Method of generating a tire profile

A grinding assembly (10) contacts a tire (T) supported by a frame (F) relative to the tire. The grinding assembly includes at least one section, and an axial positioning assembly supporting the at least one section (10A,10B). The axial positioning assembly enables the at least one section to be axially repositioned relative to the tire. The at least one section includes a grinding head (24), where the grinding head includes a grindstone rotatably supported thereon, the grindstone having rounded shoulders at its axial extremities. The grinding assembly further includes a radial positioning assembly (18) supporting the grinding head for radial movement with respect to the tire.