The objectives of this research are to develop the equations that describe the relative motion between the ball guide and the slipper retainer within an axial-piston swash-plate type hydrostatic pump. Using a relationship between spherical and Cartesian coordinates, a contact point between the ball guide and the retainer is identified and matched for an observer on the ball guide and an observer on the retainer. Once a generic contact point is established, the position of a fixed particle on the ball guide is subtracted from the position of a particle on the retainer. The trajectory of this particle relative to the fixed particle on the ball guide is then used to describe the teardrop wear patterns that are expected to appear on the ball guide. These wear patterns are confirmed by experiments. Next, the velocity of a particle on the ball guide is subtracted from the velocity of a particle on the retainer at the contact point. Based upon this result it is shown that a relative velocity between the ball guide and the retainer is always maintained for a nonzero swash-plate angle and that the minimum relative velocity between the retainer and the ball guide may be increased by increasing one or all of the following: the design value of the retainer cone-angle, the radius of the ball guide, the operating speed of the pump, or the pump swash-plate angle.

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