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You may be aware of WolframAlpha already, but if you are not it is worth checking out.I use the Omni Calculators all the time. Good stuff.
makes good since. i have the exact same issue with seat on tcase . so you gave me a path forward to figure this **** out. thanks again....Thanks guys! I am proud of how they turned out. Sometimes things come together just right.
There is mechanical advantage to having a fulcrum, but I did not gain that with the bellcrank. The front and the rear shift rails have the same travel for getting into each position. I wanted the shift levers to have the same throw, so I made the bellcranks with equal length arms for a 1:1 movement. Even though the front and rear cranks have different length arms, they have the same mechanical advantage of 1. The shift lever length compared to the distance of the first ball stud from the shifter pivot is where there is mechanical advantage. I don't have the numbers in front of me though.
The real benefit of doing it the way I did is taking advantage of the space I had available for the shifters and the location of shift rails. I wanted to be able to pull the lever backward to push the shift rail forward.
I like using the site Omni Calculator for stuff like this. Their Fulcrum Calculator is simple to fool with and you can punch in your numbers to quickly see the mechanical advantage of your system. I could have made the shifting even easier by having different length arms. Part of why the cases shift so easily in the video is that there is no load on the gears, so nothing is in a bind. They can sometimes be stubborn when the shift collars are not lined up as well.
Hopefully that makes some sense, because I am honestly having a hard time putting it into words.

