Editing Simple machine (section)

==Self-locking machines==
[[Image:BOLT SCREW UBT 199.JPG|thumb|The [[screw (simple machine)|screw]]'s self-locking property is the reason for its wide use in [[threaded fastener]]s like [[bolt (fastener)|bolts]] and [[wood screw]]s ]]

In many simple machines, if the load force <math>F_{\textrm{out}}</math> on the machine is high enough in relation to the input force <math>F_{\textrm{in}}</math>, the machine will move backwards, with the load force doing work on the input force.<ref name="Gujral2">{{cite book
  | last = Gujral
  | first = I. S.
  | title = Engineering Mechanics
  | publisher = Firewall Media
  | year = 2005
  | page = 382
  | url = https://books.google.com/books?id=JM0OG-XUyu0C&q=%22simple+machine%22+self-locking&pg=PA382
  | isbn = 978-81-7008-636-9}}</ref> So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called ''reversible'', ''non-locking'' or ''overhauling'' machines, and the backward motion is called ''overhauling''.

However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a ''self-locking'', ''nonreversible'', or ''non-overhauling'' machine.<ref name="Gujral2" /> These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left.

Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the [[screw (simple machine)|screw]], [[inclined plane]], and [[wedge (mechanical device)|wedge]]:
* The most common example is a screw. In most screws, one can move the screw forward or backward by turning it, and one can move the nut along the shaft by turning it, but no amount of pushing the screw or the nut will cause either of them to turn.
* On an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
* A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of [[compression (physics)|compression]] force from the wood walls will cause it to pop back out of the block.

A machine will be self-locking if and only if its efficiency <math>\eta</math> is below 50%:<ref name="Gujral2" />

<math display="block">\eta \equiv \frac {F_\text{out}/F_\text{in} }{d_\text{in}/d_\text{out} } < 0.5</math>

Whether a machine is self-locking depends on both the friction forces ([[Coefficient of friction|coefficient of static friction]]) between its parts, and the distance ratio <math>d_{\textrm{in}}/d_{\textrm{out}}</math> (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.

===Proof===
When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy<ref name="Rao">{{cite book
  | last1 = Rao
  | first1 = S.
  | first2 = R.
  | last2 = Durgaiah
  | title = Engineering Mechanics
  | publisher = Universities Press
  | year = 2005
  | pages = 82
  | url = https://books.google.com/books?id=vRR4FKAkJl4C&q=%22simple+machine%22+%22&pg=PA80
  | isbn = 978-81-7371-543-3}}</ref><ref name="Goyal">{{cite book
  | last1 = Goyal
  | first1 = M. C.
  | first2 = G. S.
  | last2 = Raghuvanshi
   | title = Engineering Mechanics
  | publisher = PHI Learning Private Ltd.
  | year = 2009
  | location = New Delhi
  | pages = 202
  | url = https://books.google.com/books?id=vRR4FKAkJl4C&pg=PA82
  | isbn = 978-81-203-3789-3}}</ref> the input work <math>W_\text{1,2}</math> is equal to the sum of the work done on the load force <math>W_\text{load}</math> and the work lost to friction <math>W_\text{fric} </math>
{{NumBlk2|:|<math>W_\text{1,2} = W_\text{load} + W_\text{fric}</math>|Eq. 1}}

If the efficiency is below 50% {{nowrap|(<math>\eta = W_\text{load}/W_\text{1,2} < 0.5</math>):}}

<math display="block">2W_\text{load} < W_\text{1,2} \,</math>

From {{EquationNote|Eq. 1}}
<math display="block">\begin{align}
2W_\text{load} & < W_\text{load} + W_\text{fric} \\
W_\text{load} & < W_\text{fric}
\end{align}</math>

When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction <math>W_\text{fric}</math> is the same

<math display="block">W_\text{load} = W_\text{2,1} + W_\text{fric}</math>

So the output work is
<math display="block">W_\text{2,1} = W_\text{load} - W_\text{fric} < 0</math>

Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force.