Extension piece for a motorised drive device equipped with a body which contains drive means for driving an output shaft in rotation, characterised in that the drive means are drive means for driving the output shaft in rotation and in translation relative to the body, and in that the extension piece comprises: - two sub-assemblies (30, 31) which are free in rotation and in translation relative to one another, namely: • an inner sub-assembly which comprises a flexible hose for transmitting torque and thrust force, equipped at its proximal end with a first torque input connector adapted to be fixed to a fixing end-piece of the output shaft of the device, and at its distal end with a tool attachment; and • an outer sub-assembly which comprises a sheath surrounding the flexible hose with a radial clearance, the sheath having or being able to assume a non-linear form; the sheath having at its proximal end proximal means for fixing to the body of the drive device; - a rigid tool guide fixed in a removable manner to the distal end of the sheath; - a pre-extension piece which itself comprises: • a shaft for transmitting torque and thrust force, equipped at its proximal end with a second torque input connector identical in configuration to said first torque input connector, and at its distal end with a second fixing end-piece identical in configuration to the fixing end-piece of said output shaft; and • a rigid tube for guiding the transmission shaft in rotation and in translation, that tube having at its proximal end means for fixing to the body of the drive device, and at its distal end means for fixing of the proximal end of the sheath. - two sub-assemblies (30, 31) which are free in rotation and in translation relative to one another, namely: • an inner sub-assembly which comprises a flexible hose for transmitting torque and thrust force, equipped at its proximal end with a first torque input connector adapted to be fixed to a fixing end-piece of the output shaft of the device, and at its distal end with a tool attachment; and • an outer sub-assembly which comprises a sheath surrounding the flexible hose with a radial clearance, the sheath having or being able to assume a non-linear form; the sheath having at its proximal end proximal means for fixing to the body of the drive device; • an inner sub-assembly which comprises a flexible hose for transmitting torque and thrust force, equipped at its proximal end with a first torque input connector adapted to be fixed to a fixing end-piece of the output shaft of the device, and at its distal end with a tool attachment; and • an outer sub-assembly which comprises a sheath surrounding the flexible hose with a radial clearance, the sheath having or being able to assume a non-linear form; the sheath having at its proximal end proximal means for fixing to the body of the drive device; - a rigid tool guide fixed in a removable manner to the distal end of the sheath; - a pre-extension piece which itself comprises: • a shaft for transmitting torque and thrust force, equipped at its proximal end with a second torque input connector identical in configuration to said first torque input connector, and at its distal end with a second fixing end-piece identical in configuration to the fixing end-piece of said output shaft; and • a rigid tube for guiding the transmission shaft in rotation and in translation, that tube having at its proximal end means for fixing to the body of the drive device, and at its distal end means for fixing of the proximal end of the sheath. • a shaft for transmitting torque and thrust force, equipped at its proximal end with a second torque input connector identical in configuration to said first torque input connector, and at its distal end with a second fixing end-piece identical in configuration to the fixing end-piece of said output shaft; and • a rigid tube for guiding the transmission shaft in rotation and in translation, that tube having at its proximal end means for fixing to the body of the drive device, and at its distal end means for fixing of the proximal end of the sheath.