hi martin,
there is a wealth of info on the net and in old weighty books on the 3 legged double beat escapement.
i had the custody of St John's Church Cardiff clock (plus the bells) for many years, the Gillett and Johnston clock having the 3 legged double beat escapement. when you make the parts i think you will find all becomes clear plus clearances etc.
originally designed by Sir Edmund Denison later Lord Grimthorpe for the clock in the tower of Big Ben in the Houses of Parliament. (though im no horoligical expert, so if im wrong please feel free to correct me!)
cheers,
julian