Piezo-driven precision positioning platforms with large stroke are greatly demanded in both scientific research and industrial applications. Although various principles have been proposed to design piezo-driven positioning platforms, the problem of backward motion commonly exists, greatly hindering their applications. To suppress the backward motion, in this paper, an idea by generating a forward frictional force to balance the reversed frictional force was proposed. Correspondingly, a specific arc-shape flexure hinge was designed to generate the forward frictional force via its elastic recovery. To verify the feasibility of the proposed idea, a positioning platform with alterable initial gap between contact surfaces was designed by the parasitic motion principle (PMP). By measuring the output displacement under various initial gaps, a critical initial gap was identified, at which the positioning platform could output stepping displacement without backward motion. Under this critical initial gap, effects of driving voltage and frequency on the backward motion were further investigated. In addition, the natural frequency and loading capacity of the positioning platform were tested. This study confirms that using PMP, it is feasible to design piezo-driven positioning platforms with completely suppressed backward motion, which would enhance the applications of the PMP and PMP positioning platforms.

In this paper, a novel pseudo-random diamond turning (PRDT) method is proposed for the fabrication of freeform optics with scattering homogenization by means of actively eliminating the inherent periodicity of the residual tool marks. The strategy for accurately determining the spiral toolpath with pseudo-random vibration modulation is deliberately explained. Spatial geometric calculation method is employed to determine the toolpath in consideration of cutting tool geometries, and an iteration algorithm is further introduced to enhance the computation efficiency. Moreover, a novel two degree of freedom fast tool servo (2-DOF FTS) system with decoupled motions is developed to implement the PRDT method. Taking advantage of a novel surface topography generation algorithm, theoretical surfaces generated by using the calculated toolpaths are obtained, the accuracy of the toolpath generation and the efficiency of the PRDT method for breaking up the inherent periodicity of tool marks are examined. A series of preliminary cutting experiments are carried out to verify the efficiency of the proposed PRDT method, the experimental results obtained are in good agreement with the results obtained by numerical simulation. In addition, the results of scattering experiments indicate that the proposed PRDT method will be a very promising technique to achieve the scattering homogenization of machined surfaces with complicated shapes.