The accessory e.g. lamp for illumination of the hand-held instrument (L) and the excitation coils (B1-B3) of the brushless motor (M) are all supplied with current through a rotary connector (F) from a control circuit (C1) within a fixed part of the machine or power cable. Positive and negative supply lines (L1, L2) from a voltage source (S) feed three pairs of controlled transistor switches (CE1-CE3) whose midpoints (P1-P3) are wired to terminals (b1-b3) of the star-connected coils. The lamp is fed from a separate controlled switch (T4) wired to one (N1) of its terminals; the other (N2) is returned to the free terminal (b3) of one coil.