Timing chain cycle vs. sprocket marker position

I installed my timing chain as per the Toyota official spec (I bought a 2 day subscription) and Haynes. I made sure that the double notches on the left intake camshaft sprocket line up the mark on the cam bearing and the same on the right side except that it's the single notch to be aligned. Then I turned the crank so that the marker on the crank sprocket is at 9 o'clock and then I mounted the chain so that the single yellow link straddles that crank sprocket marker and the other two that look the same and are kindof orange-ish go over the single and double notches on the right and left intake camshaft sprockets respectively. Then I released the tensioner plunger.

However, when I turned the crank to make one full cycle of the chain and when the three marker links on the chain were in the same exact position they were in when I installed the chain, I noticed that the sprockets were not in the starting position.

I think this is as designed but I just wanted to check. Here is why:

I counted the number of links total on the chain and there are 87 wide links and consequently 87 narrow links that connect them. That is 174 holes that straddle cogs on the sprockets that transfer torque. The crank sprocket has 18 cogs and each intake camshaft sprocket has 36.

So in one full cycle of the chain, the crank sprocket turns 9.66 cycles (174/18) and each camshaft sprocket turns half that many, 4.83 cycles (174/36), as it has twice as many cogs. So when the single yellow marker on the chain that was initially lined up with the sprocket dot makes one full revolution, the crank will have turned 9 full cycles and 2/3 of a cycle so the sprocket dot will be exactly at 5 o'clock and not the original 9 o'clock (9 o'clock + 240 deg = 5 o'clock). Similar applies with different numbers for the two camshaft intake sprockets.

If my reasoning is correct, the lowest common denominator of 36 (which includes 18) and 174 is 1044, which means that it takes 6 revolutions of the chain (1044 / 174) or 58 turns of the crankshaft (1044 / 18) to line them all up again. The crank sprocket marker will be aligned with the yellow link on the chain after only 3 chain revolutions (as LCD of 18 and 174 is 522, 3 x 174) but the camshafts won't be aligned until that many more because they have twice as many cogs as the driving sprocket.

I was originally expecting that the number of holes on the chain would be exactly divisible by the number of cogs on both sprocket sizes so that each revolution of the chain would position each sprocket in exactly the same position (e.g. if there were 180 links/holes on the chain). But that is obviously not the case if my analysis is correct. I am posting here to get either an affirmation or negation of my analysis.

 

Hmm, not sure because the number of revolutions would have to be the lowest common denominator of 174 and 36 divided by 174. it is not 4 because (4 x 174 = 696) / 36 = 19.33, i.e. not a whole number

 

the lowest common denominator of 36 (which includes 18) and 174 is 1044, which means that it takes 6 revolutions of the chain (1044 / 174) or 58 turns of the crankshaft (1044 / 18) to line them all up again.

 

Count the turns until they line up again and tell us.

 

I will do tonight. 58 crank revolutions (if my math is correct) instead of going to the gym.

 

Subsequently, I discovered that manufacturers purposely make chains / sprockets so that the # of chain links is not divisible by the number of sprocket cogs in order to minimize the alignment of a bad chain link and bad cogs, AKA hunting tooth frequency.

 

I have a quite a few timing lined-up pictures in my build thread. For this specific reason.

 

I think you are reading too much into this. If you installed all the markers IAW the directions ( which from your description you did ). Don't worry about it. The gears take care of everything else. The engineers at Toyota have already figured all this out in advance.

 

I did it and affirmed my hypothesis. It takes a cycle of 6 revolutions of the chain, 58 crank and 29 cam to line everything up in the exact original position.

 

Well done. Put it back together already.

 

Sir, I work FT + I am not compromising the quality of this rebuild job one iota. If it takes time, I take joy in the perfectionism of it...

 

.....loading.....