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Using a low-speed high-torque (LSHT) pump/motor to provide the speed range and torque for a hydrostatic automobile offers a number of advantages over using a high-speed low-torque pump/motor, combined with a gear reducer. However, there appear to be no LSHT units commercially available that have true variable displacement capability. Because of this void, a variable displacement pump/motor has been designed and built that could provide a direct drive for each wheel of a hydrostatic automobile. The unit uses some components such as the cylinder block, piston and modified rotating case from a commercially available radial piston pump/motor. Initial preliminary testing of the pump/motor indicates that it has good efficiency and performance characteristics, and, with further development should be very attractive for automotive use. This paper focuses on the design and kinematics of the device.