Calculation of change in Pressure Angle with change in Centre Distance

NOTE: This concept has been asked in both prelims and mains of ESE 2017.

For the involute gear profile increase in the centre to centre distance leads to increase in pressure angle so the pitch circle radius of the gears gets changed and it is increased.
Though the pitch circle radii of gears change but the base circle radii of gears are unaltered and this fact can be utilized in calculation of the new pressure angle of the gear on increasing the centre to centre distance of the mating pair.

Let the initial centre to centre distance of the mating pair is O₁O₂ . And on increasing the centre to centre distance the centre to centre distance is O^’₁O₂^’.

r – pitch circle radius of pinion.

R – pitch circle radius of gear.