The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

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The purpose of this study is to design and analyse a novel six-degrees-of-freedom (DOF) precision positioning table, which is assembled by two different kinds of three-DOF precision positioning tables: a plane-type three-DOF (X , Y , θ z ) precision positioning table and a cylindertype three-DOF (θ x , θ y , Z ) one, and each table is driven by three piezoelectric actuators (PAs). In this paper, the Bouc-Wen model is employed to describe the hysteretic phenomenon of the PAs. The transfer matrices with cross-coupling terms between the output displacements and input voltages are derived from the dynamic equations in the steady-state conditions. In order to obtain the best transfer matrix, experimental measurements of the whole six-DOF table are compared with those from the two individual three-DOF precision positioning tables. Finally, the transfer matrices with better performance for the two three-DOF tables and the novel six-DOF table are obtained.