in fig1 the bed of a grinding machine 10 has mounted thereon a slideway 12 , 13 on which a z - axis platform 14 is mounted for movement parallel to the z - axis , i . e . the axis of rotation of a workpiece generally designated 16 carried between centers 18 and 20 . a z - axis drive 22 moves the platform 14 on the slideway 12 , 13 to position the platform axially relative to the z - axis and therefore the workpiece 16 . carried on a second slideway 24 , 25 is a wheelhead 26 on which is mounted a motor 28 carrying a large diameter conventional grinding wheel 30 . an x - axis drive 32 serves to move the wheelhead 26 perpendicular to the z - axis along the slideway 24 , 25 to advance and retract the wheel 30 . the workpiece 16 includes two cylindrical regions 34 and 36 with a radial shoulder 38 between the larger diameter region 34 and the smaller diameter region 36 . the centre 18 extends from a fixed tailstock 40 and the centre 20 from a headstock 42 which includes a rotational drive motor 44 and driving device 46 for engaging a pin 48 which protrudes from the larger diameter end 34 of the workpiece 16 . the engagement between 46 and 48 causes the workpiece to be rotated relative to the centers 18 and 20 around the z - axis . a computer 50 provides control signals for the x and z drives and receives signals from one or more gauges such as 52 and optionally 53 to control the motion of the platform 14 and wheelhead 26 carried thereon so that the wheelhead and therefore the grinding wheel 30 moves relative to the machine 10 along the dotted line 54 . the computer 50 is programmable so as to alter the angle that line 54 makes to the z - axis and is also programmable so as to perform conventional plunge grinding to cylindrically grind one or both of the cylindrical regions 34 and 36 of the workpiece as required . fig1 a shows in larger scale the movement of the grinding wheel 30 towards the junction between the smaller diameter region 36 and the larger diameter region 34 of the workpiece 16 shown in fig1 . the direction of movement between the grinding wheel 30 and the workpiece is shown by the dotted line 54 in fig1 a . fig2 is similar to that of fig1 except that the wheelhead is mounted for movement parallel to the x direction only on two slideways 56 and 57 carried by the machine 10 . movement parallel to the z - axis is achieved by mounting the tailstock and headstock on a carriage 58 having its own z drive 60 . relative movement between the wheel 30 and the workpiece generally designated 16 achieved so as to describe a similar movement to that of fig1 along a line such as 62 ( shown in fig2 ), by supplying appropriate signals from a computer 50 to the x and z drives 32 and 60 so that as the wheelhead 26 is moved towards the workpiece , so the carriage 58 is moved along the z - axis . to this end the carriage is slidable on a second slideway 64 , 65 also mounted on the machine 10 . fig3 is similar to fig1 in that a grinding wheel is carried by a wheelhead 26 having an x - axis drive 32 for movement perpendicular to the z - axis on a slideway ( not shown ) carried by a platform 14 ′, itself slidable on rails 12 ′ and 13 ′ carried by the machine 10 . a z - axis drive 22 moves the platform 14 ′ along the rails 12 ′, 13 ′ parallel to the z - axis . a computer 50 provides appropriate control signals for the x and z drives 32 and 22 so that the wheelhead 26 describes a path parallel to the dotted line 70 so as to bring the wheel into engagement with the workpiece . as best seen in fig3 a , the grinding wheel edge is formed to provide major and minor frusto - conical grinding surfaces 72 and 74 respectively . the two surfaces are orthogonal so that when viewed edge , the two surfaces define two perpendicular edges 76 and 78 which are parallel respectively to the smaller diameter cylindrical surface 36 and the radial surface 38 between it and the larger diameter workpiece region 34 . by moving the grinding wheel in the direction of the arrow 80 towards the vertex between the radial surface 38 and the cylindrical surface 36 , so material can be removed from the workpiece in a single plunge grind . material still to be removed by the plunge grind is shown in the cross - hatched area 82 between the two frusto - conical surfaces 72 and 74 , and the workpiece . it is to be understood that the modified grinding wheel shown in fig3 and 3 a can also be used to remove material from the cylindrical surface 36 and / or the surface 34 away from the shoulder 38 by plunge grinding so as to bring the frustoconical surface 72 into grinding contact with the cylindrical surfaces of the workpiece as appropriate . referring back to fig1 a , it will be seen that if the grinding wheel 30 is moved closer in towards the shoulder 38 and cylindrical surface 36 along the line 54 as previously described , a point will be reached where the circular face 31 of the grinding wheel 30 will come into contact with a material which is to be removed from the shoulder 38 and the cylindrical surface 33 of the wheel 30 will simultaneously come into contact with the material which is to be removed from the cylindrical surface 36 so that continued movement along the line 54 will simultaneously remove material from the shoulder 38 and the region 36 of the workpiece until the vertex is reached and the material forming the surface 36 has been ground to size and the shoulder 38 ground back to the desired axial position along the length of the workpiece by engagement with the face 31 . in each of the cases described the grinding wheel is typically comprised of a central circular core and an abrasive annular layer containing cbn grit although it is to be understood that any other appropriate grinding material may be employed . it is of course necessary for the annular region of the grinding grit to extend radially inwardly by more than the radial depth of the shoulder which is to be ground such as 38 and in the case of the angular wheel such as shown in fig3 and 3 a , needs to have a sufficient depth to enable the two frustoconical surfaces to be formed . since wear will occur and there will be a need to redress some of the surfaces of the wheel as it is used , the annulus is of sufficient radial extent to accommodate the anticipated wear and redressing requirements so as to give the wheel a useful life before it has to be demounted and replaced .