Monolithic Flexure Research Articles

Long-range AFM profiler used for accurate pitch measurements

A long-range atomic force microscope (AFM) profiler system was built based on a commercial metrology AFM and a home-made linear sample displacement stage. The AFM head includes a parallelogram-type scanner with capacitive position sensors for all three axes. A reference cube located close to the tip acts as the counter electrode for the capacitive sensors. Below this metrology AFM head we placed a linear sample displacement stage, consisting of monolithic flexures forming a double parallelogram. This piezo actuated stage provides a highly linear motion over m. Its displacement is simultaneously measured by a capacitive position sensor and a differential double-pass plane mirror interferometer; both measuring systems have subnanometre resolution capability. For the measurement of periodical structures two operating modes are possible: a direct scanning mode, in which the position of the displacement stage is increased point by point while the AFM head measures the height, and a combined scanning mode where the displacement stage produces offsets which are multiples of the pitch to be measured while the AFM head is simultaneously scanning to locate an edge or a line centre position. Construction details, system characteristics and results from first pitch measurements are presented. The estimated relative combined uncertainties for pitch values on different standards are in the range to . Laser diffraction measurements of comparable uncertainty were performed on the same standards and show a very good agreement.

Error analysis of a flexure hinge mechanism induced by machining imperfection

Modeling of manufacturing tolerances for machining of a monolithic flexure hinge mechanism is presented. This modeling uses a computer-based method to generate the equations of motion for the mechanism and to predict the induced motion errors for various types of machining imperfections. This paper describes the modeling and the quantitative analysis of the motion errors using a well-known simple compound linear spring as an example. Based on the simulation results of the example problem, effects of the machining imperfection types on motion errors are generalized. The simulation demonstrates that the imperfection of the center position and the size of a machined hole provide an in-plane motion error X, Y, θ z. In addition, the machining error in the perpendicularity of the hole with respect to the plate also provides an out-of-plane parasitic error Z, θ y, θ y.

Optimal design of a flexure hinge based XYφ wafer stage

Optimal design o1 a XYφ micromotion stage is presented. The stage consists of a monolithic flexure hinge mechanism with three piezoelectric actuators. This paper describes the procedures of selecting parameters for the optimal design. In particular, it presents a mathematical formulation of the optimization problem. Based on the solution of the optimiiation problem, the final design of the stage is also presented. Experimental results indicate that the design procedure is effective, and the designated stage has the total range of 41.5 μm mid 47.8 μm along the X- and Y-axes, respectively, and the maximum yaw motion range of 322.8 aresec (1.565 mrad).

Elliptical flexure hinges

This paper presents closed form equations based on a modification of those originally derived by Paros and Weisbord in 1965, for the mechanical compliance of a simple monolithic flexure hinge of elliptic cross section, the geometry of which is determined by the ratio ε of the major and minor axes. It is shown that these equations converge at ε=1 to the Paros and Weisbord equations for a hinge of circular section and at ε ⇒∞ to the equations predicted from simple beam bending theory for the compliance of a cantilever beam. These equations are then assessed by comparison with results from finite element analysis over a range of geometries typical of many hinge designs. Based on the finite element analysis, stress concentration factors for the elliptical hinge are also presented. As a further verification of these equations, a number of elliptical hinges were manufactured on a CNC milling machine. Experimental data were produced by applying a bending moment using dead weight loading and measuring subsequent angular deflections with a laser interferometer. In general, it was found that predictions for the compliance of elliptical hinges are likely to be within 12% for a range of geometries with the ratio βx (=t/2ax) between 0.06 and 0.2 and for values of ε between 1 and 10.

Developing a linear piezomotor with nanometer resolution and high stiffness

A novel linear piezomotor was developed for machine tool applications. The design principles and methodology for this high stiffness linear piezomotor with nanometer resolution are presented. The linear piezomotor consists of three piezoelectric actuators and one monolithic flexure frame. The design strategy is to reduce the total number of mechanical elements and interfaces and to integrate all the elements into the frame. The finite element method is used in the design process. The principles and methodology are also applicable to other positioning systems where a high stiffness and high positioning resolution are required.

A Linear Piezomotor of High Stiffness and Nanometer Resolution

A novel linear piezomotor is developed for machine tool applications. The linear piezomotor consists of three piezoelectric actuators and one monolithic flexure frame which reduces the total number of mechanical elements and interfaces and integrates all the elements. Positioning performance tests are carried out on the linear piezomotor to identify its positioning resolution and accuracy. A laser interferometer is used in the open-loop test to investigate the resolution and positioning behavior, while a linear encoder is used in the closed-loop test to study the positioning accuracy of the linear piezomotor. A discussion is provided on the enhancement of the stiffness and positioning accuracy of the linear piezomotor.

A high performance magnetic force microscope

We have constructed a high performance magnetic force microscope optimized for operation in the force gradient detection mode. The instrument incorporates a novel differential heterodyne interferometer that has a high immunity to microphonics and interference. The detection limit of the interferometer is limited by the intrinsic thermal noise of the cantilever sensor. Positioning and scanning of the sample is undertaken by a monolithic flexure stage driven by piezoelectric actuators. The stage incorporates capacitance sensors which are used to linearize the motion of the stage via a closed loop control system. The linearity achieved is better than 1% (full scale) with a positioning stability of 1 nm (rms). Recorded bit patterns in longitudinal media and domains in an AC-demagnetized Co/Pt multilayer have been studied.

Experiment on the absolute measurement of a silicon lattice spacing at the NRLM

An experimental setup for the determination of the silicon lattice constant is described. The monolithic flexure hinge mechanisms for orientation adjustment, an optical interferometer for angle and displacement measurement, and a special tool for establishing the parallelism between the optical surface and the reciprocal lattice vector are introduced. The latest experiment gives a value for the ratio of the optical wavelength to the silicon lattice spacing which is consistent with more established values within a currently large uncertainty of one.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Mechanical Property of a Quadrilateral of Links Composed of Monolithic Notch Flexure Hinges for Precision Movements

The Mechanical Property of a Quadrilateral of Links Composed of Monolithic Notch Flexure Hinges for Precision Movements

The Bending Elasticity of a Circular Notched Bar as the Monolithic Flexure Hinges in a Precision Mechanism

The Bending Elasticity of a Circular Notched Bar as the Monolithic Flexure Hinges in a Precision Mechanism