The trio forced their way into the kitchen area of the Beefeater restaurant on the Premier Inn site in Little Colliers Field and tried to raid the safe some time between 10.40pm and 11pm on Sunday (October 9).
They threatened staff and asked where the safe was, but were unable to get access to it.
The three men fled empty-handed in a silver Volvo, which had a defective rear light and no front number plate.
The offenders are described as white with local accents.
One was about 6ft with a dark beard and a stocky build.
He wore a balaclava, Nike jogging bottoms and a black top.
He was carrying the sledgehammer.
The second was about 5ft 10in of medium build.
He wore black clothing and was carrying what looked like a crowbar.
The third offender was about 6ft of stocky build and also wore black clothing.
He grabbed a knife from the kitchen to threaten staff, none of who were injured.
The suspects are believed to have made off in a silver Volvo S60 which was captured on CCTV, which is pictured above.
Anyone with information about the armed robbery can contact Northamptonshire Police on 101 or call the independent charity Crimestoppers anonymously on 0800 555111.