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
O80 N80 NQ = ?110 mm35 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 110 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 110 mmb = 35 mm
Q = N
2.Easy
O120 N120 NQ140 mm15 mm

The handles of a pair of pliers are squeezed with 120 N each, 140 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 120 Na = 140 mmb = 15 mm
FO = N
3.Medium
200 NQ = ?12°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 12° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 12°
Q = N
4.Medium
200 NQ = ?5°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 5° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 5°
Q = N
5.Hard
8 kN5 kN5 m2 m0.75 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 high and 0.75 m to the right of A. Member AB carries a vertical load of 8 kN at K, 0.45 m (horizontally) from A, and a horizontal load of 5 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 8 kNQ = 5 kNL = 5 mH = 2 mhorizontal distance A to B = 0.75 mhorizontal distance A to K = 0.45 m
Ax = kN
6.Hard
w = 5 kN/m6 kN2 m0.4 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 5 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 5 kN/mP = 6 kNAD = 2 mAB = 2.4 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. Q = 251.4 N
  2. 2. FO = 1240 N
  3. 3. Q = 470.5 N
  4. 4. Q = 1143 N
  5. 5. Ax = 0.78 kN
  6. 6. FCD = 24 kN

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