Abstract: This design utilizes spherical balls that function as pumping members and also function as bearing loads. The housing includes channels that are used to convert rotary motion to true linear reciprocating motion relative to the center of operation by use of modified involute profile curves. The channels have an enlarged radius of curvature, four (4) contact point designs, and an arch design depending upon application and loads, etc. A variable vane shaft and variable seal plug have a make-before-break design that eliminates damaging high pressure spikes due to the trapped fluid. The vane is used to vary and control pumping arc by directing the high and low pressures. A rotor disclosed has an angle and slots that are designed to align with tangent of the involute curve. The variable displacement disclosed herein is varied by varying the pumping arc thereby causing more or less fluid to be pumped from inlet pressure to inlet pressure which actually affects displacement and input power required.