Vacuum pumps are air compressors that create space for air to expand into from the chamber.

 These are cross section diagrams of both the traditional and linear peristaltic pumps.
  Initial condition starts out with all spaces at standard atmospheric pressure.
 
 Below are the equivalent phases of a traditional rotary vacuum pump.

The first action is to  isolate a portion of the air.    The vane forms the wall  that moves away from  the chamber and the total  chamber space expands.

The air ahead of this  moving wall is being  pushed towards the exit  port.

The captive parcel of air is  compressed and expelled  to the surrounding  atmosphere.

 Diagrams are not drawn to scale.  Length is actually twice as long.
 

  In this case, the rolled hose is ten times the volume of the chamber to be evacuated.
Each complete stroke squeezeing the air out would reduce the remaining pressure in the chamber
on the right side to a tenth of the initial air pressure that previously existed before.

 Barring leaks and vaporous substances such as water or solvents, it would take only six strokes to reduce the pressure
of the chamber down to the level of vacuum in a radio tube. Unfortunately the gas from the moisture on the hose and chamber overwhelms the  action of this pump.

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