Gears & gear trains worksheet with answers

Free printable Gears & gear trains worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
N = 45, m = 3 mm

A gear with 45 teeth and a module of 3 mm turns at 1200 rpm. Find the pitch-line velocity v of its teeth.

N = 45m = 3 mmn = 1200 rpm
v = m/s
2.Easy
d1​ = 120 mmd2​ = 300 mm1450 rpmv = ?

A 120 mm pulley turns at 1450 rpm. Find the belt speed v in m/s.

d1 = 120 mmn1 = 1450 rpm
v = m/s
3.Medium
N1​ = 15N2​ = 60

A 0.75 kW motor running at 960 rpm drives a pinion with 15 teeth, which meshes with a gear with 60 teeth. The gear pair has an efficiency of 97%. Find the output torque T2 on the gear shaft.

P = 0.75 kWn1 = 960 rpmN1 = 15N2 = 60η = 97%
T2 = N·m
4.Medium
N1​ = ?N2​

Two parallel shafts are 112.5 mm apart. They must be connected by a pair of spur gears with a module of 2.5 mm and a speed reduction of 5 : 1. How many teeth N1 must the pinion have?

a = 112.5 mmm = 2.5 mmi = 5
N1 =
5.Hard
d1​ = 160 mmd2​ = 200 mm960 rpmC = 1200 mmθ = ?

An open belt connects a 160 mm pulley and a 200 mm pulley whose centres are 1200 mm apart. Find the angle of wrap θ on the smaller pulley, in degrees.

d1 = 160 mmd2 = 200 mmC = 1200 mm
θ = °
6.Hard
d1​ = 120 mmd2​ = 250 mm960 rpmC = 600 mmθ = ?

An open belt connects a 120 mm pulley and a 250 mm pulley whose centres are 600 mm apart. Find the angle of wrap θ on the smaller pulley, in degrees.

d1 = 120 mmd2 = 250 mmC = 600 mm
θ = °

Answer key

  1. 1. v = 8.482 m/s
  2. 2. v = 9.111 m/s
  3. 3. T2 = 28.95 N·m
  4. 4. N1 = 15
  5. 5. θ = 178.1 °
  6. 6. θ = 167.6 °

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