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
N1​ = 72N2​ = 80

A pinion with 72 teeth meshes with a gear with 80 teeth. Both have a module of 1 mm. Find the centre distance a between the two shafts.

N1 = 72N2 = 80m = 1 mm
a = mm
2.Easy
N1​ = 72N2​ = 12

A driving gear with 72 teeth turns at 720 rpm and meshes with a gear with 12 teeth. Find the speed n2 of the driven gear.

N1 = 72N2 = 12n1 = 720 rpm
n2 = rpm
3.Medium
d1​ = 160 mmd2​ = 450 mm2880 rpmn2​ = ?

A 160 mm pulley at 2880 rpm drives a 450 mm pulley by a belt with 4 % slip. Find the speed n2 of the driven pulley.

n1 = 2880 rpmd1 = 160 mmd2 = 450 mms = 4 %
n2 = rpm
4.Medium
d1​ = 80 mmd2​ = 400 mm1500 rpmT1​ = 500 NT2​ = 150 NP = ?

A belt runs on an 80 mm driving pulley at 1500 rpm. The tension is 500 N on the tight side and 150 N on the slack side. Find the power P transmitted, in kW.

d1 = 80 mmn1 = 1500 rpmT1 = 500 NT2 = 150 N
P = kW
5.Hard
d1​ = 120 mmd2​ = 315 mm1500 rpmC = 1000 mmT1​ = 1500 NT2​P = ?

An open belt connects a 120 mm driving pulley at 1500 rpm to a 315 mm pulley; the centres are 1000 mm apart. The coefficient of friction is 0.35 and the tight-side tension may not exceed 1500 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 120 mmn1 = 1500 rpmd2 = 315 mmC = 1000 mmμ = 0.35T1 = 1500 N
P = kW
6.Hard
A = 20B = 25C = 32D = 80

In a compound gear train, gear A (20 teeth) on the input shaft turning at 960 rpm drives gear B (25 teeth). Gear C (32 teeth) is fixed to the same shaft as B and drives gear D (80 teeth) on the output shaft. Find the output speed nout.

nin = 960 rpmA = 20B = 25C = 32D = 80
nout = rpm

Answer key

  1. 1. a = 76 mm
  2. 2. n2 = 4320 rpm
  3. 3. n2 = 983 rpm
  4. 4. P = 2.199 kW
  5. 5. P = 9.096 kW
  6. 6. nout = 307.2 rpm

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