A valveless, positive displacement pump including a living hinge for angularly adjusting a pumping head with respect to a rotatable drive member is provided. A method of manufacturing such a pump is also provided. The pump includes a block to which a pumping head and drive member are mounted. The block includes a first support pivotably connected to a second support by means of an integral, flexible hinge. The pumping head is mounted to the first support while the rotatable drive member is mounted to the second support. Movement of the first support about the flexible hinge allows the stroke of the piston, and therefore the flow rate of the pump, to be adjusted. Such a pump may be manufactured by extruding the block in elongate form and then cutting it into individual sections to which pumping heads may be mounted.