Solving the movement track of gear shaper cutter center by noncircular gear

(a) Center motion trajectory of gear shaper cutter for driving noncircular gear
(b) The movement track of the center of the gear shaper cutter for driven noncircular gears

When the gear shaper cutter Hobbes the non-circular gear, its indexing circle does pure rolling on the pitch curve of the non-circular gear, and the movement track of the center of the gear shaper cutter is the equidistant line of the pitch curve of the non-circular gear. According to the equidistant line formula, the equidistant lines (XD1, yd1) and (xd2, yd2) of pitch curves of driving and driven noncircular gears are obtained, where h = DC / 2.

Figure 1 shows the movement track of the center of gear shaper cutter. If the formula is substituted into the formula, it is not difficult to see that xdj and YDJ are essentially the same as each other φ J has a one-to-one functional relationship, based on which the relationship curve as shown in Figure 2 can be drawn; The interpolation method can be used according to the known φ 1 or φ 2. Find out the coordinates of the center of the gear shaper cutter.

(a) Driving noncircular gear (b) Driven noncircular gear
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