While a regular gear is optimized to transmit torque to another engaged member with minimum noise and wear and with maximum efficiency, a non-circular gear's main objective might be ratio variations, axle displacement oscillations and more.
For this reason NCGs in most cases are not round, but round NCGs looking like regular gears are also possible (small ratio variations result from meshing area modifications).
Generally NCG should meet all the requirements of regular gearing, but in some cases, for example variable axle distance, could prove impossible to support and such gears require very tight manufacturing tolerances and assembling problems arise.
If the axles remain fixed, the distance between the axles is also fixed: Assuming that the point of contact lies on the line connecting the axles, in order for the gears to touch without slipping, the velocity of each wheel must be equal at the point of contact and perpendicular to the line connecting the axles, which implies that: Of course, each wheel must be cyclic in its angular coordinates.
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