I think I see your problem. Yes, the rotation of the bucket DOES add fractionally to the pure vertical lift force at the pivot if you actuate both sets of cylinders at once. You are correct in that.
But that's not how the manual's spec list has described it. Look again. By definiing line two to be measured at the pivot point for the bucket, the length of the moment arm for the bucket cylinder forces is reduced to to zero. So the bucket contribution to lift is zero simply because they have defined the bucket out of the boom lifting calculations. We are only left with the vertical component of the lifting forces that are provided by the boom cylinders. Using the specs given - and their own selection of pivot points - the vertical lifting forces are simply the vertical component of the boom cylinder lifting forces around the boom pivots. Everything else goes to zero.
rScotty
It comes down to defining the pivot point. To reiterate....as defined, the bucket forces are zero for boom lift calcs becasuse of where they placed the bucket pivot point and I agree that is valid.
Now I think your question is this: Is it reality to put that pivot point where they did? Well, not completely..... and I think that is what is hanging you up. But it's the simplest way to calculate the forces - and arithmatically it is elegant. It works perfectly well.
If you do want to calculate the contribution of the bucket rotation to the lift, you have to move the bucket calculations to a different pivot point. That way the vertical component of the bucket rotation doesnt become zero. Then simply add the vertical components. By defining the pivot where they have, they have made these other calculations possible and even easily done if needed.
rScotty