends on how many gear interfaces you have I think, for each transition if flips from tooth to root). If the total distance is a multiple of half the pitch then it will still be on a tooth or root, because the distance between a tooth and a root is half a pitch.

So with all that in mind I sketched the pitch diameters and drew arcs to trace such a path, and then I add arc length dimensions to each segment. You might have different constraints that I don't know about, but in general I started with the gears in approximately the location I wanted, then I added some dimensions/constraints to leave only one degree of freedom. I made all of the arc length dimensions driven except one that ends up fully defining the sketch, and then I added them up to get a starting number for the path length.

So in the above image if you add up all of the path length dimensions you get 31.63 + 48.39 + 42.07 + 23.47 = 145.56. The arc length pitch is pi, so I round the sum to the nearest multiple of pi/2 (46.5*pi). So now you can use an equation to set the driving arc length dimension to 46.5*pi minus the rest of the arc lengths (46.5*pi - 31.63 - 48.39 - 42.07 = ~23.99). Now the locations of the gears should line up along the entire closed loop and you can confirm by eye. Unfortunately my equations are not working in SW and so I can't finish the process in my example file, but I'll attach it anyway for your reference.

If you have any questions let me know, I hope I explained the process well enough. It worked out for me and we now have gearing like this on some of our production equipment.

Maybe it is due to a cumulative error but they do not quite mesh. I eye-balled the mesh and the ends do not quite line up.

Attached is a DXF overlay. It aligns the gears counterclockwise back to the top 24T/38T mesh.

I am not quite getting the method you are using to account for the position, but indeed, you should be able to capture something like this very accurately in a sketch.

Were you just checking the alignment with that sketch? At first glance it looks like it might be close to working, all you need to do is rotate the 38 mm gear clockwise about half a tooth. But I just realized that when you change the final arc length dimension and the gears all shift a little bit then the other path lengths change a bit. So calculating out manually like I did is not the ideal way of doing this. Ideally you'd set up an equation to drive the final path length and then rebuild a few times until the sketch converges on stable values. Can you try this and then attach a dxf of the result? Then throw the actual gears in there and try to mesh them all like your original image.

Actually I fear that rebuilding might not converge on a solution, but I can't check. That's not actually how I did it before. I just left all of the path lengths driven and then set a variable equal to the sum of all of them. Then I added a center-to-center dimension between the left and right gears to fully define the sketch, and manually adjusted the dimension a tiny bit at a time until the variable reached a multiple of the half pitch. I was hoping the equation method would work better, so you can tell me if it does (or I can try tomorrow at work where my install is better.)

When I do this manually I end up with the attached sketch (my variables don't work either).

I can appreciate your direction for doing this and it clears up one thing I was assuming in my earlier design effort.

I know what the center to center values are, but the teeth do not necessarily become collinear (Duh!)

I was playing with my Lego gears and you can mesh them in the configuration shown.

The challenge is to find the "correct" values based on proper gear trains.

Can you drive a single sketch to force this level of accuracy? I suspect so.

That will take some more consideration but I think you are on the right track.

Thanks for the interest in this matter,

i have attached a model where the gears are in a 90 deg. configuration ,

and it looks like the gears mesh perfectly , and if i add all the inside arc length together and divide it with PI i get exactly 81 teeth.

but when i adjust one of the dimensions so i get very close to ex. 75 teeth , the gears will not mesh

Good one Yes, the square configuration is a real solution except that the 38T is dragging on the 100T.

I don't know what the answer is but there has to be a simple logic that can be applied to the sketch.

I think Jamil is on the right track but somewhere you have to throw in the gear ratio to get the correct arc length. The orientation of the 100T in relation to the far right 24T is one of two positions... so put a tooth of the 100T horizontal and the 24T has to be either a tooth or a valley aligned on the horizontal. Both are viable solutions and will determine where the other 2 pairs go. Therefore, we only have to solve for the pair between the 100T and the far right 24T.

You should not be adding up all of the inside are lengths, you should add up a continuous loop around the gears without changing direction. So it would be inside of the large gear, outside of next gear, inside of next gear, outside of right hand gear.

Now that I have equations working I have revisited my sketch and added global variables. Setting the final arc length with an equation and rebuilding a few times did not work as I suspected, so instead I just made global variables for the path length and the number of teeth, then I drew a construction line and set the length equal to the number of teeth, just to the value is visible in the sketch. That is the vertical line extending down from the large gear. So then I made all of the path lengths driven and I manually adjust the distance between the left and right gears until the number of teeth is a multiple of .5. After doing this and getting the path length to be 49.5 teeth, I threw it in an assembly and confirmed that the teeth mesh properly. The files are attached.

Now that I have equations working I have revisited my sketch and added global variables. Setting the final arc length with an equation and rebuilding a few times did not work as I suspected, so instead I just made global variables for the path length and the number of teeth, then I drew a construction line and set the length equal to the number of teeth, just to the value is visible in the sketch. That is the vertical line extending down from the large gear. So then I made all of the path lengths driven and I manually adjust the distance between the left and right gears until the number of teeth is a multiple of .5. After doing this and getting the path length to be 49.5 teeth, I threw it in an assembly and confirmed that the teeth mesh properly. The files are attached.