Editing Screw theory (section)

== Wrench ==
A common example of a screw is the ''wrench'' associated with a force acting on a rigid body.  Let ''P'' be the point of application of the force '''F''' and let '''P''' be the vector locating this point in a fixed frame.  The wrench {{nowrap|1=W = ('''F''', '''P''' × '''F''')}} is a screw.  The resultant force and moment obtained from all the forces '''F'''<sub>''i''</sub>, {{nowrap|1=''i'' = 1, ..., ''n''}}, acting on a rigid body is simply the sum of the individual wrenches W<sub>''i''</sub>, that is
: <math> \mathsf{R} = \sum_{i=1}^n \mathsf{W}_i = \sum_{i=1}^n (\mathbf{F}_i, \mathbf{P}_i\times\mathbf{F}_i). </math>

Notice that the case of two equal but opposite forces '''F''' and −'''F''' acting at points '''A''' and '''B''' respectively, yields the resultant
: <math> \mathsf{R}=(\mathbf{F}-\mathbf{F},  \mathbf{A}\times\mathbf{F} - \mathbf{B}\times\mathbf{F}) = (0, (\mathbf{A}-\mathbf{B})\times\mathbf{F}).</math>

This shows that screws of the form
: <math>\mathsf{M}=(0, \mathbf{M}),</math>
can be interpreted as pure moments.