How many cranks to line up copper links - answered, but what about the balance shaft?

[MongoMcG]

I just finished a valve spring and seal replacement and am ready to install the cams. Did you know...to get the copper links to line up with the marks on the camshaft AND TDC again takes a bit of synchronization between all the gears. This timing mechanism is new to me, and I'm paranoid of smashing valves. I knew I was going to be rotating the crank with the cams removed for the valve stem seal/spring upgrade, so I wanted the copper links to line up when I pulled the cams and again when the cams were installed. I didn't count how many times I rotated the motor before cam removal to get copper links and TDC, but it was a lot. I was curious to see how many cranks it actually takes to go from perfect timing marks to perfect timing marks, and wanted to find out without developing Popeye forearms...so I did a little math with gear ratios.

If my math is right...
Given: 23 teeth on the crank gear, 46 teeth on the camshaft gears, 85 chain links (2 holes for gear sprocket per link, so a 170 tooth gear, effectively)

The chain to crank gear ratio is 170:23, or 7.391304348, meaning the crank turns 7.391304348 times for every lap the chain makes. With this ratio the magic link covers the magic crank tooth every 23 laps of the chain, equaling 170 rotations of the crankshaft (and 85 rotations of the cams).

The chain to cam gear ratio is 170:46, or 3.695652174, so the cams turn 3.695652174 times for every lap the chain makes. With this ratio the magic links cover the magic cam teeth every 23 laps of the chain, equaling 85 rotations of the camshafts (and 170 rotations of the crank).

So, when starting with the copper links on the crank and cam marks, the chain need to make 23 laps (170 crank rotations) to land on both the crank and camshaft marks again (while everything is attached).

For doing the valve work on my car the cams were out, but the chain was still on the crank gear. Since I moved the crank 4 rotations (without cams) during the valve work, I needed to rotate the the crank 166 more times for the magic link to land on the magic crank tooth, and the cams can be installed in their TDC position with the copper links already lined up. I didn't want the chain to skip a tooth on the hidden crank gear, so I provided some tension on the chain with my left hand while cranking the engine with my right hand. Honestly, I did all this math after I got the chain in place and did not really count how many actual rotations I made. I am relatively confident the link is on the correct tooth on the crank gear, but since the upper valve work was done without removing the lower timing cover, I can't be 100% certain until the engine is more buttoned up and cranked by hand to check for interference. If interference is found the lower timing chain cover will need to come off and the chain reset.

Edit: I know the colored links are for install and not removal. But, a) I don't have a lot of confidence in paint markers on oily parts; b) not having the lower timing cover off adds to the mystery; c) starting from a known, indexed position increases confidence in the re-install; and d) I don't know this engine well, and anything I can reasonably do to minimize mistakes is a prudent choice for me, and I consider cranking this motor 170 times reasonable (for me).

What I don't know (although it seems obvious), and hope to find an answer to here, is: Since the chain did not come off the crank the balance shafts should still be synchronized, yes?

[Smac770]

Which is why the colored links are used only for putting the chain on, not for validating timing. Same for the balance shafts chain.

How to put the chain on the balance shafts and the cam shafts is all laid out in the workshop manual. Do all of it correctly and it'll all be fine.

Outstanding video on the subject: https://youtu.be/B-nQ9nj-C0M

(and should be 170 rotations of crank)
23 (23) on the crank
46 (2*23) on the cams
85 (5*17) on the chain
2*5*17*23=170
paint link will have moved 170*23=1955 positions, or 1955/85=46 full chain lengths on an even number of crank rotations (so cam marks are up not down). No idea the numbers for the balance cogs and links, so not sure how that would compute.

[MongoMcG]

Which is why the colored links are used only for putting the chain on, not for validating timing. Same for the balance shafts chain.

How to put the chain on the balance shafts and the cam shafts is all laid out in the workshop manual. Do all of it correctly and it'll all be fine.

Outstanding video on the subject: https://youtu.be/B-nQ9nj-C0M

(and should be 170 rotations of crank)
23 (23) on the crank
46 (2*23) on the cams
85 (5*17) on the chain
2*5*17*23=170
paint link will have moved 170*23=1955 positions, or 1955/85=46 full chain lengths on an even number of crank rotations (so cam marks are up not down). No idea the numbers for the balance cogs and links, so not sure how that would compute.

Thanks SMAC. I did all of this without removing the lower timing cover, so I needed to devise a way to make sure of what I could not see. The timing chain never came off of the crank, so I assume the balance shafts are still in sync. Without removing the lower engine cover I can't be sure.

Did I miscount the teeth on the crank gear? I counted 22 based on pictures, not the actual gear, because my crank pulley is still on the car. But if there are 23, (and 23 makes way more sense at half the cam gear size) then the chain to crank ratio is 170:23, or 7.391304348, and to get everything to line up again takes a much more reasonable 170 rotations of the crank, during which the cams rotate 85 times, the chain makes 23 laps.

I'll edit my original post.