An abrasive profiling tool that may be part of a robotic machining system for machining a trailing edge of an airfoil, includes a shank extending along a rotational axis, a bearing guide rotationally secured to a distal end of the shank for riding upon the airfoil; and an abrasive profiler projecting radially and rigidly outward from the shank for grinding at least the trailing edge as the shank rotates. The profiler may include a round-over portion for grinding the trailing edge and a chamfered blending portion for grinding adjacent surfaces of the airfoil to produce a smooth transition from the adjacent surfaces and to the trailing edge.