A bicycle comprising a bicycle frame formed with an upright elongate compartment and a horizontal axial hole intersecting and in spatial communication with said compartment, and a power assist transmission device, wherein said power assist transmission device comprises; a motor drive unit mounted in said compartment; a transmission unit including a first gear driven by said motor drive unit to rotate, a one-way clutch mounted in said compartment and connected between said first gear and said motor drive unit for allowing rotation to be transmitted from said motor drive unit to said first gear while preventing rotation from being transmitted from said first gear to said motor drive unit, and a second gear meshing with said first gear, mounted in said axial hole, and including an engaging portion having a non-circular profile; a crank unit including a crank shaft that is mounted rotatably in said axial hole, that extends along an axis of said axial hole, and that extends into said second gear along the axis, a first crank that is connected to one end of said crank shaft, and that includes a crank arm and an extending portion extending from said crank arm toward said second gear along the axis, and a second crank that is connected to the other end of said crank shaft; a driving sprocket having an inner side surface facing said axial hole and an outer side surface opposite to said inner side surface along the axis and facing said first crank characterized in that the driving sprocket is formed with a receiving groove that extends from said outer side surface toward said inner side surface, and that receives at least a portion of said extending portion of said first crank therein, and an engaging hole that extends from said inner side surface toward said receiving groove, that is in spatial communication with said receiving groove, that non-rotatably engages said engaging portion, and that has a diameter smaller than that of said receiving groove; and a unidirectional bearing mounted in said receiving groove and sleeved on said extending portion of said first crank for driving rotation of said driving sprocket in a single direction by said extending portion. a motor drive unit mounted in said compartment; a transmission unit including a first gear driven by said motor drive unit to rotate, a one-way clutch mounted in said compartment and connected between said first gear and said motor drive unit for allowing rotation to be transmitted from said motor drive unit to said first gear while preventing rotation from being transmitted from said first gear to said motor drive unit, and a second gear meshing with said first gear, mounted in said axial hole, and including an engaging portion having a non-circular profile; a crank unit including a crank shaft that is mounted rotatably in said axial hole, that extends along an axis of said axial hole, and that extends into said second gear along the axis, a first crank that is connected to one end of said crank shaft, and that includes a crank arm and an extending portion extending from said crank arm toward said second gear along the axis, and a second crank that is connected to the other end of said crank shaft; a driving sprocket having an inner side surface facing said axial hole and an outer side surface opposite to said inner side surface along the axis and facing said first crank characterized in that the driving sprocket is formed with a receiving groove that extends from said outer side surface toward said inner side surface, and that receives at least a portion of said extending portion of said first crank therein, and an engaging hole that extends from said inner side surface toward said receiving groove, that is in spatial communication with said receiving groove, that non-rotatably engages said engaging portion, and that has a diameter smaller than that of said receiving groove; and a unidirectional bearing mounted in said receiving groove and sleeved on said extending portion of said first crank for driving rotation of said driving sprocket in a single direction by said extending portion.