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
O120 N120 NQ = ?80 mm18 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 80 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 80 mmb = 18 mm
Q = N
2.Easy
O150 N150 NQ140 mm35 mm

The handles of a pair of pliers are squeezed with 150 N each, 140 mm from the pin O, and the jaws grip a wire 35 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 150 Na = 140 mmb = 35 mm
FO = N
3.Medium
200 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 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 = 25°
Q = N
4.Medium
8 kN2 m2 m1.6 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, 3.6 m high, and the horizontal tie DE is 2 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2 mheight of C = 3.6 mheight of DE = 2 m
C = kN
5.Hard
5 kN6 kN8 m2 m4.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 2 m high and 4.8 m to the right of A. Member AB carries a vertical load of 5 kN at K, 2.4 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 6 kNL = 8 mH = 2 mhorizontal distance A to B = 4.8 mhorizontal distance A to K = 2.4 m
Ax = kN
6.Hard
15 kN3 kN3 m2 m0.45 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2 m high and 0.45 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.18 m (horizontally) from A, and a horizontal load of 3 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 3 kNL = 3 mH = 2 mhorizontal distance A to B = 0.45 mhorizontal distance A to K = 0.18 m
Ax = kN

Answer key

  1. 1. Q = 533.3 N
  2. 2. FO = 750 N
  3. 3. Q = 214.5 N
  4. 4. C = 4.717 kN
  5. 5. Ax = 1.2 kN
  6. 6. Ax = 0.6975 kN

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