A flexible shaft drive transmission to be coupled between a coupling of a drive motor and a gear train of a power operated tool, the flexible shaft drive transmission comprising: a) an elongated drive shaft assembly including a rotatable drive transmitting shaft extending along a longitudinal axis (LASDT), a first driven fitting at a first end of the drive transmitting shaft and a second drive fitting at a second end of the drive transmitting shaft, the first driven fitting and the second drive fitting arranged to rotate with the drive transmitting shaft; b) an outer casing comprising a flexible tube and including first and second ends (710,780) and defining a throughbore, the outer casing receiving the drive transmitting shaft within the throughbore and supporting the drive transmitting shaft for rotation within the outer casing; and c) a motor end coupling affixed to the first end of the outer casing and adapted to be releasably connected to the coupling of the drive motor, the motor end coupling including a coupling body defining a central opening through which the drive transmitting shaft passes and characterized in the coupling body having an outer surface defining a tapered region, the tapered region having a proximal end and a distal end, the proximal end of the tapered region of the coupling body being closer in proximity to the outer casing than the distal end of the tapered region, the tapered region tapering from a first diameter (ODPRX) at the proximal end of the tapered region to a second diameter (ODDIS) at the distal end of the tapered region, the first diameter (ODPRX) being larger than the second diameter (ODDIS), the tapered region of the coupling body of the motor end coupling resulting in the coupling body having a configuration of a frustoconical tapered cone arranged to engage and interfit with the coupling of the drive motor, and the tapered region including a plurality of axially extending raised ribs radially spaced apart by a plurality of channels, each pair of adjacent ribs of the plurality of ribs being separated by a channel of the plurality of channels. a) an elongated drive shaft assembly including a rotatable drive transmitting shaft extending along a longitudinal axis (LASDT), a first driven fitting at a first end of the drive transmitting shaft and a second drive fitting at a second end of the drive transmitting shaft, the first driven fitting and the second drive fitting arranged to rotate with the drive transmitting shaft; b) an outer casing comprising a flexible tube and including first and second ends (710,780) and defining a throughbore, the outer casing receiving the drive transmitting shaft within the throughbore and supporting the drive transmitting shaft for rotation within the outer casing; and c) a motor end coupling affixed to the first end of the outer casing and adapted to be releasably connected to the coupling of the drive motor, the motor end coupling including a coupling body defining a central opening through which the drive transmitting shaft passes and characterized in the coupling body having an outer surface defining a tapered region, the tapered region having a proximal end and a distal end, the proximal end of the tapered region of the coupling body being closer in proximity to the outer casing than the distal end of the tapered region, the tapered region tapering from a first diameter (ODPRX) at the proximal end of the tapered region to a second diameter (ODDIS) at the distal end of the tapered region, the first diameter (ODPRX) being larger than the second diameter (ODDIS), the tapered region of the coupling body of the motor end coupling resulting in the coupling body having a configuration of a frustoconical tapered cone arranged to engage and interfit with the coupling of the drive motor, and the tapered region including a plurality of axially extending raised ribs radially spaced apart by a plurality of channels, each pair of adjacent ribs of the plurality of ribs being separated by a channel of the plurality of channels.