Frames & machines worksheet with answers

Free printable Frames & machines 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
O150 N150 NQ = ?90 mm25 mm

A hand squeezes the handles of a pair of pliers with 150 N each, 90 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 150 Na = 90 mmb = 25 mm
Q = N
2.Easy
5 kN3 m1.8 m1.8 m1.125 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3 m apart. A vertical load of 5 kN acts on leg AC at the point K, 1.125 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 5 kNAB = 3 mhorizontal distance A to K = 1.125 m
By = kN
3.Medium
5 kN3 m2.5 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2.5 m above the ground and 0.9 m to the right of A. A vertical load of 5 kN acts on member AB at K, 0.54 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 3 mH = 2.5 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.54 m
FBC = kN
4.Medium
100 NQ = ?20°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 20° with the line AC. A downward force of 100 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 100 Nθ = 20°
Q = N
5.Hard
12 kN6 m1.5 m1 m1.2 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 12 kNAB = 6 mheight of C = 2.5 mheight of DE = 1.5 mhorizontal distance A to K = 1.2 m
C = kN
6.Hard
10 kN6 kN8 m2.5 m3.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 2.5 m high and 3.6 m to the right of A. Member AB carries a vertical load of 10 kN at K, 2.16 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 10 kNQ = 6 kNL = 8 mH = 2.5 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 2.16 m
Ax = kN

Answer key

  1. 1. Q = 540 N
  2. 2. By = 1.875 kN
  3. 3. FBC = 1.175 kN
  4. 4. Q = 137.4 N
  5. 5. C = 7.589 kN
  6. 6. Ax = 2.052 kN

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