There is provided a transmission device comprising a rigid casing configured to be mounted perpendicularly on a pair of parallel rotatable driving and driven shafts. Annular driving and driven gears are provided in the casing. The annular driving gear is adapted for rotating simultaneously with the driving shaft, and is also adapted for forwarding rotational motion of the inner section to a transmission device. The annular driven gear is adapted for engaging and rotating simultaneously with the driving shaft and sliding over the same, and for forwarding to the inner section rotational motion received from the transmission device. The transmission device is rotatively connected to the annular driving and driven gears for transmitting rotational movement of the driving shaft to the driven shaft. There is also provided a portable boring-welding apparatus using this transmission device and a method for rotating a driven shaft using a parallel driving shaft.