The machine, mounted e.g. on the front of a tractor (T), consists of at least one cutter bar (1a, 1b, 1c) in the form of a tubular metal frame with a series of modules (2). Each module comprises a rotary cutting tool driven at over 3000 rpm by an individual asynchronous three-phase electric motor. The cutter bars can be straight or curved, and the motors are connected in parallel by three-wire electrical cables.