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
O120 N120 NQ = ?90 mm18 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 90 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 90 mmb = 18 mm
Q = N
2.Easy
O150 N150 NQ120 mm25 mm

The handles of a pair of pliers are squeezed with 150 N each, 120 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 150 Na = 120 mmb = 25 mm
FO = N
3.Medium
8 kN5 m1.2 m0.8 m1.875 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 m apart, with its apex pin C 2 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 8 kN acts on leg AC at K, 1.875 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 5 mheight of C = 2 mheight of DE = 1.2 mhorizontal distance A to K = 1.875 m
T = kN
4.Medium
150 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 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 20°
Q = N
5.Hard
10 kN4.8 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 2.4 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 4.8 mheight of C = 2.4 mheight of DE = 0.8 m
T = kN
6.Hard
F = ?3000 N8 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 8 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 120 mmh = 8 mm
F = N

Answer key

  1. 1. Q = 600 N
  2. 2. FO = 870 N
  3. 3. T = 9.375 kN
  4. 4. Q = 206.1 N
  5. 5. T = 7.5 kN
  6. 6. F = 400.9 N

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