There are several time machines, all called rings (except for the chip), that were created at different points in the series and used by different people and organizations.
The Infinity Ring was the first device. It was created by Dak's parents, although Sera was the one who added the 'Missing Piece'. Dak, Sera, and Riq used the Infinity Ring while fixing the Breaks, although it was temporarily damaged in Curse of the Ancients. This is the primary time travel device used in the series.
The Eternity Ring was created by Tilda. She stole the Infinity Ring in Behind Enemy Lines and used Sera's DNA (through hair samples) to return to the future and create the Eternity Ring. It was damaged in Behind Enemy Lines by Dak and completely destroyed in The Iron Empire when Riq smashed it, splashing himself with mysterious fluids.
The first Golden Ring appeared in the end of The Iron Empire, when a mysterious man gave Tilda a Golden Ring, which may have allowed them to travel to different dimensions to recruit Daks and Seras. The second Golden Ring was carried by a Fake Sera who convinced Dak to pilot the Ring to go to the discovery of the gunpowder in Ancient China, where fake Sera drugs Dak through cheese fllled with drugs. They also go to the creation of the hydrogen rocket where Dak escapes and travels to Greece to seek Riq. A fake Dak also approaches Sera and drugs her with tamales, and travels to Galileo's trial. She also escapes and heads back to Riq.
In Eternity, Sera's parents hide a chip inside Riq's shoulder, which allows him to time travel and survive in the present without being an anomaly. This was done because Riq's existence was caused by a Break, therefore after it was fixed, he wouldn't exist if he went to the future without the chip. It is used at will and Riq used it to carry Dak and Sera.