A reversible ratchet mechanism includes a pair of roller clutches set to operate in opposite directions when engaged by a belt. During the forward motion of the ratchet assembly in either direction of propulsion of the belt, one roller clutch is disengaged while the other is engaged and locked, thereby propelling the belt. During the backward stroke, the engaged roller clutch is free to rotate. The result is that the reciprocating motion of the assembly is converted into the linear motion of the belt. The ratchet assembly includes a shift mechanism to reverse the engagement of the roller clutches and change the direction of propulsion of the belt produced by the push/pull action of the operator. The invention is advantageously used in conjunction with a wheelchair.