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This paper presents the circular tracking performance of a flexure-based micro-motion stage. The mechanical design and prototype development are first illustrated. A double closed-loop control strategy, including the inner and outer feedback controllers, is then employed. Subsequently, main factors affecting its circular tracking performance are further analyzed. Experimental results show that the actual circular trajectory can be enlarged by increasing KP and KI. The circular tracking performance is improved when the sampling period decreases within a certain range. By contrast, it deteriorates as the amplitudes of input sinusoid signals increase. In addition, tracking errors cannot be decreased through exchanging input signals. It demonstrates that there are four parts in a certain cycle where the circular tracking performance is poor. The reason is that these parts are peak and valley points of input signals, and they are influenced by dynamic characteristics of this stage. [ABSTRACT FROM AUTHOR]

A three-legged compliant parallel mechanism (3L-CPM) achieves fully decoupled motions when its theoretical 6 × 6 stiffness/compliance matrix is a diagonal matrix, which only contains diagonal components, while all non-diagonal components are zeros. Because the motion decoupling capability of 3L-CPMs is essential in the precision engineering field, this paper presents the fundamental criteria for designing 3L-CPMs with fully decoupled motions, regardless of degrees-of-freedom and the types of flexure element. The 6 × 6 stiffness matrix of a general 3L-CPM is derived based on the orientation of each flexure element, e.g., thin/slender beam and notch hinge, etc., and its relative position to the moving platform. Based on an analytical solution, several requirements for the flexure elements were identified and needed to be satisfied in order to design a 3L-CPM with a diagonal stiffness/compliance matrix. In addition, the developed design criteria were used to analyze the decoupled-motion capability of some existing 3L-CPM designs and shown to provide insight into the motion characteristics of any 3L-CPM. [ABSTRACT FROM AUTHOR]

Purpose: This paper presents the systematic design and testing of a novel two-axial flexure-based vibration stage. Methods: The testing principle of transverse sensitivity is first established based on the conceptual level and principle level. According to three kinds of flexure-based kinematic chains, the configuration of this stage is then determined. Subsequently, the design based on increasing the degree of segmentation is discussed. Finally, an experimental platform is set up. The repeated tracking performance and measurement uncertainty of transverse sensitivity are tested. Results and Conclusions: The results indicate that it has high repeated tracking accuracy. Average transverse sensitivities for four different cycles at 80, 120, and 140 Hz are 2.487%, 2.367% and 2.281%. The total average is about 2.378%, while the total measurement uncertainty is 0.149% at these different frequencies. [ABSTRACT FROM AUTHOR]

There is an increasing demand to achieve manipulating operations in nanometric precision and a macro-range (over a millimeter) simultaneously. In principle, it is possible to satisfy both requirements in a compact size taking advantages of flexure-based mechanisms, whereas limitations such as the parasitic rotation, cross-axis coupling, saturation may adversely affect the motion quality in nanometric level practically. Here, we propose a novel design methodology to actively prevent parasitic rotation of XY compliant mechanisms. Further, by means of design synthesis and real-time motion control, the prototype of manipulator is fabricated, which enables large motion range (±3 mm) along each actuation axis. Experimental results demonstrate a travel range of 2 mm × 2 mm with high linearity, small cross-axis coupling (< 0.4%), and low parasitic rotation (< 6.9 μ rad over 0.5 mm × 0.5 mm motion range). Moreover, the high natural frequency (~ 60 Hz) of the manipulator facilitates it to achieve high-precision motion with tracking error < 80 nm (20 Hz sinusoids). The experimental results of the proposed nano-manipulator outperform most of the existing ones. [Display omitted] • A large range compliant XY nano-manipulator of active parasitic rotation rejection. • By design of axial force passing through stiffness center, the manipulator does not have parasitic rotation in principle. • High natural frequency facilitates mm stroke and nanometric tracking error as well as micro-radian parasitic rotation. [ABSTRACT FROM AUTHOR]

A three-legged compliant parallel mechanism (3L-CPM) achieves fully decoupled motions when its theoretical 6 × 6 stiffness/compliance matrix is a diagonal matrix, which only contains diagonal components, while all non-diagonal components are zeros. Because the motion decoupling capability of 3L-CPMs is essential in the precision engineering field, this paper presents the fundamental criteria for designing 3L-CPMs with fully decoupled motions, regardless of degrees-of-freedom and the types of flexure element. The 6 × 6 stiffness matrix of a general 3L-CPM is derived based on the orientation of each flexure element, e.g., thin/slender beam and notch hinge, etc., and its relative position to the moving platform. Based on an analytical solution, several requirements for the flexure elements were identified and needed to be satisfied in order to design a 3L-CPM with a diagonal stiffness/compliance matrix. In addition, the developed design criteria were used to analyze the decoupled-motion capability of some existing 3L-CPM designs and shown to provide insight into the motion characteristics of any 3L-CPM.

The paper aims to present a mechatronic device able to micro-position the workpiece and to reject disturbances due to machining operation. A decoupling method is proposed for a parallel kinematic machine (PKM) fixturing platform composed by a 3-DoF flexure-based piezo-actuated mechanism. The parallel platform, with a vertical motion and two rotations, is described and its kinematics and dynamics are studied. The coupling undesirable effect is investigated based on a set of poses. To improve the quasi-static regulator model for a set-point following system, a bump less switching controller and a fine-tuning procedure, to estimate the parameter uncertainty and enable the external disturbance containment in an extended broadband frequency range, are presented. The platform and the piezo-actuator controllers are modelled based on a gain scheduling, standard ISA form method, to guarantee the stability. The accuracy is demonstrated through a set of simulations and experimental comparisons. A sensitivity analysis that evaluates the tracking performance and the disturbance rejection based on the number of signal amplitudes, frequencies, and phases is discussed. A validation phase has shown that the developed architecture presents a steady state error lower than 1.2 µm, a vibration reduction of 96% at 1130 Hz with a maximum resolving time of 6.60 ms.

• An asymmetric flexure-based mechanism was used to realize bi-directional outputs. • A modified sawtooth wave with a cycloid fall curve was used as the driving signal. • Various experiments have been implemented on the developed prototype. A stick-slip based linear actuator was proposed in this paper, which applied the axial motion of the micropositioner to adjust the preload, and the lateral motion to drive the slider. The bi-directional motion of the micropositioner was realized through the asymmetric structure of a flexure-based mechanism, which includes two right circular flexure hinges and four leaf-spring flexure hinges. The static analysis, kinematic analysis and optimization design were successively implemented on the flexure-based mechanism. The Finite Element Analysis (FEA) proved the flexure-based mechanism could generate the bi-directional motion as designed. A prototype of the linear actuator was developed and the measuring system was constructed. A modified sawtooth wave with a cycloid fall curve was designed to improve the output property. The experimental results showed the modified sawtooth wave generated larger velocity than the traditional sawtooth wave in same driving voltages, fall times, driving frequencies and loads. The amplification coefficient and resolution of the proposed linear actuator in single step were 3.16 and 60 nm, respectively. The maximal velocity was 26.2 mm/s with the modified sawtooth wave in driving frequency of 500 Hz. [ABSTRACT FROM AUTHOR]

This paper presents a novel six degrees-of-freedom (DOF) compliant parallel mechanism (CPM) with decoupled output motions, large workspace of ≥6 mm for translations and ≥12° for rotations, optimized stiffness, and dynamic properties. The working range and the motion decoupling capability of the six-DOF CPM are experimentally verified, and the mechanical properties are shown to be predictable. The proposed CPM is synthesized by applying the beam-based structural optimization method together with the criteria for achieving motion decoupling capability. In order to improve the dynamic behaviors for the CPM, cellular structure is used to design its end effector. The obtained results show that the dynamic performance of the CPM with cellular end effector is significantly enhanced with the increase of 33% of the first resonance frequency as compared to the initial design. Performances of the three-dimensional (3D)-printed prototype are experimentally evaluated in terms of mechanical characteristics and decoupled motions. The obtained results show that the actual stiffness and dynamic properties agree with the predictions with the highest deviation of ~10.5%. The motion decoupling capability of the CPM is also demonstrated since almost input energy (>99.5%) generates the desired output motions while the energy causes parasitic motions is only minor (

Abstract Nonuniform web tension has a great negative effect on product quality of roll-to-roll printed electronics. In this paper, a roller posture adjustment device with remote-center-of-motion (RCM) characteristic is proposed to guarantee web tension uniformity. The device combines a high-stiffness spherical air bearing (SAB) and a multi-degree-of-freedom flexure-based mechanism. The nonuniform web tension in lateral direction can be divided into an equivalent force and two equivalent moments. The equivalent moments are caused by the nonuniformity of the web tension. By adjusting the roller angle around y and z -axes, the equivalent moments can be eliminated to guarantee the web tension uniformity. The multi-DOF flexure-based mechanism is composed of a linear mechanism, a rotary mechanism and a 3-DOF off-plane mechanism. Besides, the RCM characteristic of the proposed device is realized to eliminate extra parasitic movement when the roller posture is changed. Based on pseudo-rigid-body model (PRBM) method, the theoretical analysis is conducted to evaluate the kinematics, stiffness and dynamics of the device. Moreover, the parameter optimization is conducted to maximize the first two resonance frequencies of the system. After that, finite element analysis is conducted to validate the established models. Finally, a prototype of the proposed device is fabricated performance verification. The experimental results show that the proposed device has a workspace of 10.22 mrad and 8.16 mrad about two working axes with center shifts of the RCM point less than 0.75%, which demonstrate the superior property of the proposed device. Highlights • A roller posture adjustment device with remote-center-of-motion (RCM) characteristic is proposed to eliminate nonuniform web tension in lateral direction for roll-to-roll printed electronics. • The proposed device combines a high-stiffness spherical air bearing with a multi-DOF flexure-based mechanism for heavy load and precision positioning. • The proposed stage can reach a workspace of 10.22 mrad × 8.16 mrad about two axes. • Pseudo-rigid-body-model (PRBM) method is utilized to conduct theoretical analysis and dimensional optimization and finite element analysis (FEA) validation are conducted. • A prototype of the proposed roller posture adjustment device is fabricated to test the performance of it. [ABSTRACT FROM AUTHOR]

This paper presents the synthesis and evaluation of a 3-D printed three degrees-of-freedom (DOF) spatial-motion compliant parallel mechanism (CPM). The CPM was synthesized by the beam-based structural optimization method and a prototype was fabricated by the electron beam melting (EBM) technology with Ti6Al4V material. The mechanical characteristics of 3-D printed compliant mechanism for precision applications, i.e., stiffness property, dynamic response, and large elastic deformation, were experimentally evaluated. Most importantly, a coefficient factor of 1.27 was proposed to determine the effective thickness for 3-D printed compliant mechanisms with 0.5 mm thick flexures. Using the effective thickness, the characteristics of the 3-D printed CPM have shown to agree with the prediction, with a maximum deviation of 10.5%. The Ti6Al4V CPM is able to achieve the large work range up to 4 mm of linear displacement, 6 degrees of angular displacements, fast dynamic response of 119 Hz, good decoupled motions, and high non-actuating stiffness. A 3-DOF manipulator was built based on the 3-D printed CPM and actuated by three voice-coil motors. Experimental results have shown that the 3-DOF manipulator could achieve repeatable motions with resolution of 20 nm for the translation along the Z-axis, 0.14 arcsecond for the rotation about the X-axis, and 0.12 arcsecond for the rotation about the Y-axis. In conclusion, EBM technology is suitable for fabricating compliant mechanisms in precision manipulator systems; the mechanical characteristics of 3-D printed compliant mechanisms are predictable when an effective thickness is used. [ABSTRACT FROM PUBLISHER]

This paper presents the mechanical design, optimisation and tracking control of a flexure-based positioning stage to generate coupled linear and angular motions. The mechanism employs two piezoelectric actuators, with output translation and rotation proportional to the difference and sum of the input displacements. Computational optimisation utilising finite element analysis is used to develop designs that maximise the working range. A dynamic model is developed, leading to the establishment of a proposed sliding mode controller to allow the stage to track desired trajectories. An adaptive gain is implemented to reduce errors in the estimated kinematics, and accommodate creep within the mechanism. A prototype of the mechanism has been manufactured, and experimentation has been performed to verify computational predictions of the mechanism behaviour. The ability of the proposed controller to execute precise tracking of a desired trajectory within the workspace is demonstrated in the experimental study. [ABSTRACT FROM AUTHOR]

A modified Prandtl–Ishlinskii (P–I) hysteresis model is developed to form the feedforward controller for a 3-DOF flexure-based mechanism. To improve the control accuracy of the P–I hysteresis model, a hybrid structure that includes backlash operators, dead-zone operators and a cubic polynomial function is proposed. Both the rate-dependent hysteresis modeling and adaptive dead-zone thresholds selection method are investigated. System identification was used to obtain the parameters of the newly-developed hysteresis model. Closed-loop control was added to reduce the influence from external disturbances such as vibration and noise, leading to a combined feedforward/feedback control strategy. The cross-axis coupling motion of the 3-DOF flexure-based mechanism has been explored using the established controller. Accordingly, a decoupling feedforward/feedback controller is proposed and implemented to compensate the coupled motion of the moving platform. Experimental tests are reported to examine the tracking capability of the whole system and features of the controller. It is demonstrated that the proposed decoupling control methodology can distinctly reduce the coupling motion of the moving platform and thus improve the positioning accuracy and trajectory tracking capability. [ABSTRACT FROM AUTHOR]

To achieve positioning of nanometer or even sub-nanometer resolution from traditional piezoelectric actuators and giant magnetostrictive actuators, a bridge-type differential displacement reducer, which shows the capability of obtaining very large reduction ratio, is proposed. The reducer contains two bridge-type flexure mechanisms connected in a way that the output of the reducer equals the difference of the outputs of the two mechanisms. If the two bridge-type flexure mechanisms are identical, no matter how large the input is, the output will always be 0, indicating an infinite reduction ratio theoretically. Therefore, introducing a slight difference between the two mechanisms can yield a very large reduction ratio. A kinetostatic model for the reducer is developed, base on which a reducer exhibiting a reduction ratio of 100 is designed and prototyped. The results of the kinetostatic model, the finite element model and the experiment agree well with each other, validating the effectiveness of the proposed reducer and the correctness of the kinetostatic model. • A novel flexure-based displacement reducer that can achieve an infinite reduction ratio theoretically is proposed. • A kinetostatic model considering deflections of side links is developed. • A reducer exhibiting a reduction ratio of 100 is designed and prototyped. [ABSTRACT FROM AUTHOR]

This paper presents a novel piezo-driven linear-rotary inchworm actuator with a large motion range and high resolution. Such an actuator will be indispensable in precision positioning. The proposed actuator consists of four flexure modules driven by four piezoelectric actuators, namely, two clamping modules to alternately hold the actuator shaft, one linear driving module and one rotary driving module to provide the driving force and torque, respectively. Its mechanical performance is analyzed in detail and the working principle is also described. A prototype of the linear-rotary actuator is fabricated, with which a series of experiments are carried out. The experimental results show that the actuator can achieve high resolution of 0.049 μm and 10.3 μrad, the maximum velocities of 1450 μm/s and 34,270 μrad/s, and the maximum output force of 11.8 N and maximum output torque of 73.5 N mm for the linear and rotary motions, respectively. [ABSTRACT FROM AUTHOR]

This paper presents the mechanical design, computational optimization, and experimentation of a decoupled 2-DOF monolithic mechanism. In the mechanical design, statically indeterminate leaf parallelograms provide the decoupling effect, and the displacement of the piezoelectric actuator (PEA) is amplified with a statically indeterminate lever mechanism. In a piezo-driven mechanism, the contact interface between the PEA and the mechanism is a major cause of the discrepancies between the estimated and measured characteristics. However, no explicit and reliable model is available to estimate the contact stiffness. In this paper, a computational optimization based on the response surface methodology is performed and the influence of the contact interface is taken into consideration by adding adequate safety margin to the design objectives. Ultimately, a prototype is manufactured and experimentally investigated for its characteristics and performances. Experimental results show that the developed mechanism has a workspace range in excess of 82 μm × 82 μm with a first natural frequency of 423 Hz (with a 53.4-g load mass). The cross-axis coupling ratio is experimentally measured to be below 1%, indicating excellent decoupling performances. [ABSTRACT FROM PUBLISHER]

The paper aims to present a mechatronic device able to micro-position the workpiece and to reject disturbances due to machining operation. A decoupling method is proposed for a parallel kinematic machine (PKM) fixturing platform composed by a 3-DoF flexure-based piezo-actuated mechanism. The parallel platform, with a vertical motion and two rotations, is described and its kinematics and dynamics are studied. The coupling undesirable effect is investigated based on a set of poses. To improve the quasi-static regulator model for a set-point following system, a bump less switching controller and a fine-tuning procedure, to estimate the parameter uncertainty and enable the external disturbance containment in an extended broadband frequency range, are presented. The platform and the piezo-actuator controllers are modelled based on a gain scheduling, standard ISA form method, to guarantee the stability. The accuracy is demonstrated through a set of simulations and experimental comparisons. A sensitivity analysis that evaluates the tracking performance and the disturbance rejection based on the number of signal amplitudes, frequencies, and phases is discussed. A validation phase has shown that the developed architecture presents a steady state error lower than 1.2 µm, a vibration reduction of 96% at 1130 Hz with a maximum resolving time of 6.60 ms. [ABSTRACT FROM AUTHOR]

Abstract: Compensations for cross-axis coupling effect and hysteretic nonlinearity of a novel XY piezo-actuated positioning stage are presented in this study. The piezo-actuated stage utilizes a monolithic flexure-based mechanism (FBM) to achieve translations in X- and Y-axes instead of using stacked mechanisms. A hysteresis model with crossover term is proposed to alleviate the cross coupling effect between X- and Y-stages during precision positioning tasks. System identifications using real-coded genetic algorithm (RGA) and clonal selection algorithm (CSA) are compared with particle swarm optimization (PSO). The results show that PSO provides better performance than the others. Therefore, a feedforward controller with cross-axis coupling compensation is studied and the used for the piezo-actuated FBM to enhance the precision of the coarse positioning stage. The experimental results confirm that the proposed controller can achieve precision tracking tasks with submicron precision. [Copyright &y& Elsevier]

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii (PI) model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo-driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a result, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified PI model is significantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibration. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire working range of the flexure-based mechanism. The mechanism's hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the dynamic modelling and performance evaluation methodologies of a flexure-base mechanism for ultra-precision grinding operation. The mechanical design of the mechanism is briefly described. A piezoelectric actuator is utilized to drive the moving platform. A flexure-based structure is utilized to guide the moving platform and to provide preload for the piezoelectric actuator. By simplifying the Hertzian contact as a linear spring and damping component, a bilinear dynamic model is developed to investigate the dynamic characteristics of the flexure-based mechanism. Based on the established model, the separation phenomenon between the moving platform and the piezoelectric actuator is analyzed. The influences of the control voltage and the preload stiffness on the maximum overshoot are extensively investigated. The slope and cycloidal command signals are utilized to reduce and/or avoid the overshoot of such flexure-based mechanism for rapid positioning. The effects of the rising time of the command signals on the maximum overshoot and the settling time are also explored. Experiments are performed to verify the established dynamic model and the performance of the developed flexure-based mechanism. [Copyright &y& Elsevier]

This paper presents a robust adaptive constrained motion tracking control methodology for piezo-actuated flexure-based micro/nano manipulation mechanisms. This unique control approach is established for the tracking of desired motion trajectories in a constrained environment exhibiting some degree of uncertain stiffness. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also nonlinearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for the dynamic modeling of a flexure-hinged four-bar micro/nano manipulation mechanism operating in a constrained environment are established. A lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano manipulation mechanism is developed for the formulation of the control methodology. Stability analysis of the proposed closed-loop system is conducted and the convergence of the motion tracking errors is proven theoretically. Furthermore, precise motion tracking ability in following a desired motion trajectory is demonstrated in the experimental study. An important advantage of this control approach is that it does not require the exact values for the system parameters and the force conversion function in the physical realization. This proposed constrained motion tracking control methodology is very useful for applications demanding high-precision motion tracking with force sensing and feedback. [ABSTRACT FROM AUTHOR]

This paper presents a robust methodology for constrained motion tracking control of piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This unique control approach is established for the tracking of desired motion trajectories in a constrained environment exhibiting some degree of uncertain stiffness. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also nonlinearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for the dynamic modelling of a flexure-hinged four-bar micro/ nano manipulation mechanism operating in a constrained environment are established. A lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano manipulation mechanism is developed for the formulation of the control methodology. Stability analysis of the proposed closed-loop system is conducted, and the convergence of the motion tracking errors is proven theoretically. Furthermore, precise motion tracking ability in following a desired motion trajectory is demonstrated in the experimental study. This robust constrained motion tracking control methodology is very useful for the development of high performance flexure-based micro/nano manipulation applications demanding high-precision motion tracking with force sensing and feedback. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the methodology for modeling and control of a high precision flexure-based mechanism for ultra-precision turning operation. A high performance piezoelectric actuator is used to driven the flexure-based mechanism. A parallel flexure hinge mechanism is utilized to guide the moving platform and to preload the piezoelectric actuator. A high resolution capacitive sensor is used to measure the displacement of the flexure-based mechanism for closed-loop control. With consideration of the driving circuit, the dynamic model of the flexure-based mechanism has been established. The effect of the driving circuit on the dynamic response of the precision mechanism is investigated. Experimental tests have been carried out to verify the established model and the performance of the flexure-based mechanism. [Copyright &y& Elsevier]

Abstract: This paper presents a novel robust generalised impedance control methodology for piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This control approach is proposed for compliant manipulation in which desired motion and force trajectories are controlled to achieve a specified generalised impedance. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also non-linearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for dynamic modelling of a flexure-hinged four-bar micro/nano mechanism making contact with its environment are established. A lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano mechanism is established for the formulation of the proposed control methodology. The stability of the control approach is analysed, and the convergence of the tracking errors to achieve the generalised impedance is proven theoretically. Desirable control performances in following the desired motion and force trajectories are demonstrated in the experimental study. An important advantage of this control methodology is that this approach does not require the exact values for the system parameters and the force conversion function in the physical realisation. This proposed compliant manipulation control methodology is useful for the implementation of high performance flexure-based micro/nano manipulation applications demanding for both sensing and control of motion and force trajectories. [Copyright &y& Elsevier]

Abstract: This paper establishes and investigates an enhanced adaptive motion tracking control methodology for piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This control methodology is proposed for tracking desired motion trajectories in the presence of unknown or uncertain system parameters, non-linearities including the hysteresis effect, and external disturbances in the motion systems. In this paper, the equations for the modelling of a flexure-hinged four-bar micro/nano mechanism are established. These include the angular stiffness, ‘static’ linear stiffness, equation of motion, and lowest structural resonance of the mechanism. In addition, a lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano mechanism is established for the formulation of the proposed control methodology. The stability of the control approach is analysed, and the convergence of the position and velocity tracking errors to zero is proven theoretically. A precise tracking performance in following a desired motion trajectory is also demonstrated in the experimental study. An important advantage of this control methodology is that the approach requires only a knowledge of the estimated lumped system parameters in the physical realisation. This proposed motion tracking control methodology is very attractive for the implementation of high performance flexure-based micro/nano manipulation control applications. [Copyright &y& Elsevier]

Abstract: This paper presents a robust motion tracking control methodology for a flexure-based four-bar micro/nano manipulator driven by a piezoelectric actuator. This control methodology is proposed for tracking desired motion trajectories in view of the problems of unknown or uncertain system parameters, non-linearities including the hysteresis effect, and external disturbances in the system. In this paper, equations of the angular stiffness, ‘static’ linear stiffness, and structural resonance of a flexure-hinged mechanism are presented. In addition, a lumped parameter dynamic model is established for the formulation of the proposed control methodology. The convergence of the position tracking error to zero is assured by the approach in the presence of the aforementioned conditions. The stability of the closed-loop system is proven theoretically, and a precise tracking performance in following a desired motion trajectory is demonstrated in the experimental study. One of the most important advantages of this control methodology is that the approach requires only a knowledge of the estimated lumped parameters in the physical realisation. With the capability of motion tracking, the robust motion control methodology is very attractive in realising high-performance flexure-based control applications in the field of micro/nano manipulation. [Copyright &y& Elsevier]

This paper presents a novel six degrees-of-freedom (DOF) compliant parallel mechanism (CPM) with decoupled output motions, large workspace of ≥6 mm for translations and ≥12° for rotations, optimized stiffness, and dynamic properties. The working range and the motion decoupling capability of the six-DOF CPM are experimentally verified, and the mechanical properties are shown to be predictable. The proposed CPM is synthesized by applying the beam-based structural optimization method together with the criteria for achieving motion decoupling capability. In order to improve the dynamic behaviors for the CPM, cellular structure is used to design its end effector. The obtained results show that the dynamic performance of the CPM with cellular end effector is significantly enhanced with the increase of 33% of the first resonance frequency as compared to the initial design. Performances of the three-dimensional (3D)-printed prototype are experimentally evaluated in terms of mechanical characteristics and decoupled motions. The obtained results show that the actual stiffness and dynamic properties agree with the predictions with the highest deviation of ~10.5%. The motion decoupling capability of the CPM is also demonstrated since almost input energy (>99.5%) generates the desired output motions while the energy causes parasitic motions is only minor (<0.5%). [ABSTRACT FROM AUTHOR]

• The proposed motion-converter mechanism is only 10.5 mm. • The proposed motion-converter mechanism can generate a single-degree-of-freedom output motion. • The proposed motion-converter mechanism does not have any resonance peaks at frequencies below 1000 Hz. • The error between the numerical and the experimental results can vary but not more than 15%. A thin flexure-based mechanism is proposed that is useful in applications with limited build space. The proposed mechanism converts the initial in-plane motion of two piezoelectric stack actuators to an out-of-plane translational motion. Two actuators in the symmetric design of the proposed APA can be used to ensure a pure translation output motion. A Finite Element (FE) model is used to analyze the rigid multibody model of the proposed mechanism. The rigid multibody model is used to design the desired flexural mechanism in a three-dimensional space. The proposed design is then manufactured and is subjected to an experimental study. Measurements validate the performance of the proposed design with an error of less than 15%. A parametric study on the effect of the applied voltage to the actuators of the proposed mechanism reveals good agreement between the numerical model and the manufactured mechanism. [ABSTRACT FROM AUTHOR]