The Timetables are items retrieved from Davesprite's timeline. They resemble a pair of records floating on rotating gears. By scratching the records, he is able to control the flow of time in a variety of ways. He seems to be able to use standard time travel to go forward and backwards in time and uses this ability in battle. He mentions to Alternate Future Rose that he's spent four months skipping back and forth. After returning to the main timeline, he gives the timetables to Present Dave before jumping into the sprite.
Aradia's Music Box Time Machine
Aradia possesses a similar set of objects, known as her Music Box Time Machine. While Dave's timetables are built on red gears, reminiscent of the ones in the Land of Heat and Clockwork, Aradia's devices appear to be the comb and cylinder of a music box encased in large quartz rocks, reminiscent of her own Land of Quartz and Melody. Just as Dave spins the records to travel through time, she presumably revolves the cylinder forwards or backwards to move along the time stream.