definition of cylindrical grinding machine. cylindrical, conical or other shaped surface of the outer surface and the shoulder end of the grinding machine. the workpiece is supported between the two tips of the head frame and the tailstock, and is rotated by the dial of the head frame for circular feeding motion.,wondering about getting a cylindrical grinder,jul 25, 2021 2006. first off, either fix current lathe, or get a better lathe, a cylindrical grinder is not the answer for a bad lathe. i have a nice grinder, but it does not get used much. if you decide you really want one, keep your eyes open, they can be had for less than 5k if you are patient. 07-25-2021, 0258 pm 17.