A controlled delivery drive mechanism includes a drug container having a barrel and a plunger seal; a drive housing within which at least initially partially resides a piston having an interface surface and a drive rack; and a power spring. The piston is configured to contact and axially translate the plunger seal within barrel. The mechanism may be configured to convert rotational movement of a drive pinion to axial translation of the drive rack, or to convert axial force of a linear power spring into torsional motion of a drive pinion. A regulating mechanism meters the drive pinion such that the piston is axially translated at a controlled rate. The drug container may contain a drug fluid within a drug chamber for drug delivery at a controlled rate. The regulating mechanism may be an escapement regulating mechanism. A drug delivery pump includes such controlled delivery drive mechanisms.