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
OAB150 NQ = ?100 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 150 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 150 NOA = 100 mmOB = 120 mm
Q = N
2.Easy
O120 N120 NQ = ?140 mm40 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 140 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 140 mmb = 40 mm
Q = N
3.Medium
5 kN5 m2 m1.5 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 2 m above the ground and 1.5 m to the right of A. A vertical load of 5 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 5 mH = 2 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.9 m
FBC = kN
4.Medium
150 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 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 = 25°
Q = N
5.Hard
F = ?1500 N25 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 25 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 = 200 mmh = 25 mm
F = N
6.Hard
F = ?1000 N25 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1000 N at the slider C? Neglect friction and weights.

Q = 1000 NAB = BC = 120 mmh = 25 mm
F = N

Answer key

  1. 1. Q = 125 N
  2. 2. Q = 420 N
  3. 3. FBC = 1.814 kN
  4. 4. Q = 160.8 N
  5. 5. F = 378 N
  6. 6. F = 426 N

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