The Paradox machine was a type of technology that was capable of creating a tear in space and time.
The Master used such a machine by cannibalising the Doctor's TARDIS in order to allow his army of Toclafane to invade Earth. The device created a tear in the sky, allowing millions of the sphere-like aliens to attack the planet and its populace. (DW: The Sound of Drums) However the TARDIS still managed to apparently partly preserve itself as it kept the same appearance and seemed to be ringing its cloister bell even though (until the Doctor found it) nobody could hear. It is not known exactly when the Master cannibalised the TARDIS but it is assumed he did it after he had taken Lucy to the end of the universe but before he became Prime Minister.
The device was designed to prevent a time paradox from occurring and The Master called it his "masterpiece". As the Toclafane were Humans from the future, their attacks on their ancestors would normally have meant that they were destroying themselves and thus would have been erased from history. However, the use of the paradox machine prevented such an outcome from happening, allowing the Toclafane to continue their enslavement of their ancestors. The device was destroyed by Captain Jack Harkness who shot it with a machine gun. The destruction of the Paradox Machine reversed time to the point it was activated undoing everything that had occured since then. (DW: Last of the Time Lords)
The appearance of the paradox machine was a dark glow of red all around the inside and the main console was contained inside a metal cage, the console had gone under many modifications and various appendages were attached to it by the Master. Emerging from the console was a pipe going to another area of the TARDIS and on this was a dial showing the pressure build-up inside. It is unknown exactly how much of the TARDIS was cannibalised or whether any other rooms were lost or ejected. However, the paradox machine appeared to somehow use steam power and pressure as when it was activated it shot out steam in puffs from the console.
- As the TARDIS was capable of preventing a paradox as long as the people creating the paradox stayed inside, the machine may have simply increased this power so that it could be used outside of the TARDIS.