Abstract: An arrangement for grinding the hardmetal pins of drill bits, e.g. the tungsten carbide buttons (31) of button bits (1), comprises means (parallel arms pairs 9 and 10) for adjusting the position of a grinding pin (15) in relation to the drill bit (1) and also journalling means (4) operative to cause the grinding machine (3) to move relatively slowly in a circuit path around the button on the drill bit (1) to be ground and to cause the grinding pin (15) to rotate rapidly around its longitudinal axis. The drill bit is clamped securely in a stationary holder arrangement (2) which includes a tiltable table (35) which can be adjusted to and locked in selected angular positions.