Quadriggers were engineers on Gallifrey who worked on TARDISes. Stoyn was a Quadrigger who was working on decommissioning the Doctor's TARDIS when the First Doctor stole it. (AUDIO: The Beginning)
Quadriggers were set to work on a TARDIS stolen by the Master when he first left Gallifrey. With the Quadriggers never having a chance to overhaul the craft, the TARDIS fell apart almost as soon as the Master used it to escape. (AUDIO: The Destination Wars)
Later advancements in TARDIS technology had rendered the Quadriggers largely obsolete by the time of the Type 54 TARDIS. (AUDIO: Luna Romana)
Quadriggers utilised many items of equipment including Ganywrenches and Inspection panoptics. (AUDIO: The Beginning [+]Loading...["The Beginning (audio story)"]) Another piece of their equipment allowed them to have a portable console to effectively work a TARDIS, Heleyna used one in her mission for the Dalek Time Strategist in Vassarian's TARDIS. (AUDIO: Eye of Harmony)