Involute Spur Gear Kinematics

Mechanical Engineering

How It Works

Involute spur gears satisfy the fundamental law of gearing by maintaining a strictly constant angular velocity ratio throughout tooth meshing. The involute tooth profile ensures that the common normal at the contact point continuously coincides with the line of action tangent to both base circles at the pressure angle (α). Gear speed varies inversely with the tooth number ratio.

Governing Equation
ω₁ / ω₂ = r₂ / r₁ = N₂ / N₁ , p_b = π · m · cos α , v_pitch = ω₁ · r₁ = ω₂ · r₂