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 = ?200 mm150 mm

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

F = 200 NOA = 200 mmOB = 150 mm
Q = N
2.Easy
15 kN2.4 m1 m2 m0.9 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2.4 m apart. A vertical load of 15 kN acts on leg AC at the point K, 0.9 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 2.4 mhorizontal distance A to K = 0.9 m
By = kN
3.Medium
OAB80 NQ300 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (300 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 300 mmOB = 100 mm
FO = N
4.Medium
250 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 250 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 250 Nθ = 15°
Q = N
5.Hard
2 kN2 m1.8 m2.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 4 m high, and are tied by the horizontal bar DE at 1.8 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 2 mheight of C = 4 mheight of DE = 1.8 m
T = kN
6.Hard
12 kN1.5 kN2.5 m2.5 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2.5 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 1.5 kNAB = 2.5 mAC = 2.5 m
T = kN

Answer key

  1. 1. Q = 266.7 N
  2. 2. By = 5.625 kN
  3. 3. FO = 253 N
  4. 4. Q = 466.5 N
  5. 5. T = 1.818 kN
  6. 6. T = 18.03 kN

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