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This thesis introduces a new family of high-performance, low-cost, six-degree-of-freedom positioning systems for high-dynamic, high-accuracy applications. This machine is designed to achieve sub-micron (~~ 50nm) accuracy with meso-scale (~~ 1mm) motions with simple machine elements and commercially available components. The motion platform presented is a parallel kinematic machine supported by six flexural legs that each ride on a ball screw assembly. The required degrees of freedom and range of motion for the flexural and rolling elements are analyzed. The stiffness and stress analysis of each element is presented along with a model for system level stiffness, inertia, and natural frequency. A forward kinematic model describes how the motions of individual actuators can be directly related to the motions of the output stage, unlike a traditional hexapod which requires inverse kinematics. This thesis presents initial sizing rules of thumb, fundamental scaling laws, simulation and experimental results, and practical considerations for manufacturing. Prototypes were built and tested to confirm the models presented and inform the design of future machines. The operating theory of this machine can be extended beyond the exact elements described for applications which require larger range of motion, higher load capacity, or only need quasi-static operation.