A patch pump utilizes piezoelectricity to dispense medicament from a cartridge syringe to a patient. Pump can include a plurality of piezoelectric elements that when energized cause linear motion of a pushrod that interfaces with the syringe in the cartridge to advance the syringe and dispense the medicament. The high torque generated by the piezoelectric elements is directly converted into the same amount of torque on the lead screw, so no torque increasing gear reduction system is needed and the pushrod utilized to drive the syringe can be contained within and connected directly to the motor assembly. Such a piezoelectric-based system can therefore be made smaller and with fewer moving parts than an electromagnetic motor of the same capability such that the pump has a smaller size than has heretofore been possible with prior art electromagnetic-based syringe pumps and other pumps that utilize gear reduction systems.