I have to create a clock-type cog (60 teeth) that is driving a flat panel with (hopefully) matching grooves (see attached pic).
The absolute dimensions are not particularly important, but I was hoping some math whizz out there could clue me in as to relationship of cog teeth to panel teeth? I'm faffing around doing it by eye, but there has to be a more scientific solution/formula...?
If cog = diameter x and inner diameter y and has 60 teeth, then panel must have grooves of z width and depth.
circumference = πD and the circumference is the same distance the plate needs to move to keep pace with the outside of the rotating cog so, if the panel teeth go all the way in (touch the inner diameter of the cog wheel) use the inner diameter of the cog wheel for D -
distance the plate needs to move = π x Cog inner diameter
there are 60 teeth so each panel tooth needs to be 1/60th of that distance apart