meaning of slack, gear, clearance and teeth in this context

[Learning_English]

"Backlash" = "slack in the system, or the taking up of the slack in a system."

A typical example would be the slack in the coupling of rail cars. When a train first starts to move, all the slack must be taken up and you feel the jerks as each car's slack is taken up.

Gears also have clearance between the teeth. If you turn a gear clockwise and then counter-clockwise (anti-clockwise) the clearance is the "backlash" and also the impact of the backlash is called "backlash".

We also use the term "backlash" in connection with firearms. If you pull the trigger of a gun slowly you will release the hammer and fire the weapon. Any travel that the trigger does after the hammer is released from the sear, is called "over-travel" or "backlash".

In any event, I believe that the "backlash" as we hear it most often used nowadays is derived from this earlier usage.

What do the `slack', `sear' and `taking up the slack' mean in the context? [I think, slack may be a `coal' and `taking up the slack' is `fill with coal']
Also please explain the bold parts [Gears........teeth]
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Please let me know if I have made any mistakes in any of my sentences.

[Lost_Soul]

nope, slack here means something which is too loose (here it has to do with a piece of cord conecting any 2 cars )
take a look at this definition of slack: http://dictionary.cambridge.org/define.asp?key=74265&dict=CALD
Maybe someone else will elaborate on your question