In this paper

it is pointed out that the engagement angle of non-circular gears is variable

and the calculation of the engagement angle is worked out. The elliptical gears and the eccentric gear are taken as examples to show the change of engagement angle and the constraints on the engagement angle in design. In the case of elliptical gears

the engagement angle increases with the eccentricity increasing

and becomes into a right angle if the eccentricity is big enough

and the tooth can not contact.Thus

the cause of out-of -mesh is theoretically explained

and one of the bases is given for the design of non-circular gears.