Abstract: Flexible transmission devices, for example for use a tool extensions for effecting rotation of fasteners that are difficult or impossible to access straight on using the normal output of a tool. A series of internal couplers are connected together end-to-end by constrained ball and socket joints that allow tilting between the axes of the couplers while constraining relative rotation of the couplers about said axes. The internal couplers form a flexible shaft inside an outer casing formed by a series of collar-shaped links joined in adjacent pairs by a single-axis pivot connection, each positioned to coincide with a respective one of the ball and socket joints.