Inside the Torchwood Hub
The Rift Manipulator that was located in the Torchwood hub was designed to control the Cardiff Rift. A central piece of Torchwood's activities in Cardiff, it was hidden inside the Water Tower sculpture dominating Roald Dahl Plass, which ran right down to the main hall of the hub itself. If activated, the Water Tower acted akin to an amplifier/antenna for the Rift Manipulator (TV: Captain Jack Harkness, End of Days). It could, to a limited degree, stabilise the Rift or open the Rift wider. It had very hit-or-miss effects.
The Manipulator was used to rescue Jack Harkness and Toshiko Sato after the Rift sent the two into 1941. Owen Harper, sick and tired of "living in its shadow" decided to use the Manipulator to try and bring them back. Owen first had to find several missing components of the Manipulator, one in the possession of Bilis Manger and the other in the safe in Jack's office. He also had to use the Rift equations which Tosh had written in 1941 and left for her team-mates to find in the future, so that they could rescue Jack and her.
Owen and Ianto Jones fought. Ianto was certain that Owen should not use the Manipulator. In the fight, he shot Owen in the shoulder, but not before Owen successfully reactivated the Manipulator. With the Rift opened, Jack and Tosh walked through the Rift back to their time period. (TV: Captain Jack Harkness)
Owen's use of the Manipulator caused the Rift to fracture across parts of the entire Earth, causing time slips worldwide. More Weevils than ever appeared in Cardiff. With the exception of Jack, the Torchwood Three team saw visions of missing loved ones tempting them to use the Manipulator to open the Rift so that the Rift could undo the damage it was causing. The death of Gwen Cooper's love, Rhys Williams, brought Gwen to believe that opening the Rift would bring Rhys back, so she joined Tosh, Ianto and Owen in a mutiny against Jack.
The mutinying team took retinal scans of themselves and of Jack to unlock the Rift Manipulator, and successfully activated it and opened the Rift, unintentionally releasing Abaddon in the process. (TV: End of Days)
Captain John Hart used the Rift Manipulator to cause a Rift surge at Cardiff Castle to send himself and Jack to 27 AD Cardiff, where Jack was to be buried beneath the city as it grew on top of him. (TV: Exit Wounds)
The Rift Manipulator was later used by Jack, Ianto and Gwen in conjunction with Mr Smith to manipulate the Rift and boost the signal of Martha Jones' superphone and contact the Tenth Doctor, who was outside of the Medusa Cascade as a result of the Earth being stolen. (TV: The Stolen Earth)
The Manipulator was subsequently used again to send the Rift's energy to the TARDIS for a tow rope for the Earth to be taken back to where it belonged. With the energy looped around the TARDIS by Mr Smith, this plan worked. (TV: Journey's End)
In 2009, the Rift Manipulator was destroyed when a bomb detonated in the Hub. (TV: Children of Earth: Day One) However, parts from the Rift Manipulator were later salvaged by Torchwood, using them to create a tracker to trace residual space-time holes following the closure of the Cardiff Space-Time Rift. (AUDIO: More Than This)
The Rift equations
Toshiko Sato developed equations to serve as guidelines to operate the Manipulator. With the possible exception of Jack Harkness (TV: Captain Jack Harkness) and John Hart, (TV: Exit Wounds) who had come from a more technologically advanced time, of all of the Torchwood Three team, Tosh seemed to have the greatest understanding of how to operate the machine. (TV: Captain Jack Harkness)
Two parts of the Rift Manipulator, both crucial to its activation, remained absent: one, kept in Jack's safe, the other in the possession of Bilis Manger, inside a grandfather clock. (TV: Captain Jack Harkness)
Portable Rift manipulator
In 1918, Gerald Carter and Harriet Derbyshire were given instructions by a future version of Tommy Brockless to send Tommy into suspended animation so he could use the portable Rift Manipulator to close the time shifts and prevent the two times from happening simultaneously at the moment he was in both times.
In the 21st century, Tommy awoke and gave Gerald and Harriet their message. After doing this, Tommy returned to 1918, but entered a state of shell shock. Toshiko Sato projected a psychic image of herself and reminded Tommy to turn the mechanism. He did so, stopping the time shifts. (TV: To the Last Man)
Behind the scenes
The series 1 version of the Torchwood website had a "rift memo", dated 13 April 1913. It alerted the "chief" that on that day there was a sudden increase in Rift activity that manifested as "a series of small ground tremors". It was concerned about Robertson's conclusions from the data: it seemed to be a ripple from a "much bigger" event, or "[a]n aftershock washing back to towards us through time – call it a preshock, if you will." Robertson calculated that it orginated at some point in the 21st century. The memo claimed that Cardiff has "got about a century to go before the rift tears it apart." It said it "might be an idea" to increase safeguards on the rift manipulator.