How does 話{はなし}が噛{か}み合{あ}わない work?


I saw this phrase discussed on esaura.cc

> 話が噛み合わない  
>  'There's a gap in their conversation.'  
>  'They can't meet on common ground.'  
>  'They have been at odds with each other.'  
>  'They have not been on the same page.'

Is this the same `噛み` as in `[噛]{か}み[付]{つ}く` 'to bite (at), to snap at, to
snarl at' or `噛{か}む` 'to bite, to chew, to gnaw'? If so, or if not so, would
anyone care to explain or expand on the metaphoric implications of the
original sentence (on the assumption that it uses a metaphor)?

Here is the original page: <http://esaura.cc/questions/598>




A definition from [Jim Breen's
EDICT](http://jisho.org/words?jap=%E5%99%9B%E3%81%BF%E5%90%88%E3%81%86&eng=&dict=edict):

> 噛み合う かみあう  
>  (v5u,vi) to gear (engage) with; to be in gear (mesh); to bite each other

Gears have teeth, so it could be said that they "bite" into each other.

[![gears](https://i.stack.imgur.com/fl1Ll.gif)](http://en.wikipedia.org/wiki/File:Gears_animation.gif)




A definition from [Jim Breen's
EDICT](http://jisho.org/words?jap=%E5%99%9B%E3%81%BF%E5%90%88%E3%81%86&eng=&dict=edict):

> 噛み合う かみあう  
>  (v5u,vi) to gear (engage) with; to be in gear (mesh); to bite each other

Gears have teeth, so it could be said that they "bite" into each other.

[![gears](https://i.stack.imgur.com/fl1Ll.gif)](http://en.wikipedia.org/wiki/File:Gears_animation.gif)

