A dog clutch construction is provided for selectively rotationally connecting or disconnecting two coaxially arranged shafts. The dog clutch includes teeth on each shaft which are axially juxtaposed to each other. A toothed sleeve is engaged over the teeth. The sleeve is axially movable from a first position located on only one set of teeth to a second position located on both sets of teeth. A new meshing process is provided for meshing the teeth of the sleeve with the other two sets of teeth. A means for axially driving the sleeve from the first position to the second position is also provided, including an annular power piston positioned coaxially with the sleeve and a mechanism for transmitting the driving movement of the piston to the sleeve. The mechanism for tansmitting the driving movement is also annular and uniformly engaging around the sleeve and incorporates an axial resiliency to soften the driving action of the piston particularly at the instant of the meshing of the teeth of the sleeve with the other two sets of teeth, while ensuring uniform driving of the sleeve over all peripheral portions thereof.