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
O80 N80 NQ140 mm20 mm

The handles of a pair of pliers are squeezed with 80 N each, 140 mm from the pin O, and the jaws grip a wire 20 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 140 mmb = 20 mm
FO = N
2.Easy
4 kN5 m1.2 m1.2 m0.625 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 5 m apart. A vertical load of 4 kN acts on leg AC at the point K, 0.625 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 5 mhorizontal distance A to K = 0.625 m
By = kN
3.Medium
300 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° with the line AC. A downward force of 300 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 300 Nθ = 25°
Q = N
4.Medium
4 kN4 m3 m2.4 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m above the ground and 2.4 m to the right of A. A vertical load of 4 kN acts on member AB at K, 0.6 m (horizontally) from A. Find the force FBC in member BC.

P = 4 kNL = 4 mH = 3 mhorizontal distance A to B = 2.4 mhorizontal distance A to K = 0.6 m
FBC = kN
5.Hard
F = ?1500 N12 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 12 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 120 mmh = 12 mm
F = N
6.Hard
6 kN6 kN3 m2 m0.45 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 m high and 0.45 m to the right of A. Member AB carries a vertical load of 6 kN at K, 0.225 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 = 6 kNQ = 6 kNL = 3 mH = 2 mhorizontal distance A to B = 0.45 mhorizontal distance A to K = 0.225 m
Ax = kN

Answer key

  1. 1. FO = 640 N
  2. 2. By = 0.5 kN
  3. 3. Q = 321.7 N
  4. 4. FBC = 0.68 kN
  5. 5. F = 301.5 N
  6. 6. Ax = 0.3263 kN

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