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
A = 32B = 72C = 16

Gear A (32 teeth) turns at 1440 rpm and drives an idler gear B (72 teeth), which in turn drives gear C (16 teeth). All three gears are on separate shafts. Find the speed nC of gear C.

NA = 32NB = 72NC = 16nA = 1440 rpm
nC = rpm
2.Easy
d1​ = 200 mmd2​ = 400 mm720 rpmv = ?

A 200 mm pulley turns at 720 rpm. Find the belt speed v in m/s.

d1 = 200 mmn1 = 720 rpm
v = m/s
3.Medium
d1​ = 100 mmd2​ = 200 mm1440 rpmn2​ = ?

A 100 mm pulley at 1440 rpm drives a 200 mm pulley by a belt with 2 % slip. Find the speed n2 of the driven pulley.

n1 = 1440 rpmd1 = 100 mmd2 = 200 mms = 2 %
n2 = rpm
4.Medium
N1​ = 20N2​ = 80

A 7.5 kW motor running at 2900 rpm drives a pinion with 20 teeth, which meshes with a gear with 80 teeth. The gear pair has an efficiency of 98%. Find the torque T1 on the motor shaft.

P = 7.5 kWn1 = 2900 rpmN1 = 20N2 = 80η = 98%
T1 = N·m
5.Hard
d1​ = 200 mmd2​ = 450 mm960 rpmC = 1000 mmT1​ = 800 NT2​P = ?

An open belt connects a 200 mm driving pulley at 960 rpm to a 450 mm pulley; the centres are 1000 mm apart. The coefficient of friction is 0.35 and the tight-side tension may not exceed 800 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 200 mmn1 = 960 rpmd2 = 450 mmC = 1000 mmμ = 0.35T1 = 800 N
P = kW
6.Hard
A = 36B = 45C = 32D = 45

In a compound gear train, gear A (36 teeth) on the input shaft turning at 960 rpm drives gear B (45 teeth). Gear C (32 teeth) is fixed to the same shaft as B and drives gear D (45 teeth) on the output shaft. Find the output speed nout.

nin = 960 rpmA = 36B = 45C = 32D = 45
nout = rpm

Answer key

  1. 1. nC = 2880 rpm
  2. 2. v = 7.54 m/s
  3. 3. n2 = 705.6 rpm
  4. 4. T1 = 24.7 N·m
  5. 5. P = 5.119 kW
  6. 6. nout = 546.1 rpm

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