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
O100 N100 NQ = ?80 mm15 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 80 mm from the pin O. The jaws grip a bolt 15 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 80 mmb = 15 mm
Q = N
2.Easy
O50 N50 NQ = ?100 mm35 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 100 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 100 mmb = 35 mm
Q = N
3.Medium
500 NQ = ?10°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 10° 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 = 10°
Q = N
4.Medium
OAB200 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 150 mmOB = 150 mm
FO = N
5.Hard
20 kN8 kN5 m3 m1.5 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 3 m high and 1.5 m to the right of A. Member AB carries a vertical load of 20 kN at K, 0.6 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 20 kNQ = 8 kNL = 5 mH = 3 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.6 m
Ax = kN
6.Hard
5 kN3 m0.8 m1.7 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 5 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 3 mheight of C = 2.5 mheight of DE = 0.8 mhorizontal distance A to K = 0.75 m
C = kN

Answer key

  1. 1. Q = 533.3 N
  2. 2. Q = 142.9 N
  3. 3. Q = 1418 N
  4. 4. FO = 282.8 N
  5. 5. Ax = 0.4 kN
  6. 6. C = 1.667 kN

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