Bi-directional, constant velocity, carriage shuttling mechanisms particularly suitable for use in dot matrix line printers, are disclosed. The carriage shuttling mechanisms comprise a pair of identically sized bi-lobed, second order elliptical gears (41, 45) connected together in a 90.degree. phase relationship either directly or via a belt. One of the bi-lobed gears is rotated at a constant velocity and the other is eccentrically linked (47) to the carriage (11) to be bi-directionally shuttled at a constant velocity.