The Yoyodyne Propulsion Systems propulsion technology was utilized in DY-500-class starships in the early-2120s and allowed them to serve as early Earth colony ships. (TNG: "Up The Long Ladder", production art)
The propulsion system was also used in the late-23rd century on Whorfin-class starships utilized by El-Aurians. The YPS pulse fusion propulsion system allowed the transports to travel at a maximum warp speed of warp factor 4. (Star Trek Generations, production art)
According to the Star Trek: The Next Generation Companion, the use of the term "Yoyodyne" is a "in-joke" reference to the 1984 cult classic science fiction film The Adventures of Buckaroo Banzai Across the Eighth Dimension!, which in turn took the name from Thomas Pynchon's novels The Crying of Lot 49 and V..