This is interesting. Good rule illustration Greg.
"A" set up with the thumb facing X+, the Y and the A are identical as far as + and - directions go. (relative to the tool)
"A" set up with the thumb facing Y+, the X and the A are opposite, ie a pos. A move will be the tool going to the left instead of right.
Considering a standard knee mill. Would a gantry router be similar ?
Does mach know the difference ?