Involute curves are not just visually pleasing: they are a practical standard in machine design because their tooth geometry supports smooth meshing.
Figure 1. Circle and its involutes
For involute gears, profile is determined by: tooth count (z), pressure angle (α), and pitch diameter (d0). To mesh correctly, gears must share compatible pressure angle and module/size relationships.
The gallery below shows generated gears for different tooth counts and pressure angles (same pitch diameter), all derived from parametric equations.
12 teeth, 10 degrees
24 teeth, 10 degrees
48 teeth, 10 degrees
12 teeth, 20 degrees
24 teeth, 20 degrees
48 teeth, 20 degrees
12 teeth, 30 degrees
24 teeth, 30 degrees
48 teeth, 30 degrees