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What are the parts of a spanner?

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Parts of a spanner: head, shaft, profile.

Head

Single head of spanner used to grip the nut of a fixing. Spanners have one or two heads. The head is the part of the tool that fits over, around or into the fastener to grip it.

Profile

Profile has contact with nut because of its size and shape. The profile is the shape and size of the part of the head that makes contact with the fastener. Spanners have fixed profiles meaning they only fit one size and shape of fastener and cannot be adjusted (see Are there any alternatives to spanners? for similar, adjustable tools known as ‘adjustable wrenches’).
Head size of spanners is between the flat surfaces of the jaws corresponding to the head of the nut or bolt size. The size of the spanner is usually the width between two flat sides of the profile, the same distance as the width across the top of a nut or bolt with a corresponding profile. The exceptions to this rule are the older standard sizes (see What spanner sizes are available?).
Imperial and metric systems are both used to define spanner sizes and fasteners. The sizes can be in metric or imperial units. Modern imperial sizes are often written with the abbreviation AF which stands for ‘across flats’ and indicates the size is the width between the flat sides of the profile, as above.
 AC across corners, this measurement is not used to define spanner profile sizes Another measurement that could be taken is the width between two opposite corners of the profile, this would be indicated with AC (‘across corners’) but is not used to define spanner size.

Shaft

Holding the spanner by the shaft to use it as a handle and lever to turn the nut. The shaft is the handle of the spanner. It is gripped by the user and used as a lever to turn the fastener gripped by the head.
Shaft length increases with profile size because it needs to be a bigger lever. The length of the shaft increases with the size of the profile. Larger fasteners need more leverage to turn them so the handle needs to be longer and stronger.
Stubby spanners have short shafts so they can be transported around. Most spanners have shafts long enough to be held by one or two hands but some have a ‘stubby’ design so they fit into a smaller space. Remember that these don’t have so much leverage.