A turf groomer is coupled to a reel cutting unit in advance of the cutting reel and is powered by a gearbox having a rotary gear drive that is capable of selectively rotating the turf groomer in opposite directions at different speeds. The rotary gear drive is symmetrical about a plane through the axes of the input and output shafts thereof to permit the gearbox to be inverted to drive the turf groomer from either the left or right sides without requiring that two different models of the gear drive be available. The gearbox is connected to the reel cutting unit only by connecting the end of the input shaft to a shaft of the cutting reel and through a connection to a height adjuster for the turf groomer.