Stand for making twisted pairs (see figure): two vices at a needed length from each other (e.g 4 m). One holds a coil with wire (it should rotate freely), another holds a portable drill with a hook clumped in it. The hook should be covered with a soft material to protect wire isolation (a piece of thick aluminium wire in PVC isolation, or covered with adhesive tape, etc.)
Wire is pulled from the coil to the hook and back and then cut. Weights are attached to both ends. For thicker and harder wire heavier weights should be used. For 0.140 mm constantan wire I use M8x40 bolts with nuts, for 0.080 mm copper wire - M6x20 bolts. Weights can be attached with a pieces of adhesive tape.
One person holds both ends of the wire using two fingers. Wire goes around fingers and weights can freely rotate. Another person switches the drill. While the wires are twisting, distance between ends should be decreased to keep angle more or less constant.
When twisting is finished, take the pair firmly with fingers and cut away weights without releasing pair tension. Then slowly release the pair letting it rotate backward a few turns. You should get a staight pair without any curling.