1. Introduction
Generally, in situ nanoindentation devices use mechanical components for online detecting and observing of the deformable mechanics and mechanical properties of biomaterials [
1]. In particular, in situ nanoindentation was applied in the field of implants (e.g., bone, teeth, femur, prosthetics) [
2,
3]. However, the mechanical components, (e.g., machine base, shaft, bush, gear, cam, sliding rail, ball screw, and ball nut) have existing restrictions, such as clearance, friction, wear, and vibration. Consequently, these mechanical devices are complicated for obtaining a precise transmission. In addition, a compact structure is a recent tendency in designing a new in situ nanoindentation tester in order to reduce energy consumption. Especially, in situ nanoindentation often requires many force and displacement feedback sensors to achieve a precise positioning capability. In such in situ nanoindentation applications, the two main modules consist of an indenter driving stage and a bio-material sample locating stage. However, the existing stages still have a slow responding speed, i.e., low resonant frequency [
4,
5]. Additionally, they are difficult to install positioners in in situ nanoindentation with a scanning electron microscope (SEM) or transmission electron microscope (TEM) due to their large size. Therefore, a new structural design of the stage with a faster responding speed has an increasing demand.
In the two last decades, many designs of in situ nanoindentation in SEM/TEM were developed. Rabe et al. [
6] developed an SEM nanoscratch instrument with the indenter driving stage of 20 μm. A TEM nanoindentation was proposed for deformation testing of Al–Mg films [
7]. Considering the mechanical and electrical properties of nanomaterials, a survey on SEM in situ nanoindentation was investigated deeply [
8]. The nanomechanical properties of micro/nano materials were observed through in situ nanoindentation in SEM [
9]. Nano thin-films for an MEM force sensor were tested by in situ nanoindentation in SEM and TEM [
10]. One-D nanostructure materials were checked via this technique [
11]. Presently, according to the crucial benefits of compliant mechanisms include smooth motion without friction and backlash, monolithic structure, slight mass, cheap price and miniature structure [
12,
13,
14], it has been expansively utilized to research and gradually substitute conventional structure. Particularly for the nanoindentation tester, an indenter driving stage of 11.44 μm was developed by Huang [
15]. Additionally, Huang et al. [
16] developed another stage with 40 μm. Besides, Zhao et al. [
17] developed an indenter driving stage with 15 μm. In practical applications, a nanoindentation device requires an excellent locating precision, high operating travel and a high material strength [
15,
18].
Along with the applications in in situ nanoindentation, compliant mechanisms have been extensively exploited for prospective applications, e.g., positioner [
19], lithography [
20], microscopy [
21], and micromanipulator [
22]. Specifically, a diamond turning operation was developed using a compliant mechanism [
23]. Several complaint reconfigurable stages were developed in a module architecture [
24]. The compliant mechanism was applied for polishing operations [
25]. However, the stroke of a piezoelectric actuator is often small. In order to obtain the larger working travels, the previous stage was integrated with displacement amplifiers [
26]. An effective design of a 3-DOF positioner with a lever amplifier type was well developed [
7]. Then, a two-lever displacement magnification mechanism was proposed [
27]. A hybrid lever-bridge amplifier was designed [
28]. A Scott–Russell mechanism was used as a displacement amplifier [
29]. In the design synthesis of compliant mechanisms, formulating modeling approaches in predicting the mechanical behaviors is often complex because the kinematic and mechanical behaviors are coupled, i.e., these behaviors are ambiguous. At present, modeling compliant mechanisms is conducted in two main approaches. Primarily, analytical approaches comprise of a pseudo-rigid-body model (PRBM), compliance matrix method, elastic beam theory, and Castigliano’s second theorem [
30]. Besides, intelligence-based computational methods were well-formulated such as fuzzy logic, artificial neural network, and adaptive neuro-fuzzy inference system (ANFIS) [
31]. Especially, the PRBM is well blended with the Largange method to rapidly assess the primary superiority performances of the positioners, e.g., force-displacement curve and dynamic response.
Although many micro/nanopositioners have been dedicated for ultra positioning engineering but there has been lack of studies on the precision stages for driving the indenter which can be embedded into the nanoindentation tester for biomedical samples (e.g., bone, teeth, femur implants). Additionally, the working travel for stages for driving the indenter is still small and they are difficult to apply for a diverse variety of many nanoindentation applications. With the purpose of fullfiling the technical demands for an in situ nanoindentation, a miniaturized size, a fast response, and an effective computation method of the indentation should be balanced. In other words, the symmetry in designing and analyzing phases of indentation should remain to reduce the complexity of the design and facilitate more effective computation techniques. Therefore, the present paper proposes a new design of the stage/positioner with one degree of freedom (01-DOF). The stage is created based on a displacement amplifier with six levers and a symmetric parallelogram mechanism to achieve a high output displacement and reduce parasitic motion error for indenting a material specimen, especially a bio-specimen. The new novelties of this article are summarized as follows: (i) A new design of a compliant 01-DOF stage with a good dynamic performance in bio-specimen nanoindentation application. (ii) An new optimization design and synthesis approach that is proposed based on the PRBM, Largange, and Firefly algorithm to improve the quality response of the 01-DOF stage.
This article is motivated to develop a new design for the 1-DOF stage. The stage is built by integrating the six-lever displacement amplifier and the parallel driving mechanism. First of all, the kinematic and dynamic equations are established using a combination of PRBM and Lagrange method. Then, according to established analytical equations, the Firefly algorithm is utilized to enhance the frequency of the proposed stage.
2. Conceptual Design of Compliant 1-DOF Stage
In our previous research [
32], a potential application of the compliant 1-DOF stage, or the so-called Z-positioning stage, is shown in
Figure 1. The coarse
Z-axis positioner, a coarse XY-positioner, an XY-fine positioner, and a fine
Z-axis positioner are among the main components of the system. The coarse XY positioner is used to determine an initial location of a bio-specimen, the XY-fine stage is used to define fine location, and the coarse
Z-axis positioner is used to move the testing bio-specimen toward the indenter. Eventually, the 1-DOF positioner is used to drive the indenter to the checking specimen. In the present article, the compliant 1-DOF stage is developed for such a nanoindentation system.
In this work, the lever amplifier is aimed to enlarge the displacement of the stage.
Figure 2 describes a basic lever mechanism. Specifically, point O indicates a fixed link which presents for the lever rotation location. Additionally, the input position and the output position are noted as P and Q, respectively. The operating principle of an amplifier comprises of the following steps: (i) an input displacement
affects at point M, the lever revolves an angle
. Subsequently, the position Q transfers to Q’ in order to obtain the deformation
. Meanwhile, the one-lever amplifier causes a significant decoupling error. Consequently, to decrease the decoupling error and enhance the output displacement, a symmetric six-lever displacement amplifier is monolithically designed in the proposed positioner, as illustrated in
Figure 3. Moreover, a combination of the symmetric six-leaf parallel mechanism and the amplifier is to decline the parasitic motion error, as shown in
Figure 4. Especially, this guiding mechanism significantly reduces the parasitic motion error for the compliant 01-DOF positioner. Based on the working principle, the amplifying ratio are approximately obtained:
In
Figure 4, the displacement amplifier includes three floors with six levers which are employed to enlarge the working displacement of the stage. Specifically, the number of odd floors ensures that the input displacement has the same direction with the output displacement. For this purpose, controlling the number of floors will ensure the amplification ratio and the direction of the output displacement in order to effectively monitor the indentation process. Meanwhile, the parallel guiding mechanism that consists of six leaf hinges, which is aimed to generate the translation motion, i.e., eliminated parasitic motion errors from the remaining (x and y) axes. It consists of a lever amplification mechanism of floor 1 (LAM #1), lever amplification mechanism of floor 2 (LAM #2), and lever amplification mechanism of floor 3 (LAM #3). The input is acted via a piezoelectric actuator (PZT).
The material of the proposed 01-DOF stage was manufactured by material Al-7075 because of its outstanding properties of this material. The 01-DOF stage comprises of: (i) fixed holes, (ii) a PZT actuator, (iii) a parallel guiding mechanism, and (iv) a six-lever displacement amplifier. The sum dimensions of the stage are around 171 mm × 108 mm × 10 mm. The elliptical hinge was chosen for the stage due to its excellent benefits [
33].
Figure 5 shows the dimensional diagram of the stage.
Table 1 provides the key dimensions of the stage. Specifically,
G is the thickness of the elliptical hinge of the LAM #1 and LAM #2,
R is the thickness of the elliptical hinge of the LAM #3,
S is the thickness of the right circular hinge of the output end, and U is the thickness of the leaf hinge of the output end.
5. Conclusions
This article developed a new design of the 01-DOF stage. It was designed to include the six-lever displacement amplifier and the parallel guiding mechanism. An efficient integration of the PRBM-based Lagrange method was to build the dynamic equation of the 1-DOF stage. Based on the analytical equation, the Firefly algorithm was implemented to define the optimal parameters.
The optimized parameters were found at G = 0.75 mm, R = 0.7 mm, S = 0.65 mm, and U = 0.6 mm. The optimized first natural frequency was about 226.8458 Hz. In addition, the FEA verification results showed that the first natural frequency was 250.01 Hz. Moreover, the verification error among the optimization and FEA results was 9.27%. The simulation verification was close with the optimal result from the hybrid approach. Moreover, the optimization result was better than the primary design.
In the future investigations, some prototypes will be fabricated based on the additive manufacturing method or computerized wire cutting method for evaluating with the numerical analysis and analytical calculation results. A practical manufacture of the stage will be embedded into a development of an in situ nanoindentation device.