Dalek time machine (The Chase)

The first Dalek time machine, (TV: The Chase) also known as simply the Dalek spacecraft, (AUDIO: The Daleks) was roughly comparable in abilities to a Time Lord TARDIS, and, indeed, easier to steer accurately than the Doctor's TARDIS. It was dimensionally transcendent and created for the express purpose of chasing the First Doctor through time and space.

Operation
According to the Dalek Survival Guide, the crew of the time machine were actually criminals forced to chronicle Dalek history as punishment. These prisoner Daleks noticed the Doctor using a Time-Space Visualiser before being pursued by a squad of Daleks they recognised as their future selves. They knew the Visualiser was scientifically impossible, but in order to ensure their future freedom, they built what would serve as an apparent Time-Space Visualiser that actually displayed recordings of the Daleks' human slaves performing reenactments of the events they knew the Doctor and his companions would view.

The criminal Daleks smuggled themselves out of prison, but were allowed to continue their plan by the Dalek Supreme, who knew they were incompetent and broadcast their attempt for the amusement of other Dalek chroniclers. The criminal Daleks left their fake visualiser on the Xeron Space Museum for the Doctor to find. One of the Daleks was killed by a Morok curator due to not paying admission and became an exhibit, while the rest were indeed those that chased the TARDIS crew through time. (PROSE: Dalek Survival Guide)

It enabled the Doctor's companions Ian Chesterton and Barbara Wright to return home. At first the Doctor refused, insisting it was too dangerous but he changed his mind. The Doctor instructed the pair to set the ship for self-destruction after it had transported them to London on 26 June 1965. (TV: The Chase; PROSE: The Time Travellers)

Legacy
This operation consumed all of the Daleks' taranium supply and this with the destruction of the time machine, (PROSE: The Chase) severely crippled the Daleks' existing time travel research, (PROSE: Mission to the Unknown) though it also deprived the Time Lords of an opportunity to study Dalek time technology, as they would lament during the Last Great Time War. (PROSE: Dalek Combat Training Manual) Through strenuous, long-term efforts the Daleks eventually harvested sufficient quantities of taranium to continue to use the time machines and proceed with the research. (PROSE: The Mutation of Time) The Daleks later constructed a modified version which would pursue the Doctor during the Time Destructor Incident. (PROSE: Dalek Combat Training Manual)