An arm module, modular robot arm or industrial robot has a housing with first and second connection sides. The first connection side has a first connection plate, a first fluid contact device and a first contact device. The second connection side is mechanically connected to the housing in a torque-proof manner, and has a second connection plate. The first fluid contact device and first contact device are arranged on the first connection plate, parallel to a mounting axis. The first connection side is connectable to another arm module. An external thread is arranged about the first mounting axis, on an outer circumferential side of the first connection plate. The second connection plate is circumferentially embraced by a fastening ring with an internal thread corresponding to the external thread. The fastening ring is connected to the housing in an axially fixed manner, rotatable about a second mounting axis.