1 Introduction

Because they provide a variety of advantages over conventional linear stages, such as solidity, cost savings, and improved presentation, compliant XY motion stages are viable substitutes. Such applications as micro-assembly, semiconductor placement, fibre alignment, and AFM scanners are among the numerous sectors that employ these stages. By combining them with micro-motion applications, high levels of accuracy and repeatability in the nanoscale range have been made achievable. Compliant stages are free of backlash, friction, noise emission, and the requirement for lubrication. They do, however, have a number of drawbacks, including non-linear behaviour and a constrained working space.

The literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] has reported a number of compliant XY motion stages with motion ranges ranging from 110 to 128 mm2 and positioning accuracy ranging from 10 m to a few nanometres. High accuracy and a sizable working area are frequently only possible with cost effective metrology equipment, such as ultra-high-resolution sensors and actuators with enormous range capabilities. In this study, the idea of two-range manipulation is applied in an effort to achieve positioning accuracy of a few micrometres inside a workspace at a reasonable cost.

The use of two sets of actuators and/or sensors inside the same system is known as dual-range manipulation. The second set covers a smaller area, corrects the positioning mistake of the coarse mechanism, and offers higher precision than the first set, which allows placement in a wider workspace but with less accuracy. The cost reductions, together with the avoidance of difficult calibration requirements and stringent manufacturing and assembly tolerances, are the key benefits of dual-range manipulation.

The design and assembly of traditional dual-range micro-motion stages are made simpler by the use of two serially coupled stages. Some stages use ultra-high resolution sensors, such as laser interferometers, to achieve high absolute positioning precision across a wide range of motion. However, this strategy frequently involves high expenses and has a detrimental effect on the environment. For instance, one stage design [20] layers a piezo (PZT) actuated stage on top of a DC motor-driven stage to provide a workspace of 300 mm2 with positional accuracy of 10 nm. Another step [21] produces a workspace of 500500 mm2 with nanometer-scale precision and a repeatability of 50 nm by using voice coil actuators (VCAs) for fine positioning and linear motors for coarse positioning. An alignment stage described in [22] combines a 2-DOF coarse positioning stage powered by linear motors with a 6-DOF fine positioning stage powered by VCAs and magnetic bearings. Within a 300mm2 area, this combination yields precision of 10 nm and 15 nm along the X and Y axes, respectively. A 3-DOF stage [23] with two linear motors and four PZT actuators has an operating range of 200 mm2 with an accuracy of 13 nm. The combination of VCAs with PZT actuators in the next step [24] results in an accuracy of 20 nm across a 30 mm2 working area. Additionally, a 1-DOF stage [25] uses a VCA for fine motion and a linear motor for coarse motion to achieve positioning precision of 10 nm across a 350 mm working range. The geometrical dimensional values for the mechanism are represented in Table 1.

Table 1 Basic XY motion stage geometrical dimensions
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However, these expensive, highly accurate, and spacious stages are not appropriate for applications requiring the assembly of miniature products [26, 27]. Additionally, stacking two stages on top of one another adds to the moving mass, slowing the dynamic response. As an alternative, some stages employ capacitive sensors, which have excellent resolution and short range capabilities, enabling precise placement [28,29,30,31,32,33,34]. This method involves relative positioning based on, yet it lowers equipment expenses while keeping the same positioning precision.

2 XY motion stage design compliant

The design reported in reference [35] and the implementation in reference [36] served as the foundation for the compliant XY motion stage that is detailed in this work. The beams' dimensions were specially designed for this stage; they were 50 mm long to maximise range of motion, 8 mm tall to maintain z axis stiffness and 0.8 mm thick to reduce input force requirements. This stage is made of aluminium, a substance recognised for its high reversible strain properties, which is consistent with the bulk of compliant stages covered in the literature. At both ends of the beams, rounded corners with a radius of 0.8 mm is given to remove the factor of stress concentration.

2.1 Dynamic analysis

Ensuring the initial natural frequency of the compliant stage is as high as possible is critical to minimize the influence of external vibrations. It is also preferable to maintain a significant ratio between the first two natural frequencies and the third natural frequency. This ensures that the stiffness along the two motion directions remains much lower than the stiffness along other directions, effectively preventing undesired motion. According to existing literature [4, 5, 10,11,12, 37,38,39], the typical range for the ratio of stiffness in compliant stages varies from 3 to 6.

In Fig. 1, the Lanczos Eigen solver is employed for dynamic analysis in ABAQUS on the stage. The research findings indicate that the first two modes correspond to concurrent vibrations along the X and Y axes at a frequency of 57.128 Hz. In the third mode, the Z-axis undergoes rotation, with a frequency of 260.15 Hz, while the fourth mode, at a frequency of 320.03 Hz, depicts vibrations along the Z-axis. This is of utmost importance as the ratio between the first two natural frequencies and the third natural frequency exceeds 4, satisfying the essential stiffness ratio criterion.

Fig. 1
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FEM modal analysis with mode shapes for the mechanism

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3 Manufacturing of XY micro-motion stage

Wire electric discharge machining is used to create the majority of the compliance stages stated in the literature. Although pricey, this method provides flawless surface polishing and excellent tolerances. Alternatives including laser cutting and CNC machining were taken into consideration, but these couldn't mill 0.8 mm-thick beams. While CNC machining would result in beam bending because of the applied cutting force, laser cutting would cause the beams to melt. The stage construction was given corners with a radius of 0.8 mm in order to lessen stress concentration (Fig. 2). With an 18 mm stroke, a continuous force of 73.2 N, and a force constant of 23.16 N/A, the stage is driven by two Moticont VCA (Voice Coil Actuator). High-precision micro guides from SKF that are preloaded are used to guide the moving coils. A 12-bit Analog-to-Digital Converter (ADC) that can resolve position instructions down to 1.201 m over 4 mm in both directions is produced by two drives operating the VCAs. The displacement of the actuators is determined by means of two Renishaw linear encoders with 115 nm precision.

Fig. 2
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XY stage designed and manufactured mechanism (37)

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3.1 Analysis of frequency response

Using testing apparatus that permits the stage to freely vibrate, the frequency response of the XY motion stage is examined as shown in Fig. 3. A 3-D accelerometer is positioned in the middle of the stage to measure the vibrations produced along the X, Y, and Z axes by an impulse. The accelerometer in use has a sensitivity of 115 mV/G. A Dual Channel Accelerometer Amplifier processes the output signal from the accelerometer, and a National Instruments data capture device with a 15 kHz sampling rate records the amplified signal.

Fig. 3
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Test setup for the experimentation with all components

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The Fast Fourier Transform (FFT) technique is used with LabVIEW software to examine the frequency domain response of each direction of motion. Peaks may be used to identify the natural frequencies along each of the motion axes by looking at the amplitude spectrum. The acquired findings are compared to the FEA predictions after accounting for the accelerometer's mass.

Along the X, Y, and Z axes, the measured resonance frequency is determined to be 50 Hz, whereas it is 281 Hz along the other two axes. The associated errors are found to be 18% along the X, Y, and Z axes and 16% along the Z axis when compared to the FEA findings. The lack of adequate preloading of the beams during screwing by the mounts may account for the disparity in measurements.

4 XY two-series locating micro-motion stage

A complete XY motion range is shown in Fig. 4. It is made up of a platform that is positioned right in the centre of the complying stage. Displacement of output stage is measured using two small plates that are positioned on the platform as targets. The movable mass of the stage as a whole is around 1.8 kg.

Fig. 4
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Developed XY stage mechanism

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4.1 Initial position control

A proportion-integral-derivative loop used to regulate the linear displacement of the VCAs for input position control. The stage's output displacement is sent back by the two linear encoders. Two Micro-Epsilon capacitive sensor heads (CS1) and DT controllers are employed to precisely detect the output displacement. These sensors have a obtained accuracy of 0.8 m across a series of 3 mm and a resolution of 110 nm. Two L12-P micro linear actuators are used to move them along a guide rail while they are placed on a carrier. These actuators feature a 14 mm stroke and 0.3 mm repeatability.

LABVIEW 2014 is used to control the input displacements along the X and Y axes of the XY motion stage using the analogue outputs of a Lab jack U6 Pro DAQ system.

The stage is displaced along the Y direction by a range of 0 to 4 mm during the single direction displacement test. The findings show that there is a 7 μm disparity between the input and output displacements. There is also a parasitic movement of 60 m in the transverse direction, which translates to a coupling of 3% (Fig. 11). Throughout the bi-directional loading test, the stage maintains the 3 mm input displacement along the Y direction while gradually applying a 4 mm input displacement along the X direction. The results, as shown in Fig. 12, are consistent with the FEA predictions with a maximum error of less than 5 m for the 4 mm input displacement. The largest parasitic displacement that has been observed is 60μ m. These data validate the stage's behaviour in comparison to the projected outcomes from finite element analysis (FEA), demonstrating the correctness and consistency of the stage's performance.

4.2 Two-range positioning

In the XY motion stage, a dual-range positioning method is used to resolve the coupling and positioning inaccuracy that have been noticed. To immediately monitor the stage's output displacement and correct the positioning fault, high-resolution sensors are used. With a 12 mm stroke and a repeatability of 0.3 mm, Firgelli L12-P micro linear actuators are used to move the sensors along a guiding rail while they are mounted on a carrier. Following are the processes involved in the two-range positioning technique for either direction of motion:

  1. 1.

    As a coarse positioning step, the stage is first pushed into the required location in open-loop mode.

  2. 2.

    Next, the moving platform is approached by the high-resolution sensors, and the distance between them is measured. This distance serves as the starting location for the following phase.

  3. 3.

    An outside system is used to measure the positioning inaccuracy.

  4. 4.

    The stage is moved in closed-loop mode utilising the high-resolution sensors' feedback, and the detected positioning error is used to correct the location. The step of fine placement is this.

The output displacement of the stage is modified by a second PID loop using information from the high-resolution sensors. Gains are first adjusted by trial and error, and if more fine-tuning is necessary, it may be carried out at a later stage of development. The streamlined plant model is shown in Fig. 5, which also shows how the PID control loop and high-resolution sensors were integrated. This dual-range positioning strategy improves the XY motion stage's precision and control, providing more precise and dependable placement for a variety of applications.

Fig. 5
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Control system for accurate position for the motion stage

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The user's choice of the XY motion stage's integration into the larger system determines which external system will be used to measure positioning inaccuracy. To find the location of the movable platform where a calibration grid is placed, for instance, one possibility is to use a high-resolution vision system. In a previous study, the positional error was measured using a coordinate measuring machine (CMM) [36].

4.3 Selection of a sensor

It is crucial to use a high-resolution sensor, even when doing so requires making a trade-off between measurement precision and system cost. Table 2 uses information from RENISHAW®, KEYENCE Ltd., and MICRO-EPSILON Ltd. to offer a qualitative analysis of four alternative sensor types for this specific application. The capacitive sensor stands out as the best choice among these alternatives since it strikes a balance between price and precision. As a result, the linear actuators are utilised in conjunction with the same sensors that were used to monitor the compliant stage's open-loop behaviour for the closed-loop control of precise placement. Figure 3 shows the layout of the XY motion stage with dual-range arrangement.

Table 2 Description of the sensors
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5 Experimentation

Capacitive sensors may be used to evaluate the relative positioning precision by sensing the stage's location directly. The force disturbance is thought to be more severe for larger displacements because of the nonlinear stiffness of the compliant stage. Tests are conducted with input displacements of 4 mm in both directions and no deflection in either direction in order to evaluate this. In fine positioning mode, measurements from the sensors are collected during a 28-s period, and accuracy is calculated based on the maximum oscillation amplitude after the system enters steady state.

It's also important to keep in mind that the analog-to-digital converter (ADC) that the data acquisition card uses to understand position instructions only has a 12-bit resolution. 1.8 μm of incremental position resolution is the outcome. It might be possible to achieve higher positioning precision by using controllers with higher resolution.

The steady-state response for zero loading in both directions as no external applied forces on the mechanism as shown in Fig. 6. It is clear that the greatest oscillation amplitude is less than 0.8 m, which exceeds the capacitive sensors' reading accuracy. Figure 7 on the other hand shows the reaction at steady state for a ± 4 μm bidirectional loading. The oscillation's amplitude grows until it reaches ± 4 μm demonstrating the presence of nonlinearities brought on by the compliant stage.

Fig. 6
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X and Y axis positioning output readings from the capacitive sensors (initial 0 mm)

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Fig. 7
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X and Y axis positioning output readings from the capacitive sensors (final 4.0 mm)

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The design, characterization, and production of an aluminium compliant XY micro-motion stage. With a coupling ratio of 2.9%, it provides a travel range of around 4 mm in both the X and Y axes. The working area and stiffness results from the simulation are in good agreement with those from the finite element analysis (FEA). A maximum displacement inaccuracy of 75 m was noted during the coarse positioning mode evaluation of the micro-motion stage.

5.1 Analysis of displacement versus force

The actuators are sized and the stage's travel range is determined using FEA analysis utilising ABAQUS. A buckling analysis and a stress/strain analysis make up the analysis.

The travel range of the stage is determined by the buckling analysis, which identifies the buckling point of the beams. Short beams may need to be subjected to much higher pressures than necessary to attain the material's yield strength before they buckle. Buckling, however, could happen before the yield strength is attained for longer or thinner beams. In this instance, buckling is observed at the inner beams Fig. 8 and the stage's difference between input and output displacement considerably widens when the stress at the centre abruptly increases. The buckling point is predicted to occur at a displacement input of about 4.257 mm, or a force input of 363.123 N, in accordance with Fig. 9.

Fig. 8
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Buckling point load applied in X direction

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Fig. 9
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Response of large displacement for the stress versus displacement

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The input displacement is gradually delivered on one side of the stage until the material's yield strength is attained before continuing with the stress/strain analysis. Throughout this evaluation, the output displacement, maximum stress, and response force are noted. In this specific instance, the reaction force of 210.011 N and the yield strength of 514 MPa are attained with an input displacement of 3.4025 mm. Thus, the stage's travel range is primarily constrained by the yield strength of the aluminium.

The final design limits the travel range in the x and y axes to 3 mm in order to guarantee a long fatigue life and reduce the needed force input. The input force associated with this restriction is approximately 70 N.

The axial deformation of the inner parallelogram beams is taken into account as well as a comparison of the output displacement to the input displacement. This distortion causes a little discrepancy between the output and input displacements. According to the data, the discrepancy between input and output displacements can be as much as 7 μm for input displacements between 0 and 4 mm.

5.2 Coupling analysis

For a compliant stage, minimising cross-coupling between the axes of motion is preferred. A computation is done to determine the parasitic displacement in the Y direction when a load is applied in the X direction in order to explore this. In the beginning, as represented in Fig. 10, a input displacement of 3 mm is applied along the Y direction. According to the calculations, a coupling of 5% corresponds to a maximum parasitic displacement of 75 μm (Fig. 11). Then, a 4 mm input displacement along the X direction is progressively applied. According to the findings, the greatest Y-direction displacement error is 71 μm (Fig. 12).

Fig. 10
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X Y stage direction deformation for the motion stage

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Fig. 11
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One direction estimation of parasitic displacement for XY loading

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Fig. 12
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Error for the XY displacement

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5.3 Force–displacement test

The relationship between input displacement and the corresponding response force was investigated in this study. While the X-axis remained fixed, the input displacement was varied along the Y-axis within the range of 0 to 4 mm. To measure the positions of the Variable Compliance Actuator (VCA), linear encoders were employed since the servo motors incorporated current sensors [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]. The force was subsequently determined using the VCA's force constant, and the results, depicted in Fig. 13, reveal that the primary source of initial force inaccuracies can be attributed to internal friction in the bearings, which can be considered negligible [56,57,58,59,60,61]. When compared to the Finite Element Analysis (FEA) results, the largest force discrepancy, occurring at a 3 mm displacement, amounts to 14%. When trying to find answers to the numerous issues that are encountered in the manufacturing sector, there are a wide variety of approaches and methods that can be tried [62,63,64,65,66,67,68,69,70]. In the beginning, the experimental method was utilized to solve a broad variety of issues that were connected to the manufacturing sector [71,72,73,74,75,76,77,78,79,80,81,82,83,84,85]. As a result of developments in technology, the experimental procedures can now be evaluated, and the outcomes of those tests can be anticipated, prior to the methodologies actually being put into exercise [86,87,88,89,90,91,92,93,94,95,96,97,98,99,100] The characterization strategies and procedures that are utilized by a variety of specialists in the course of the component manufacture are essential to making a significant contribution to the fields of materials and manufacturing [101,102,103,104,105,106,107,108,109,110,111].

Fig. 13
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One direction stiffness for the mechanism

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6 Conclusions

A system of dual-range manipulation has been developed, utilizing capacitive sensors to enhance positioning accuracy significantly. In the most challenging scenarios, relative location accuracy has been improved to less than ± 4 μm. The implementation of sensors with even higher resolution and advanced motor controllers is expected to further reduce this level of inaccuracy. These findings underscore the substantial potential of dual-range positioning for creating small, cost-effective, and exceptionally precise micro-motion systems. Incorporating this stage into a hybrid system for assembling miniature products will further expand its range of applications.