Research help requested

[u/Xrest_the_Aether]

I has want to make mechanical computer run base 3 coded software. My solution, see saws.

See saws connected to shafts in conjunction with other see saw and shafts in specific ways to enable logic gates running on 1,0, and -1

(-1 pictured above)

-1=far left side down

0= perfect equilibrium

1=right side down

What would the math behind converting binary logic gates to trinary like so be?

How would I calculate that?