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
OAB200 NQ = ?150 mm100 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 100 mm above O. Find Q.

F = 200 NOA = 150 mmOB = 100 mm
Q = N
2.Easy
4 kN3 m1.5 m2.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 4 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 4 kN acts at C. Find the tension T in the tie DE.

P = 4 kNAB = 3 mheight of C = 4 mheight of DE = 1.5 m
T = kN
3.Medium
500 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 500 Nθ = 15°
Q = N
4.Medium
10 kN4 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 4 mheight of C = 2.4 mheight of DE = 0.8 m
C = kN
5.Hard
6 kN3 kN2 m2 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 3 kNAB = 2 mAC = 2 m
A = kN
6.Hard
F = ?3000 N20 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 20 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 = 150 mmh = 20 mm
F = N

Answer key

  1. 1. Q = 300 N
  2. 2. T = 1.2 kN
  3. 3. Q = 933 N
  4. 4. C = 8.004 kN
  5. 5. A = 7.649 kN
  6. 6. F = 807.2 N

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