The peaks of Thangorodrim were insanely tall peaks on top of Angband.
A tunnel ran under the Iron Mountains from Thangorodrim in the south to Angband in the North. Thangorodrim was built over the entrance to the tunnel and was the gatehouse of Angband.
People have been building and maintaining and repairing tall towers for hundreds and thousands of years. There is a 36 foot tall statue of William Penn 547 feet above the ground at the top of the tower of the Philadelphia, Pennsylvania city hall. It is a custom to dress the statue in a giant team jersey when a Philadelphia team wins a championship. I think that the maintenance crew could find a way to chain someone to the side of the tower if ordered to by a dictator.
It is a trivial problem to think of ways Maedhros could have been chained to the side of a Thangorodrim tower. With the available evidence it probably is an impossible problem to deduce which way was used.