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
OAB120 NQ = ?100 mm150 mm

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

F = 120 NOA = 100 mmOB = 150 mm
Q = N
2.Easy
12 kN6 m1 m3.5 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 6 m apart. A vertical load of 12 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 6 mhorizontal distance A to K = 1.5 m
By = kN
3.Medium
15 kN6 m1.8 m2.2 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 6 mheight of C = 4 mheight of DE = 1.8 mhorizontal distance A to K = 0.75 m
T = kN
4.Medium
OAB300 NQ120 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 300 N at A (120 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 300 NOA = 120 mmOB = 100 mm
FO = N
5.Hard
F = ?2500 N15 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 15 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2500 N at the slider C? Neglect friction and weights.

Q = 2500 NAB = BC = 150 mmh = 15 mm
F = N
6.Hard
10 kN6 m1.8 m2.7 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 4.5 m high, and are tied by the horizontal bar DE at 1.8 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 6 mheight of C = 4.5 mheight of DE = 1.8 m
T = kN

Answer key

  1. 1. Q = 80 N
  2. 2. By = 3 kN
  3. 3. T = 2.557 kN
  4. 4. FO = 468.6 N
  5. 5. F = 502.5 N
  6. 6. T = 8.333 kN

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