THE y VALUE MAY BE CALCULATED ON A COMPUTER BY DETERMINING THE SLOPE OF THE LINE PASSING THE POINT OF APPLICATION OF THE LOAD AND TANGENT TO THE TROCHOID (FILLET) OF THE GEAR TOOTH. THE FOLLOWING EQUATIONS ARE FOR A HOBBED GEAR.

FROM ANALYTICAL MECHANICS OF GEARS.

TROCHOID OF CORNER OF RACK TOOTH AT ROOT OF GEAR

When the rack tooth represents the form of the generating tool, then this trochoid gives the form of the fillet of the gear tooth. When no undercut is present, this trochoid will be tangent to the generated gear-tooth profile. The equations for this trochoidal path are derived as follows:

Let	R	= pitch radius of gear
	b	= distance from pitch line of rack to sharp corner of rack tooth
	r t	= any radius of trochoid
	? t	= vectorial angle of trochoid
	? t	= angle between tangent to trochoid and radius vector
	? t	= angle of rotation of gear
	x t	= abscissa of corner of rack tooth measured from the pitch point
	?	= angle between origins1 of the trochoid and the gear-tooth profile

We have the following from the geometrical conditions shown in Fig. 3-2:

(3-1)

(3-2)

Figure 3-2

When the rack is represented by the cutting tooth of a rack-shaped cutter or of a hob, the corners of these cutting teeth are generally rounded. In such cases, the center of the rounding will follow the...