The Collaborative International Dictionary of English v.0.48:

Engaging \En*ga"ging\, a.
   Tending to draw the attention or affections; attractive; as,
   engaging manners or address. -- En*ga"ging*ly, adv. --
   En*ga"ging*ness, n.
   [1913 Webster]

   Engaging and disengaging gear or Engaging and disengaging
   machinery, that in which, or by means of which, one part is
      alternately brought into gear or out of gear with another
      part, as occasion may require.
      [1913 Webster]