What types of pumps does the positive displacement principle apply on?

any piston pump or gear or screw pump which sucks the fluid at its on end, displaces it to other end as the cavity at feed side increases and that at the discharge side decreases.

Positive displacements pumps divided into two types due to operation:
1- Fixed
2- Variable
1- Fixed: *Gear Pump.
*Screw Pump.
*Vane Pump.
*Piston Pump (Radial/Axial): -Axial Piston Pump (Swash Plate/ Bent Axis)
2- Variable: *Vane Pump (Balanced / Unbalanced).
*Piston Pump (Radial/Axial): -Axial Piston Pump (Swash Plate/ Bent Axis) All mentioned pumps applies the positive displacement principle.

positive displacement pump can be classified to 

1-rotary pump 

2- reciprocating pump 

type of rotary pump

1-lobe pump

2-screw pump

reciprocating pump 

1-piston pump

2-plunger pump

3-diaphram pump

 

all reciprocating and rotary gear pumps are applied positive displacement principil

three screw pump

all the plunger types and piston types pumps are included

it works as archimides principle The operating principle of a positive displacement pump can be demonstrated by carefully dropping a rock into a bucket of water.
Some of the water will be forced out of the bucket because the rock cannot occupy the same space as the water at the same time.
The amount of water displaced (pushed out) by the rock is equal to the volume of the rock.

Mr. Tariq Jilani has the closest answer. Equal volume per cycle in is the same as the volume out.  This applies to plunger pumps, rotary pumps (gear, lobe, screw), plunger pumps. diaphram pumps, peristaltic pumps, just to name a few.  These types of pumps should always be operated with a pressure relief device in the system for safety!

Types of positive-displacement pumps are reciprocating, metering, and rotary pumps.

Reciprocating (piston pumps...)and rotary (screw or vin) pumps are positive and application on hydraulic circuites.

The pump which have constant suction and discharge volume means, suction volume = discharge volume