Sensors and Actuators A 205 (2014) 6–14

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

A novel compliant micropositioning stage with dual ranges and resolutions Qingsong Xu ∗ Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira S.J., Taipa, Macao, China

a r t i c l e

i n f o

Article history: Received 29 June 2013 Received in revised form 10 October 2013 Accepted 11 October 2013 Available online xxx Keywords: Compliant mechanisms Flexure hinges Mechanism design Micropositioning Precision engineering

a b s t r a c t Dual-range stages are demanded in precision positioning applications that call for fine resolution in a smaller motion range and coarse resolution in a larger range. Traditional dual-range stages are realized using two actuators, which complicates the mechanism and control design procedures. This paper presents the design and testing of a novel dual-range, dual-resolution precision positioning stage driven by a single linear actuator. The stage structure is devised with leaf flexures to achieve a large stroke. Strain sensors are employed to provide different resolutions in the two motion ranges. To quantify the design of the motion ranges and fine/coarse resolution ratio, analytical models are established and verified through finite element analysis simulations. A proof-of-concept prototype is fabricated for experimental investigations and the experimental results validate the effectiveness of the proposed design. The reported ideas can also be extended to the design of multi-axis micropositioning stages. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Micro-/nanopositioning systems are widely applied in the domain of precision manipulation and assembly. Resolution and range are the two fundamental performances in a precision positioning stage. Due to the sensing limitations, a high positioning resolution is usually obtained in a small motion range while a large range is achieved with a low resolution. In practice, many applications demand a micropositioning stage with both a large range and a high resolution to execute diverse tasks. For instance, in scanning probe microscopy, a positioning stage with a large range and high resolution is needed to scan a large specimen surface with a fine imaging resolution [1]. A dual-range positioning stage offers a promising solution by delivering both large range and high resolution using the combined coarse and fine stages. To generate a micropositioning stage with dual ranges and resolutions, the dual-actuation approach is commonly employed to construct a dual-servo stage. This type of dual-stage is generally composed of a coarse stage and a fine stage that are connected in serial. The former provides a large motion range with coarse positioning resolution and the latter delivers a smaller range with fine positioning resolution. For example, dual-servo stages based on different actuation principles have been developed in the literature [2–8]. In the aforementioned works, various types of actuators have been adopted to drive the positioning stages. To achieve a precise

∗ Tel.: +853 83978462; fax: +853 28838314. E-mail addresses: [email protected], [email protected] 0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2013.10.010

positioning, piezoelectric actuators have been popularly employed. Nevertheless, the drawback of a piezoelectric actuator is its short stroke (typically, tens of micrometers) and piezoelectric nonlinearity (e.g., hysteresis and creep) [9,10]. The voice coil motor (VCM), another linear actuator based on electromagnetic principle, is capable of delivering a longer stroke without nonlinear effect. Hence, a VCM is more suitable to drive a micropositioning stage with large motion range [11]. In addition, sliding guideways are typically used to guide the output motion of the stage [3,5]. In contrast, flexure bearings are more preferred for precision engineering applications due to their merits in terms of no backlash, no friction, vacuum compatibility, and easy manufacturing [12]. Thus, flexures have been widely employed in the recent development of micropositioning systems [13–16]. The major issue of a dual-servo stage arises from the interference caused by the interaction between the coarse and fine stages. It has been shown that the interaction behavior of a dual-servo stage can lead to an unstable open-loop control system [17]. To mitigate this adverse interference effect, control and mechanical design approaches have been developed. For instance, the interference behavior can be reduced by designing a multiple-input-multipleoutput (MIMO) control system [18,19]. Additionally, the interaction effect can also be alleviated by resorting a careful mechanical design [7]. Even so, employing two types of actuators complicates the control and mechanism design processes. Here, we devise a novel single-drive micropositioning stage with dual ranges and dual resolutions. In particular, we propose a conceptual design for a dual-range and dual-resolution compliant stage based on an unequal-stiffness compliant mechanism. In

Q. Xu / Sensors and Actuators A 205 (2014) 6–14

F

K1

K2

which describes the driving force of the actuator. It allows the following generation:

M Mover

Backward stopper

R1 =

Output platform

Linear actuator

δ

δ

7

Forward stopper

K1 D1 . K1 + K2

(3)

Afterwards, if the driving continues in the forward direction, only the bearing K2 will be deformed in that the deformation of bearing K1 is stopped by the forward stopper. Under this situation, the overall stiffness of the mechanism becomes:

Fig. 1. Schematic of a micropositioning stage with dual ranges.

the small and large ranges, the mechanism is designed to exhibit different stiffness values, which are contributed by leaf flexures suffering from different bending deformations. The large and small deformations are monitored using two strain sensors to offer fine and coarse resolutions for the two ranges, respectively. Rather than dual-servo stages, the presented technique enables the achievement of a dual-range motion by adopting a single actuator. This reduces hardware costs and control design effort. Moreover, the single-drive design eliminates the conventional interference effect. We use both simulation and experimental investigations to verify the proof-of-concept design. The remainder of this paper is organized as follows. Section 2 presents the conceptual design of the dual-range, dual-resolution stage. Then, the mechanical design of a flexure-based compliant stage is outlined in Section 3, where the motion range, resolution ratio design, and sensing and actuation issues are addressed in detail. Section 4 reports on a case study and provides a performance evaluation of a compliant stage through both analytical modeling and finite element analysis (FEA) approaches. A fabricated prototype stage is described in Section 5, where a collection of experimental studies are performed to verify the conceptual design. Section 6 concludes this paper.

Krange2 = K2 .

(4)

After the moment when the mover contacts the forward stopper, if a maximal driving displacement D2 is produced by the actuator, then D2 will be transmitted as the displacement of the output platform M. Hence, the overall output displacement of M can be derived as follows: Rall = R1 + R2 =

K1 D1 + D2 . K1 + K2

(5)

Thus, the forward motion range of M is divided into two intervals of [0, R1 ] and [R1 , R1 + R2 ], which are assumed to be the smaller and larger ranges, respectively. Similarly, the output platform can also be driven to move in the backward direction. Its backward motion range is divided into two intervals of [−R1 , 0] and [−R1 − R2 , −R1 ] by the backward stopper. Unlike the conventional variable stiffness mechanism, which usually exhibits a specified stiffness profile [20,21], the proposed design possesses two discrete stiffness values in the overall motion range. In the small and larger ranges, the equivalent stiffness of the system is unequal, although the stiffness remains constant in each range. In the next section, a dual-resolution stage is devised based on the aforementioned dual-range design.

2. Conceptual design

2.2. Design of a compliant stage with dual resolutions

The conceptual design of a micropositioning stage with dual ranges and dual resolutions is detailed in this section.

Given the foregoing analysis, it is observed that in the smaller motion range of [−R1 , R1 ], the deformation is experienced by both bearings, whereas in the larger motion ranges of [−R1 − R2 , −R1 ] and [R1 , R1 + R2 ], the deformation of the mechanism is attributed to bearing #2 alone. In the smaller range, the deformations 1 and 2 of the bearings #1 and #2 are related by:

2.1. Design of a compliant stage with dual ranges The schematic for a one-axis, dual-range micropositioning stage is depicted in Fig. 1. The output platform M is actuated by a linear actuator through a compliant guiding bearing #1, which has an effective stiffness K1 . In addition, the platform M is connected to a fixed base via a compliant guiding bearing #2, which exhibits a stiffness K2 . To yield two motion ranges for M, a mechanical mover is linked to the driving end of the actuator. The bidirectional translation of the mover is constrained by two mechanical stoppers, which are fixed on the output platform M. It is notable that the two stoppers move along with the output platform M. Without loss of generality, it is assumed that the clearances (ı) between the mover and the two stoppers are identical. Referring to Fig. 1, once the actuator drives the output platform to move forward (to the right), both bearings #1 and #2 are compressed. The overall equivalent stiffness can be expressed as Krange1 =

1 . (1/K1 ) + (1/K2 )

(1)

Assume that the relationship of K1 < K2 holds. After a particular driving displacement of D1 , the mover translates over a distance of ı (i.e., the clearance between the mover and forward stopper) with respect to M. Then, it contacts the stopper. The corresponding displacement R1 of the output platform can be calculated in view of the relationship: K1 (D1 − R1 ) = K2 R1 ,

(2)

K1 1 = K2 2 ,

(6)

which describes the driving force of the actuator. Assume that K1 < K2 , then it can be deduced from (6) that 1 > 2 , i.e., the deformation of bearing #1 is greater than that of bearing #2. It is known that strain type sensors can be employed to measure the displacement of compliant mechanisms indirectly by detecting the varying strain of deformed material [22]. If the same kind of strain sensor is adopted to measure the two different deformations, the larger the deformation is, the larger the output signal amplitude will be. That is, a larger deformation results in a higher signal-to-noise ratio, i.e., higher measurement resolution. Therefore, the deformation of bearing #1 can be monitored using a strain sensor to obtain a higher position resolution in the smaller range of [−R1 , R1 ]. However, the deformation of bearing #2 can be measured with a lower resolution in the larger ranges of [−R1 − R2 , −R1 ] and [R1 , R1 + R2 ] by the same type of sensor. In this way, a micropositioning stage with dual ranges and dual resolutions is devised. Specifically, the higher and lower resolutions are generated in the smaller and larger motion ranges, respectively. 3. Mechanism design An embodiment of the proposed compliant stage is designed as shown in Fig. 2. The leaf flexures are adopted to enable a large

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Q. Xu / Sensors and Actuators A 205 (2014) 6–14

3.2.1. Smaller range design To produce a smaller motion range R1 , the absolute deformation of bearing #1 can be derived as follows:

K1 Stopper

h1

l1

K2

h2

ı = D1 − R1 ,

l2

where D1 is the driving displacement of the actuator. Then, inserting (3) into (9), a fundamental operation gives

Linear actuator

Output platform

R1 =

K1 ı, K2

(10)

which indicates that the magnitude of smaller motion range R1 is governed by the clearance ı and the effective stiffnesses K1 and K2 of the two bearings. Hence, to get a smaller range R1 , the clearance between the mechanical mover and each stopper should be designed as

Mover

Fixing holes

Strain gauge #1

(9)

ı=

Strain gauge #2

Fig. 2. Schematic of a compliant micropositioning stage with dual ranges and dual resolutions.

motion range in the compliant stage. Note that the mechanical stopper is mounted on the rear side of the mechanism. Referring to Fig. 2, the bearing #1 is denoted by its effective stiffness K1 , and the remaining flexures belong to bearing #2, which possesses an effective stiffness K2 . The bearing #2 is designed using compound parallelogram flexures to generate a large motion range while maintaining the mechanism’s compact size. More discussions can be found in the literature [23]. A relatively large transverse in-plane stiffness is guaranteed by the bearing #2. To produce a stage with the desired performance in terms of motion ranges and fine/coarse resolution ratio, the parameters of the flexures require a careful design, as stated below.

K2 R1 , K1

(11)

which is calculated from (10). The required input displacement from the actuator can be obtained from (3) D1 =



1+



K2 K1

R1 .

(12)

Meanwhile, to avoid the plastic deformation of the flexures, the stress induced by the deflection ı of the bearing #1 should stay within the yield stress of the material. The allowable maximum motion range of bearing #1, i.e., the allowable maximum clearance, can be computed as follows: ımax =

2y l12 3Eh1

,

(13)

where  y denotes the yield stress of the material. To ensure the safety of the material, the magnitude of the smaller motion range should be designed as follows: 2y l12 K1 K1 max ı = . K2 3Eh1 K2

3.1. Stiffness calculation

R1 ≤ R1max =

First, the equivalent stiffnesses of the two guiding bearings are calculated. Bearing #1 consists of four fixed-guided flexures, that experience identical deformation due to having the same dimensions. Given the serial and parallel connections of these flexures, the equivalent stiffness can be derived as follows [23]:

3.2.2. Larger range design Taking into account that only bearing #2 is deformed in the larger motion interval of R2 , the required driving displacement from the actuator is derived as D2 = R2 .

3

K1 =

Ebh1 l13

,

(7)

where E is the Young’s modulus of the material, and b, h1 , and l1 represent the thickness, width, and length of the leaf flexures (see Fig. 2), respectively. In addition, considering that bearing #2 is composed of two basic modules of compound parallelogram flexure [23], its stiffness value can be derived as

(15)

Similarly, to guarantee the safety of the material, the allowable maximum motion range of bearing #2 is calculated as max = 2

4y l22 3Eh2

.

(16)

Therefore, the span of the larger motion range should be designed as follows: R2 ≤ R2max = max − R1 = 2

3

K2 =

Ebh2 l23

(14)

,

(8)

where h2 and l2 describe the width and length of the associated leaf flexures (see Fig. 2), respectively.

3.2. Motion range design Assume that the smaller and larger motion ranges are [0, |R1 |] and [|R1 |, |R1 + R2 |], respectively. The following design allows the generation of these ranges.

4y l22 3Eh2

− R1 ,

(17)

so that the safety of the material is guaranteed. 3.3. Motor stroke and driving force requirement We adopt a VCM to generate a relatively large motion range. To produce a one-sided entire motion range of R1 + R2 , a driving displacement of D1 + D2 = (1 + (K2 /K1 ))R1 + R2 is needed. This displacement should not exceed the one-sided stroke Dstroke of the selected actuator, i.e. Dtotal =



1+

K2 K1



R1 + R2 ≤ Dstroke .

(18)

Q. Xu / Sensors and Actuators A 205 (2014) 6–14

9

Table 1 Main parameters of a compliant micropositioning stage.

R

R

−

Vo

+

+

Vs

−

R

R + dR (strain gauge)

Fig. 3. Wheatstone bridge circuit with a single strain gauge and three fixed resistors.

Parameter

Value

Unit

b h1 l1 h2 l2 ı E y

10 0.35 35 0.35 20 1.08 71.7 503

mm mm mm mm mm mm GPa MPa

where ε is the corresponding strain induced by the deformation of the flexure bearing. The strain ε is related to the experienced stress  of the flexure by  = E ε,

In addition, considering that VCM typically delivers a not-large driving force, the stage should be compliant enough that the elastic energy can be overcome by the VCM. Assume that K1 < K2 , then it can be deduced from (1) and (4) that Krange1 < Krange2 ; that is, the stiffness in the smaller motion range is lower than that in the larger range. Thus, it can be deduced that the maximum force is needed to produce the extremum of the larger motion range. The required maximum driving force is calculated as follows: Fmax = Krange2 (R1 + R2 ) ≤ Factuator ,

(19)

where Factuator denotes the maximum driving force of the VCM actuator. Substituting (4) and (8) into (19) yields 3

Fmax =

Ebh2 l23

(R1 + R2 ) ≤ Factuator ,

(20)

which provides a guideline for the stage’s parameter design.

To measure the displacement of the compliant stage in the smaller and larger motion ranges, two sets of strain gauges are employed. The position of the maximum stress can be determined by conducting an FEA simulation. To enhance the signal-to-noise ratio, the strain gauges are attached around the maximum-stress positions of the leaf flexures related to bearings #1 and #2, respectively, as depicted in Fig. 2. The relationship (6) indicates that K2 1 = . K1 2

(21)

By selecting K1 < K2 , the relation of 1 > 2 can be determined. It follows that in the smaller motion range, the length change value of strain gauge #1 is larger than that of gauge #2. Therefore, a higher signal-to-noise ratio is expected for gauge #1. Hence, gauge #1 achieves a better displacement resolution than gauge #2. Without loss of generation, assume that the output displacement of the stage is measured by the strain gauge sensors through quarter-bridge signal conditioning circuits, as shown in Fig. 3. The output voltage of the bridge circuit can be approximated by [24] Vo =

Vs × dR, 4R

(22)

where dR and R represent the change value and nominal value of the gauge resistance, respectively. The gauge factor is expressed as S=

dR/R , ε

where E is the Young’s modulus of the material. Given the mechanics of material, the relationship between the stress  and guided deflection  of a leaf flexure can be derived as =

Khl , 4I

(23)

(25)

where K = Ebh3 /l3 and I = bh3 /12 are the linear stiffness and moment of inertia for a leaf flexure, respectively. In view of the above equations, a relationship between the circuit output voltage Vo and flexure deflection  can be derived as =

4l2 Vo . 3hSV s

(26)

It is notable that the deflections of the flexures (1 and 2 ) in bearings #1 and #2 are equal to a half and a quarter of the entire translations (1 and 2 ) of the bearings, respectively. Hence, the ratio of output voltages of the two strain gauges is obtained as 2h1 l22 1 Vo1 = . Vo2 h2 l12 2

3.4. Sensor deployment

(24)

(27)

Given (21), the above relation becomes 2h1 l22 K2 Vo1 = . Vo2 h2 l12 K1

(28)

In the following section, a dual-range, dual-resolution compliant stage is devised to illustrate the proposed design procedures. 4. Performance evaluation Once the desired motion ranges R1 and R2 of the compliant stage are specified, the relationships involving (13), (14), (17), (18), and (20) provide the guidelines for the parameter design. As a case study, a micropositioning stage is designed to produce the smaller and larger motion ranges of R1 = 0.2 mm and R2 = 3.0 mm, respectively. The VCM provides a stroke of ±5 mm and a maximum driving force of 29.2 N. The stage material is chosen as Al 7075 and the stage parameters are designed as shown in Table 1. 4.1. Analytical model results The stiffnesses K1 and K2 of the two bearings are calculated using (7) and (8), respectively. The results are summarized in Table 2. The analytical models predict that R1max = 3.05 mm, R2max = 10.48 mm, Dtotal = 4.28 mm, and Fmax = 12.30 N, which all satisfy the aforementioned design criteria. In addition, the calculated overall motion range of the stage is ±3.2 mm. Moreover, the parametric design leads to an output voltage ratio of Vo1 /Vo2 = 3.50. Therefore, the signal-to-noise ratios (SNRs)

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Q. Xu / Sensors and Actuators A 205 (2014) 6–14

Table 2 Stage performances evaluated by analytical models and FEA simulations. Performance

Analytical model

FEA simulation

Model error (%)

K1 (N/m) K2 (N/m) R1max (mm) R2max (mm) D1 (mm) D2 (mm) Fmax (N)

717.0 3842.7 3.05 10.48 1.28 3.00 12.30

750.3 4006.7 3.02 9.36 1.268 3.00 12.82

−4.44 −4.09 0.99 11.97 0.95 0 −4.06

of the two strain gauge sensors can be derived as SNR1 /SNR2 = 3.50. This means that the resolution ratio of the two strain sensors is about 1/3.50; that is, the resolution in the smaller range has been improved by 3.50 times as compared with that in the larger motion range. 4.2. FEA simulation results To verify the performance of the stage, FEA simulations are conducted using an ANSYS software package. 4.2.1. Static analysis results First, the static performance of the designed stage is evaluated using static structural FEA. The simulations are carried out by applying an input force to produce the smaller and larger motions, respectively. For the smaller motion range, the deformation result of the FEA is illustrated in Fig. 4(a). To generate a motion range of ±0.2 mm, the required driving displacement is D1 = ±1.268 mm. Taking the FEA result as the benchmark, it can be seen that the analytical model result is 0.95% higher than that of the FEA. Moreover, the simulation results reveal that the maximum value of the smaller range is R1max = 3.02 mm. The discrepancy between the analytical model and the FEA is about 1%. Fig. 4(b) displays the positions at which the maximum stress occurs for bearings #1 and #2. Regarding the larger motion range, the FEA results indicate that the maximum deflection R2max = 9.36 mm. Compared with the FEA results, the analytical model overestimates the larger motion range by 11.97%. In addition, to generate a one-sided overall motion range of 3.2 mm, the FEA predicts that the required maximum driving force is Fmax = 12.82 N. The difference between the analytical and FEA results is 4.06%. For a clear comparison, the results of the analytical models and the FEA simulations are tabulated in Table 2. The model errors mainly arise from the adopted assumption for the analytical models, which only consider the bending deformations of the leaf flexures. The model accuracy can be enhanced by means of the nonlinear modeling. 4.2.2. Dynamic analysis results The modal analysis simulation is performed to evaluate the dynamic performance of the stage. To generate a better assessment through FEA simulation, all of the moving components including the moving coil of the VCM, the mechanical mover, and the sensor target are added to the stage. In addition, to obtain the resonant modes excited by the actuation, a cylindrical constraint is added to restrict the movement of the moving coil in the axial direction only. The simulation results of the first-four resonant modes are shown in Fig. 5. It is observed that the first mode shape indicates a translation along the working direction with a resonant frequency of 20.58 Hz, whereas the second mode (68.45 Hz) is attributed to the in-plane translations of the moving coil and output platform in opposite directions. The third mode (120.96) is caused by the rotational

Fig. 4. Static FEA simulation results. (a) Deformed shape and (b) stress distribution.

Fig. 5. The first-four resonant modes of the stage.

Q. Xu / Sensors and Actuators A 205 (2014) 6–14

11

Input voltage (V)

0.2 (a) 0.1 0 −0.1 −0.2 0

5

10 Time (s)

15

20

−4

Output voltage (V)

2

x 10

(b)

Strain gauge 1

1 0 −1 Strain gauge 2 −2 0

5

10 Time (s)

15

20

5

10 Time (s)

15

20

Displacement (μm)

200

Fig. 6. (a) CAD model and (b) fabricated prototype of the micropositioning stage.

motion of bearing #1, which is not likely to be induced by the actuation in a linear direction. In addition, the fourth mode (172.90 Hz) is contributed by the translations of the intermediate flexures associated with the two bearings. Note that the output platform only undergoes a slight movement under this resonant mode. 5. Prototype development and experimental studies In this section, a prototype micropositioning stage is described and its performances are verified by means of experimental studies. 5.1. Prototype development Fig. 6(a) depicts a CAD model of the stage, and a photo of the prototype stage is shown in Fig. 6(b). The prototype is fabricated from a plate of Al 7075 alloy by wire-electrical discharge machining. Note that the four intermediate flexures in bearing #1 of the prototype have been snipped to comply with the design. The stage possesses a dimension of 110 mm × 100 mm × 10 mm. Concerning the actuator, a VCM is selected by considering the stroke and force requirements. In particular, the VCM (model: NCC04-10-005-1A, from H2W Techniques, Inc.) is chosen to provide the maximum driving force of 29.2 N and a stroke of 10.2 mm. The VCM is driven by the NI-9263 analogy output module (from National Instruments Corp.) through a VCM driver. The stage output displacements in the small and large ranges are measured by two strain gauges (model: SGD-3/350-LY13, from Omega Engineering Ltd.), each of which owns a nominal resistance of 350 , a gauge factor of 2, and a dimension of 7 mm × 4 mm. To measure the quarter-bridge circuit (see Fig. 3) output, the NI-9945 quarter-bridge completion accessory is used to complete the 350  sensor. The NI-9945 contains three high-precision resistors of 350 . Generally, the output voltage of a Wheatstone bridge is very small. The bridge output can be accurately acquired by using a high-resolution data acquisition device. In this research, the

(c) 100 0 −100 −200 0

Fig. 7. (a) Input voltage; (b) output voltages of the two strain gauges and (c) output displacement measured by the laser sensor.

NI-9237 bridge input module is employed, which provides a 24-bit resolution. It produces the maximum voltage output of ±25 mV per volt of excitation voltage. For the calibration of the strain sensors, a laser displacement sensor (model: LK-H055, from Keyence Corp.) with a resolution of 25 nm and a measurement range of 20 mm is employed. In addition, a NI cRIO-9022 real-time controller combined with a NI-9118 chassis is adopted as the control hardware. NI LabVIEW software is employed to implement a deterministic real-time control of the micropositioning system. 5.2. Static and dynamic testing First, the sensor resolutions in the two motion ranges are tested. By applying a sinusoidal voltage signal with a frequency of 0.1 Hz and an amplitude of 0.15 V (see Fig. 7(a)) to the VCM driver, the output position of the stage is measured by the two strain gauges (see Fig. 7(b)) and the laser sensor (see Fig. 7(c)). It is observed that the two strain gauges produce the voltage ranges of 2.5485 × 10−4 and 8.2139 × 10−5 V, respectively. This leads to an output voltage ratio of Vo1 /Vo2 = 3.10. Assuming the same magnitude for the two sensor noises, the SNR ratio of the two strain gauge sensors can be obtained as 3.10, which is close to the analytical prediction of 3.50. The two strain gauge sensors are calibrated by comparing their output voltages to the laser sensor output. The calibrated sensors provide the output displacements as shown in Fig. 8, which indicates that the output of sensor #2 is noisier than that of sensor #1. With zero voltage input, the noises of the two sensors are recorded as shown in Fig. 9, and they closely follow normal distributions with standard deviations () of 1.6525 and 5.2514 ␮m, respectively.

12

Q. Xu / Sensors and Actuators A 205 (2014) 6–14 Table 3 Comparison of the desired and actual stage performances.

Displacement (μm)

200 (a)

Performance

100 0 −100 −200 0

5

10 Time (s)

15

20

5

10 Time (s)

15

20

Displacement (μm)

200 (b) 100 0 −100 −200 0

Desired

Experiment

Small range (mm) [−0.2, 0.2] [−0.22, 0.23] [−3.2, −0.2] & [0.2, 3.2] [−2.8, −0.22] & [0.23, 3.2] Large range (mm) Fine/coarse resolution ratio 1/3.50 1/3.18

Fig. 8. Experimental results of the calibrated strain sensor #1 (a) and strain sensor #2 (b).

Second, the magnitudes of the two motion ranges are tested by applying a sinusoidal signal with an amplitude of 3 V, as shown in Fig. 10(a). The output displacements are measured by the two strain sensors as plotted in Fig. 10(b) and (c), respectively. Sensor #1 saturates in the range around [−220 ␮m, 230 ␮m], which represents the smaller motion range of the stage. In the larger motion ranges of [−2800 ␮m, −220 ␮m] and [230 ␮m, 3200 ␮m], the output displacement is measured exclusively by sensor #2, which provides a worse resolution than sensor #1, as tested earlier. Third, the dynamic performance of the stage is examined by the frequency response method. Specifically, a swept-sine signal with an amplitude of 0.02 V and a frequency range of 1−500 Hz is applied to drive the VCM. The frequency responses of the stage output position are shown in the Bode plots in Fig. 11, which are generated from the outputs of the laser sensor and two strain sensors. The two strain sensors capture the first-three modes at 16.7, 44.9, and 117.5 Hz, respectively. In contrast, the laser sensor is only able to detect the first two modes. 5.3. Discussion

By adopting 3 as the resolution, the resolutions of the fine and coarse sensors are calculated as 4.9575 and 15.7542 ␮m, respectively. Hence, the minimum steps of this stage that can be detected in the fine and coarse ranges are 4.9575 and 15.7542 ␮m, respectively. In addition, the resolution ratio of the two sensors can be derived as 1/3.18, which is very close to the analytical prediction of 1/3.50. Therefore, the resolution in the smaller range has been improved by 3.18 times compared with that in the larger motion range.

For a better understanding of the results, a comparison of the desired and actual performances of the stage is shown in Table 3. The smaller motion range is larger than the design goal of ±0.2 mm while the larger range is slightly lower than the design specification of ±3.2 mm. The overall motion range of 6.0 mm is very close to the design objective of 6.4 mm, which also indicates that the driving displacement lies within the stroke of the employed VCM actuator. The fact that the static testing results of the bidirectional motion range are not exactly symmetric with respect to zero may

10

10 (b)

5

Noise (μm)

Noise (μm)

(a)

0 −5 −10 0

30

5

10 Time (s)

15

0 −5

30

(c)

2000

10 0 −10 −20

4000 Counts

6000

(d)

20 Noise (μm)

Noise (μm)

σ = 1.6525

−10 0

20

20

−30 0

5

σ = 5.2514

10 0 −10 −20

5

10 Time (s)

15

20

−30 0

2000

4000 Counts

6000

Fig. 9. (a) Time history of the measured noises of strain sensor #1 and (b) the noise histogram; (c) time history of the measured noises of strain sensor #2 and (d) the noise histogram.

Q. Xu / Sensors and Actuators A 205 (2014) 6–14

Input voltage (V)

4 2 0 −2 (a) −4 0

5

10 Time (s)

15

20

5

10 Time (s)

15

20

5

10 Time (s)

15

20

Displacement (μm)

400 200 0 −200 (b) −400 0

Displacement (μm)

4000 2000 0 −2000 (c) −4000 0

Fig. 10. Experimental results of motion range tests: (a) input voltage; (b) smaller motion range measured by strain sensor #1; and (c) larger motion range measured by strain sensor #2.

100 Magnitude (dB)

80 60 40 20 0 −20 0 10

Laser sensor Strain sensor 1 Strain sensor 2 Mode 1 Mode 2 Mode 3 1

10

2

10

1000 Phase (degree)

0 −1000 −2000 −3000 −4000 −5000 0 10

1

10 Frequency (Hz)

2

10

Fig. 11. Bode plots of the frequency responses obtained by three sensors.

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be attributed to manufacturing errors and the unequal clearance between the mover and each stopper. The discrepancy between the desired and actual resolution ratios for the two ranges may be caused by manufacturing errors and the variations in the adhesive layers of the two strain gauges. The two strain sensor outputs are compared under the assumption that they are glued on the flexures under the same conditions in terms of the thickness of the adhesive layers and operation temperature, etc. The resolutions of the two strain sensors are tested using the quarter-bridge circuits without adopting filters. The resolutions can be improved two-fold or four-fold by using half-bridge or full-bridge circuits, respectively. Moreover, the resolution can be further enhanced by removing the low-frequency noises of the sensor outputs. Regarding the dynamic performance testing, all three sensors predict a first-mode frequency of 16.7 Hz, which is 18.85% lower than the FEA simulation result of 20.58 Hz. The discrepancy between the simulation and experimental results for the resonant frequencies mainly comes from a fabrication error in the stage parameters. In practice, input signals with the frequency component around 17 Hz will excite the first resonant mode, and the first natural frequency limits the usable bandwidth of the system. Thus, a high first natural frequency is important to achieve a large control bandwidth. In addition, a comparison of the frequency responses generated by the laser sensor and the two strain sensors shows that the laser sensor is only able to detect two of the three modes in the specified frequency range of 1–500 Hz. Why the laser sensor cannot capture the other resonant mode can be explained by considering the measurement principles of the sensors. Specifically, the two strain sensors measure the displacement of the output platform indirectly by monitoring the strain deformation of the internal flexures associated with the two compliant bearings. The laser sensor is fixed at the base, and it directly measures the output displacement of the platform through the sensor target, which is attached to the platform. As predicted by FEA simulation (see Fig. 5), the first and second modes are attributed to the translations of the output platform and the two bearings. Thus, they are detected by all three of the sensors. However, the other resonant mode (117.5 Hz) is dominantly contributed by the deformation of the intermediate flexures, as evaluated by FEA (see Fig. 5(d)) while the output platform only experiences a negligible translation. Hence, this mode is not detected by the laser sensor, which monitors the output platform displacement, but it is captured by the two attached strain sensors. The experimental results verify the resonant mode shapes evaluated by FEA simulation. The drawback of the proposed stage is that the fine positioning resolution only applies to a smaller range, although the coarse resolution can be used in both smaller and larger ranges. Hence, fine tuning can only be implemented in the smaller motion range around the home position of the stage. When the lower stiffness mechanism impacts the stopper, the flexure may vibrate and the larger motion may be affected by the impact. The impact effect cannot be observed in Fig. 10(b) and (c) because these results are generated by applying an input signal with a low frequency (0.1 Hz). An input signal with a higher frequency (e.g., 1 Hz) will lead to an apparent impact effect. Yet, unlike the interference in dual-servo stages, where the interaction occurs during the entire positioning of the fine stage, the impact effect in the presented dual-range stage only appears at the two limits of the smaller motion range. To avoid this impact, a low positioning speed at the two limits can be commanded. Additionally, the experimental results as shown in Fig. 11 are generated at the stage’s home position; that is, the experiments are conducted in the smaller motion range. If the experiments were conducted in the larger range, the impact between the mover and stoppers would induce unwanted vibrations.

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Q. Xu / Sensors and Actuators A 205 (2014) 6–14

Fig. 12. Microassembly application using the proposed dual-range X stage. The microgripper is driven by a piezoelectric actuator (PZT).

The proposed dual-range stage has promising applications in precision positioning situations. For instance, the dual-range stage can be employed to execute an microassembly task, as illustrated in Fig. 12. In such a case, the dual-range stage is adopted as an X stage and a microgripper is mounted. More details about the gripper can be found in [25]. The fragile micro-objects to be assembled are supported by a coarse YZ stage. First, the object is transported to the vicinity of the gripper tips. If the X stage only provides a coarse resolution [26], an accurate alignment of the gripper tips with respect to the object may not be realized in the x-axis direction. As a result, the fragile object is prone to be damaged or not grasped by the gripper. Alternatively, by employing a dual-range stage as the X stage, the x-axis position of gripper tips can be finely adjusted using the smaller range of the stage for precise gripping. Once the object is grasped, the larger range of the X stage is used to transport the object to a planned assembly destination. It is notable that the resolutions of the stage have been characterized under open-loop drive status. This motivates further work on closed-loop control to realize the precision control of the developed compliant stage. The positioning accuracy and repeatability of the stage will be determined by conducting a closed-loop control. Moreover, the ideas presented here can also be extended to the design of multi-axis micropositioning stages. 6. Conclusion The design and verification of a single-drive compliant micropositioning stage with dual ranges and dual resolutions was presented in this paper. Based on the concept of unequal stiffness, a proof-of-concept design for a novel flexure-based stage was proposed. Analytical models were established to predict the motion ranges, fine/coarse resolution ratio, and driving force and stroke, all of which were verified by finite element analysis and experimental studies. The results show that the single voice coil motor is able to produce dual motion ranges and the same kind of strain gauge sensor is capable of providing fine and coarse resolutions in the small and large ranges, respectively. In future work, control schemes will be developed to accomplish precise positioning for related applications. Acknowledgments This work was supported by the Macao Science and Technology Development Fund under Grant No.: 070/2012/A3 and the Research Committee of the University of Macau under Grant Nos.: MYRG083(Y1-L2)-FST12-XQS and MYRG078(Y1-L2)-FST13-XQS. References [1] T. Tuma, W. Haeberle, H. Rothuizen, J. Lygeros, A. Pantazi, A. Sebastian, A dualstage nanopositioning approach to high-speed scanning probe microscopy, in: Proc. of 51st IEEE Conf. on Decision and Control, Maui, Hi, USA, 2012, pp. 5079–5084.

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Biography Qingsong Xu received the B.S. degree in Mechatronics Engineering (with honors) from Beijing Institute of Technology, Beijing, China, in 2002 and the M.S. and Ph.D. degrees in Electromechanical Engineering from the University of Macau, Macao, China, in 2004 and 2008, respectively. He was a visiting scholar with the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, and the National University of Singapore, Singapore. Since 2010, he has been an assistant professor in the Department of Electromechanical Engineering at the University of Macau. His current research interests include micro-/nanosystems, micro-/nanomechatronics, smart materials and structures, and computational intelligence.