Advanced Engineering Drawing
Mechanical Drawing
Drawing Gear Teeth
The involute System
The curved surface of the gear tooth profile must be of a definite geometric form if the gears are to operate
smoothly with a minimum of noise and vibration. The most common form in use today is the involute
profile.
In the involute system, the shape of the tooth depends basically upon the pressure angle. The pressure angle
is either 14 1/2 degrees or 20 degrees. The pressure angle determines the size of the base circle. The
involute curve is generated from the base circle.
Construction of the Base Circle
Draw the pitch circle, the addendum circle, and the root circle. Add the vertical and horizontal center lines.
Mark point (P) at the intersection of the vertical center line and the pitch circle.
Construct a line perpendicular to the pressure angle (14 1/2 degrees) from the center of the pitch circle to at
least the addendum circle.
Construct a line perpendicular to the pressure angle line just constructed and passing through point (P).
Mark this intersection as point (J).
The base circle is constructed with the center being the center of the pitch circle and the radius equal to the
distance from the center to point (J).
CONSTRUCTION OF THE BASE CIRCLE
1
Construction of the tooth profile
Set off the tooth spacing along the pitch circle. You can use two methods to space the teeth; chordal
thickness, or equal angles.
chordal thickness: tc = D x (sin(90 degrees/N))
equal angles: angle = 360 degrees/ (2 x N)
Draw the gear tooth face from point (P) to point (A) with a radius (R) derived from the Wellman's Involute
Odontograph chart. The center of the radius is on the base circle. Do not use the radius values given
directly from the chart. Each value must be divided by the Diametral Pitch (P) for the given gear.
Drawing Radius (r) = Given radius from chart (r)/P
Drawing Radius (R) = Given radius from chart (R)/P
Draw the flank portion from (P) to (O) with a radius of (r) derived from the Wellman's Involute
Odontograph chart as described above. The center of the radius is on the base circle.
The portion of the tooth below the base circle is a straight line drawn to the gear center.
CONSTRUCTION OF THE TOOTH PROFILE
Fillet the corners of the straight portion of the gear tooth and the root circle. The fillet radius can be derived
from the following formulas:
Fillet Radius = 1 1/2 x Clearance
Fillet Radius = 1.5 (.157/P)
Clearance = .157/P
Clearance = B - A
The remaining tooth profiles can be constructed using the same process, constructing a tooth profile through
every other mark on the pitch circle. The opposite tooth profile can be drawn through the remaining marks
located on the pitch circle by mirroring the above construction process.
2
Wellman's Involute Odontograph Chart
Number of
Teeth
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37-39
40-44
45-50
51-60
61-72
73-90
91-120
121-180
Over 180
14 1/2 degrees
R
r
2.87
.079
3.02
.088
3.17
.097
3.31
1.06
3.46
1.16
3.60
1.26
3.74
1.36
3.88
1.46
4.02
1.56
4.16
1.66
4.29
1.77
4.43
1.87
4.57
1.98
4.70
2.08
4.84
2.19
4.97
2.30
5.11
2.41
5.24
2.52
5.37
2.63
5.51
2.74
5.64
2.85
5.77
2.96
5.90
3.07
6.03
3.18
6.17
3.29
6.36
3.46
6.82
3.86
7.50
4.46
8.40
5.28
9.76
6.54
11.42 8.14
0.118 x N
0.122 x N
0.125 x N
20 degrees
R
r
3.21
1.31
3.40
1.45
3.58
1.60
3.76
1.75
3.94
1.90
4.12
2.05
4.30
2.20
4.48
2.35
4.66
2.51
4.84
2.66
5.02
2.82
5.20
2.89
5.37
3.14
5.55
3.29
5.73
3.45
5.90
3.61
6.08
3.77
6.25
3.93
6.43
4.10
6.60
4.26
6.78
4.42
6.95
4.58
7.13
4.74
7.30
4.91
7.47
5.07
7.82
5.32
8.52
5.90
9.48
6.67
10.84 7.92
12.76 9.68
15.32 11.96
0.156 x N
0.165 x N
0.171 x N
3