A time twister was a time travel device.

Casimer received a time twister as an early Christmas present on 23rd century Earth. After the TARDIS got caught in the wake of Casimer's first trip to the past, the Third Doctor chased her through time around Sommerton Manor. He eventually caught her and returned her to her proper timezone in the TARDIS, then took apart the time twister so it could not be used again. (PROSE: The Sommerton Fetch)