The present invention relates to a machining unit for use on a machine tool, having a head carrier (K) that is attachable to the machine tool, having a head carrier housing (K1), a swivel head (SW) that is provided to swivel relative to the head carrier (K) about a swivel head rotation axis and has a swivel head housing (SW1), a spindle head (SP) that is attached to the swivel head (SW) and has a working spindle (SP1), and a cable run (L) that extends inside the head carrier housing (K1) to the swivel head (SW) and has a plurality of members (1) that are arranged in succession along the cable run (L) and are connected movably together. Adjacent members (1) are in this case able to rotate and swivel relative to one another, and each member (1) has a central piece (2) and a sheathing (31, 32) spaced apart therefrom. The central piece (2) is connected to the sheathing (31, 32) via one or more connecting elements (4).