Chapter 1
Introduction

Abstract: This chapter presents a brief introduction of micropositioning systems and their concerned design and control problems. The compliant translational and rotational guiding mechanisms are described, the related actuation and sensing issues are raised, and the motion control problem is summarized. An outline of the remaining chapters of the book is provided.

Keywords: Micropositioning, Compliant mechanisms, Flexure hinges, Translational guiding, Rotational guiding, Actuators, Sensors, Control.

1.1 Micropositioning Techniques

Micropositioning systems refer to precision positioning devices which are capable of delivering displacement down to sub-micrometer resolution and accuracy. Micropositioning devices have been widely applied in the domain of precision manipulation and manufacturing, such as scanning probe microscopy, lithography manufacturing, and wafer alignment. To cater for the precision demands in relatively low-loading applications, flexure-based compliant mechanisms have been widely employed. Unlike traditional mechanical joints, the repeatable output motion of a flexible element is generated by the elastic deformation of the material. As a consequence, compliant mechanisms enable some attractive advantages - including no backlash, no friction, no wear, low cost, vacuum compatibility, etc. [1, 2].

According to the motion property, micropositioning can be classified into two general categories in terms of translational and rotational micropositioning. The combination of these two types of motion forms a hybrid micropositioning. Typical flexure mechanisms can deliver a translational displacement of less than 1 mm and a rotational displacement smaller than within the yield strength of the materials. In modern precision engineering applications, there is a growing demand for micropositioning systems which are capable of producing large-range (e.g., over 10 mm or ) precision motion, yet have a compact size at the same time. Such applications involve large-range scanning probe microscopy [3], lithography and fabrication [4], biological micromanipulation [5], etc. For instance, in automated zebrafish embryo manipulation, a precise positioning stage with a long stroke is needed to execute accurate operation [6].

In addition, a precision positioning stage with compact size allows theapplication inside a constrained space. For example, a compact positioning device is required to provide ultrahigh-precision positioning of the specimens and tools inside the chamber of scanning electron microscopes for automated probing and micromanipulation [7]. Moreover, a compact physical size enables cost reduction in terms of material and fabrication. Hence, this book is concentrated on the design and implementation of compact micropositioning stages with large motion ranges.

1.2 Compliant Guiding Mechanisms

Concerning the motion guiding mechanism of the positioning stage, although aerostatic bearings [8] and maglev bearings [9] are usually adopted, flexure bearings are more attractive in the recent development of micropositioning systems, due to the aforementioned merits of compliant mechanisms [10]. Compared with other mechanisms, compliant flexures can generate a smooth motion by making use of the elastic deformation of the material. Nevertheless, their motion range is constricted by the yield strength of the material, which poses a great challenge to achieving a long stroke. From this point of view, once the kinematic scheme is determined, the structural parameters of the flexure mechanism call for a careful design to make sure that the material operates in the elastic domain without plastic deformation and fatigue failure.

Given the requirements on the motion or force property, a compliant guiding mechanism can be designed by resorting to different approaches, such as the rigid-body replacement method [11], building-block method [12], topology optimization method [13], topology synthesis method [14], etc. Without loss of generality, the element flexure hinges and the translational and rotational positioning mechanisms are introduced in the following sections.

1.2.1 Basic Flexure Hinges

A basic flexure hinge functions as a revolute joint. In the literature, various profiles of flexure hinges have been used to construct a flexure stage [15]. For example, the in-plane profiles of typical flexure hinges including right-circular, elliptic, right-angle, corner-filled, and leaf hinges are shown in Fig. 1.1. More types of flexure hinges are referred to in the books [2, 16].

Figure 1.1 Profiles of typical flexure hinges: (a) right-circular hinge; (b) elliptic hinge; (c) right-angle hinge; (d) corner-filled hinge; (e) leaf hinge.

Referring to Fig. 1.1, if one terminal of the flexure hinge is fixed and the other terminal has an applied force along the -axis or a moment around the -axis, an in-plane bending deformation of the hinge will be induced. Generally, these element flexure hinges are considered as revolute joints, which deliver a rotational motion of the terminal with respect to the fixed terminal around a rotation center. To generate a translational motion or a multi-axis rotational motion like a universal or spherical joint, multiple basic flexure hinges can be combined to construct a compound flexure hinge [17].

During the bending deformation of the element flexure hinge, the rotation center will be varied. The notch-type flexure hinge, especially the right-circular hinge, is able to deliver a rotation with smaller amount of center shift. However, this is achieved at the cost of a relatively small rotational motion range due to the stress concentration effect. In order to accomplish a large motion range, the leaf flexure hinge is usually employed due to the mitigation of the stress concentration effect. In addition, leaf flexures have been widely employed in micromechanism design in microelectromechanical systems (MEMS) devices [18]. The design methods of the beam-based leaf flexures are referred to in the book [1].

1.2.2 Translational Flexure Hinges

As a compound type of flexure, parallelogram flexure is a popular design to achieve translational motion. For example, the translational flexure hinges constructed by right-circular hinges are shown in Fig. 1.2. To generate a larger translational motion range, the translational flexure hinges can be designed using leaf hinges, as shown in Fig. 1.3.

Figure 1.2 Translational flexure hinges constructed by right-circular hinges: (a) parallelogram flexure; (b) compound parallelogram flexure (CPF).

Figure 1.3 Translational flexure hinges constructed by leaf hinges: (a) parallelogram flexure; (b) compound parallelogram flexure (CPF).

As shown in Fig. 1.3(a), when the output stage of a parallelogram flexure translates a displacement in the -axis, it also undergoes a parasitic translation in the -axis. For some applications, the translation can be employed to enhance the resolution of the displacement due to the displacement deamplification effect. Concerning a large-range positioning in the specified direction, the parasitic translation is unwanted. In order to obtain a larger straight motion while eliminating the parasitic translation, a compound parallelogram flexure (CPF), as shown in Fig. 1.3(b), can be employed.

Intuitively, a longer stroke can be realized by using a longer and more slender leaf flexure. However, in practice, the length of the flexure hinge is constrained by the requirement of compactness and the minimum width is restricted by the tolerance of the manufacturing process. It is challenging to design a flexure micropositioning stage with a large stroke and compact size simultaneously. To overcome the aforementioned problem, the concept of multi-stage compound parallelogram flexure (MCPF) [19], as shown in Fig. 1.4(a), is employed in this book.

Figure 1.4 (a) A multi-stage compound parallelogram flexure (MCPF) with two modules; (b) an improved MCPF with enhanced transverse stiffness in the -axis.

Compared with conventional CPF, the motion range of a MCPF is enlarged times without changing the length and width of the flexures, where is the number of basic CPF modules. Note that CPF is a special case of MCPF with = 1. To enhance the transverse stiffness in the -axis direction, an improved MCPF is presented as shown in Fig. 1.4(b), which is constructed by connecting the two secondary stages together.

1.2.3 Translational Positioning Mechanisms

A translational positioning mechanism is usually required to provide the translational motion in the two-dimensional plane or three-dimensional space. To generate the translational positioning in more than one direction, a suitable mechanism design is necessary. As far as a kinematic scheme is concerned, the positioning stages, which are capable of multi-dimensional translations, can be classified into two categories in terms of serial and parallel kinematics. The majority of the commercially available stages employ a serial-kinematic scheme. For example, some micropositioning stages have been developed by stacking the second single-axis positioning stage on top of the first one or nesting the second stage inside the first one [20-22]. In this way, the entire second stage is carried by the first one, as illustrated in Fig. 1.5(a), where the X stage serves as the output platform of the XY stage. As an example, the computer-aided design (CAD) model of...