A transmission system for transmitting a change of speed between two rotating shafts, includes a planetary gear box having a sun gear arranged for rotation with a first shaft travelling at a first speed. Planet gears contained within a ring gear are arranged to orbit the sun gear when the sun gear rotates and the ring gear is in a fixed position. Each planet gear is mounted for rotation on a centrifugal carrier. An output carrier includes a body having arms and the arms are each aligned with an axis of rotation of a planet gear and held to the centrifugal carrier by one or more supports extending in a radial plane. An output shaft extends from the body in coaxial alignment with the input shaft. A connector which is stiff in a radial dimension but flexible under torsional load is arranged between the output carrier and the centrifugal carrier.