1. Basic profile parameters and definitions
Taking the involute profile as an example, Figure shows an illustration of the involute profile.
In Figure, the curve AH is involute, intersecting point A and point H with the top circle and the root circle of flexible gear with radii RA and RF respectively. The center of circle is O1, the radius is R4 root chamfer and the root circle of tooth profile AH and tooth root circle are tangential to point B and point C respectively; theta 1 is the center angle corresponding to half pitch. The tooth thicknesses and the width e of standard spur gear on the indexing circle R are equal, and the ring wall thickness h is the root circle to the inner wall of the flexible wheel.Distance.
2. Positive displacement profile
To avoid tooth profile interference, a positive modified involute profile (Figure 6) is used. The positive modified profile can increase the strength of the root . The upper circular tooth thickness Si of the flexible gear teeth with RI upper half diameter is used.
Where the involute function inv alpha i=tan alpha i-alpha i, alpha I is the pressure angle, and alpha 0 is the reference tooth angle;
Referring to the fact that the thickness of indexing circular teeth of standard spur gear equals the width of the slot, there is a circle (figure) with radius rk along the height of the tooth for the positively deformed involute profile, which is derived from the thickness sk=width EK of the slot:
2.1.3 Wide Groove Profile
Wide-groove profile can greatly reduce ring stress. For this reason, a wide-groove flexible profile is constructed and a slot width ratio is defined.
Narrow teeth with slot v=1. Literature  Forms wide-slot flexure wheel by reducing tooth height and removing adjacent teeth and gives experimental curves; however, the height, number and pitch of wide-slot flexure wheel remain unchanged in practical application, and the width of slot is increased by reducing tooth thickness. Therefore, the wide-slot flexure wheel model in this paper represents wide-slot tooth profile with v>1 as dashed line in Figure.