Stick-slip Principle Research Articles

A spatial 3-DOF piezoelectric robot and its speed-up trajectory based on improved stick-slip principle

Piezoelectric robots have been proven to be suitable for high-precision, cross-scale micro-nano manipulation due to their nanometre resolution and high flexibility. To make up for the limited stroke of micro-nano positioning platforms, a spatial three-degrees-of-freedom (3-DOF) piezoelectric robot is proposed in this study to enable three-dimensional micro-nano manipulation of objects. The robot utilizes the deformation of the piezoelectric stack as the source of displacement. It is comprised of a parallel compliant mechanism and a guided compliant mechanism in series, resulting in a compact robot body. The robot is capable of linear displacement in x-, y- and z-axes. The stiffness of the guided compliant mechanism is calculated using theoretical modeling and compared with the finite element simulation results, with a deviation of less than 5.6% verifying the accuracy of the model. The robot operates using two motion principles: the direct drive principle, which has a resolution of 16, 15, and 11 nm in x-, y- and z-axes, and a motion space of 13×11×7 μm3; and the improved stick-slip principle, which has a theoretical infinite stroke and a maximum speed of 4.2 and 3.9 mm/s in x- and y-axes. The speed of the improved stick-slip principle is 42% higher than that of the traditional stick-slip principle in x- and y-axes. The robot has a spatial 3-DOF, nanometre resolution, millimeter speed, and can carry more than 500 g.

Development of a bipedal piezoelectric actuator with flexible mechanism based on the frog-leg inspiration

A new piezoelectric actuator with flexible mechanism using stick-slip principle based on the frog-leg inspiration is developed in this work. It utilizes bipedal design, and the slider can be driven by only one foot or two feet alternately, which depends on the exciting situation of the used two PZT stacks. The extension of the PZT stack can be transmitted into the vertical and horizontal deformations on two driving feet due to the frog-leg inspiration. They are used to press and actuate the slider. The configuration of this actuator is presented and its working principle is illustrated. Finite element simulation is carried out to investigate the statics performance. A prototype of the proposed actuator is fabricated and series of mechanical output characteristics are measured. The results demonstrated that the proposed actuator obtained the output velocity of 4.23 mm/s when the voltage and frequency were 100 V and 400 Hz. The maximum vertical loading capacity was 9 N under the voltage of 100 V. The corresponding results in this work validated the feasibility of the proposed bipedal piezoelectric actuator with flexible mechanism based on the frog-leg inspiration.

Development of a Novel Piezoelectric Actuator Based on Stick-Slip Principle by Using Asymmetric Constraint.

In this work, a novel piezoelectric actuator based on the stick-slip principle is proposed. The actuator is constrained by an asymmetric constraint approach; the driving foot produces lateral and longitudinal coupling displacements when the piezo stack is extended. The lateral displacement is used to drive the slider and the longitudinal displacement is used to compress the slider. The stator part of the proposed actuator is illustrated and designed by simulation. The operating principle of the proposed actuator is described in detail. The feasibility of the proposed actuator is verified by theoretical analysis and finite element simulation. A prototype is fabricated and some experiments are carried out to study the proposed actuator's performance. The experimental results show that the maximum output speed of the actuator is 3680 μm/s when the locking force is 1 N under the voltage of 100 V and frequency of 780 Hz. The maximum output force is 3.1 N when the locking force is 3 N. The displacement resolution of the prototype is measured as 60 nm under the voltage of 15.8 V, frequency of 780 Hz and locking force of 1 N.

Development of a piezoelectric actuator based on stick-slip principle inspired by the predation of snake.

A new piezoelectric actuator based on the stick-slip working principle inspired by the predation of the snake is proposed and developed in this work. A lead zirconate titanate (PZT) stack is used and inserted into the stator with an asymmetric configuration. Then, the elongation of the PZT stack can be transmitted into the vertical and horizontal displacements on the driving foot. They are used to press and drive the slider, respectively. In this design, the motion of the actuator imitates the predation process of the snake. The principle of the proposed actuator is clarified in detail. The statics characteristics are conducted by using the FEM method. The dynamics model of the actuator was established to show the motion behavior of the slider in theory. Finally, the output characteristics of the developed piezoelectric actuator are tested. The results stated that this actuator obtained the maximum output speed of 11.44 mm/s under a voltage of 100V and a frequency of 600Hz. The output force of the developed actuator was 2.8N under the preload force of 3N. In conclusion, the feasibility of the proposed piezoelectric stick-slip type actuator inspired by the predation of the snake is verified.

A smooth-drive scheme for piezoelectric stage by coupling of stick-slip motion and inertial impact

The piezoelectric stick-slip stage is very important in industrial manufacturing and precision machining. However, due to the stick-slip principle, it is inevitable to produce backward motion, which leads to a decrease in precision and efficiency. A novel smooth-drive scheme for piezoelectric stage is proposed by coupling stick-slip motion and inertial impact in this paper. In the coupling counteract phase, the sliding friction force of stick-slip driving mechanism (SDM) is counteract by the impact force of inertial impact driving mechanism (IDM), thus eliminating the backward motion and realizing the smooth driving of the stage. The feasibility of the stage is analyzed by theoretical calculation and transient dynamics simulation. In addition, the designed stage is fabricated and conducted a complete set of experimental tests. The external dimensions of the stage is 45 mm (L) × 24 mm (W) × 22 mm (H), and the mass is 84 g. Experimental results show that the piezoelectric stage can not only achieve smooth driving, but also actively adjust the output smoothness by adjusting the excitation voltage of PZT I and PZT II. The linear fitting correlation coefficient R2 of the displacement curve can reach above 0.999, and it still keeps good smoothness at 200 Hz. The maximum vertical mass load of the stage is 4 kg, which is about 47 times the mass of the stage, and the resolution of stick-slip state is about 85 nm. The scheme has positive reference value in the field of stable and accurate positioning.

A Dual-Driven High Precision Rotary Platform Based on Stick-Slip Principle

Aiming at the realization of high precision angle adjusting, this article proposed a rotary platform based on stick-slip principle, which adopted a dual-driven working mode to realize large circular motion stroke and high loading capacity. Based on flexure hinges, a symmetrical flexible mechanism with two driving feet was designed to generate coupled driving displacement. By actuating the piezoelectrics alternatively, the proposed dual-driven working principle was described in detail, which could effectively suppress the back-off phenomenon and improve loading capacity. The theoretical analysis and finite element simulation were conducted to investigate the characteristic of flexible driving unit. The dynamic model of dual-driven working mode was established and simulated in MATLAB/Simulink, and the influence of preloading coefficient and initial preloading force were investigated, which provided a guidance for the design and optimization of stick-slip actuator. Additionally, a prototype was fabricated, and a series of experiments were conducted. The results indicated that the maximum rotary speed and loading capacity of rotary platform were 48.3 mrad/s and 98.8 mN·m, respectively.

Design, analysis and experiments of a stick-slip piezoelectric actuator working under the self-deformation mode

In this paper, the self-deformation mode of the stick-slip principle was proposed, and accordingly a piezoelectric actuator based on the self-deformation mode was designed, which could achieve stable bidirectional outputs with long stroke. To increase the stepping displacement of the output end and reduce the structural stress, an arc-shape flexible hinge with variable section was employed as the output part of the flexible hinge mechanism. The self-deformation motion was obtained by the deformation of the driving mechanism caused by the reaction force of the mover in the driving process. The stepping and self-locking characteristics of the actuator under various initial gaps were tested, and the evolution of stepping characteristics with the driving voltage, frequency and external load was analyzed. The experimental results showed that by the self-deformation mode, the long stroke with good linearity could be easily achieved for both the forward and reverse motions, and the maximum self-locking force reached 5 N. Furthermore, the maximum driving speed reached 2754 μm s−1 under the driving voltage of 120 V.

Study on improving the resolution of an H-shaped piezoelectric ultrasonic actuator by stick-slip principle

Improving the performance of the motion stages driven by piezoelectric actuators is an enduring topic for expanding their applications. For the motion stage with a travel range of tens of millimeters, trade-offs are inevitable between getting high speed (hundreds of millimeters per second) and high resolution (tens of nanometers), due to the inherent limitations of the operating principles of the piezoelectric actuators. In order to improve the output resolution of an H-shaped piezoelectric ultrasonic actuator, sawtooth excitation voltages are used in this work rather than the conventional sinusoidal voltages in previous works. The configuration and operating principle of the actuator are discussed in detail. The actuator consists of two vertical and two horizontal longitudinal transducers. The ends of the vertical transducers act as the driving tips and drive the stage forward with the alternating slow extensions and rapid contraction, during which stick motions and slip motions of the stage are acquired. An analytic model is developed to estimate the horizontal and vertical output displacement of the driving tip. The maximum error between the predicted value of the analytical model and the experimental value is about 14%. A prototype of the motion stage is fabricated and experiments are carried out to evaluate its output characteristics. The experiment results confirm the operating principle and show that the resolution is upgraded to tens of nanometers. The prototype obtains a resolution of 19 nm, a maximum speed of 2.22 μm s−1, and a maximum carrying load of 16.94 kg.

Design and Analysis of a Stepping Piezoelectric Actuator Free of Backward Motion

Although the stick-slip principle has been widely employed for designing piezoelectric actuators, there still exits an intrinsic drawback, i.e., the backward motion, which significantly affects its output performances and applications. By analyzing the generation mechanism of backward motion in stick-slip piezoelectric actuators, the elliptical trajectory was employed to design a novel stepping piezoelectric actuator free of backward motion. Accordingly, a prototype of piezoelectric actuator was designed, which utilized a flexure hinge mechanism and two vertically arranged piezoelectric stacks to generate the required elliptical trajectory. The compliance matrix method was used to theoretically analyze the flexure hinge mechanism. The theoretical and measured elliptical trajectories under various phase differences were compared, and the phase difference of 45° was selected accordingly. Under a critical relative gap, output performances of the actuator working under the elliptical trajectory were characterized, and then compared with that obtained under the normal stick-slip driving principle. Experimental results indicated that forward and reverse stepping displacement with completely suppressed backward motion could be achieved when employing the elliptical trajectory, verifying its feasibility. This study provides a new strategy for designing a stepping piezoelectric actuator free of backward motion.

Inertial Piezoelectric Rotary Motor Based on Low Profile Stator with Trapezoidal Waveguides

Results of numerical and experimental investigations of a novel inertial piezoelectric rotary type motor based on a low profile stator with trapezoidal waveguides. The proposed motor has a simple design and is well scalable. Moreover, the proposed design of the motor allows mount it on a printed circuit board and use it in a small-size mobile positioning and actuating systems. The structure of the stator is based on a square type hollowed steel frame with four straight trapezoidal waveguides that are used to transfer vibrations of the stator to the rotation of the rotor. Piezo ceramic plates are glued on both sides of the stator. The thickness of the assembled stator is 0.9 mm, while the total area needed for stator mounting does not exceed 625 mm2. The driving of the rotor is based on the stick-slip principle, which is induced by excitation of the second in-plane bending mode of the four bimorph plates applying two saw tooth waveform signals with a phase difference by π. The numerical and experimental investigation was carried out to validate the operation principle of the motor and to measure the mechanical and electrical characteristics. The maximum angular rotation speed of 1304 RPM was achieved at a resonance frequency of 44.81 kHz when a preload of a 7.35mN was applied.

A direction-guidance hybrid excitation method for inertial flexible hinge piezoelectric actuator with high speed performance

Piezoelectric actuators play a crucial role in both scientific research and industrial applications. With the increasing demand on the high speed performance piezoelectric actuators, various inertial flexible piezoelectric actuators driven by sawtooth wave based on the stick slip principle have been proposed to satisfy the requirement, but the problem of low speed performance commonly exists. This paper proposes a direction-guidance hybrid (DGH) excitation method which can overcome the limitation. The excitation method is achieved by a direction-guidance hybrid (DGH) wave. Different from the existing excitation methods, not only the DGH wave can make the actuator produce a pre-deformation which can guide the slider to move and adjust the locking force, but also can drive the actuator to move with high speed even at a low voltage. In order to verify the excitation method, a novel inertial flexible hinge piezoelectric actuator is designed and manufactured. Furthermore, the finite element method (FEM) and experiments are conducted to detect the superior high speed performance of the prototype driven by the proposed excitation method. Compared with the existing actuators, the prototype driven by the DGH excitation method, even at less than 1/10 of input voltage, can achieve a 1.5 times higher speed.

Development of stick–slip nanopositioning stage capable of moving in vertical direction

Nanopositioning stage, based on the stick–slip principle, is a hot research topic due to its unparallel merits such as compact structure, high resolution, and long travel stroke. However, most of the conventional stick–slip nanopositioning stages only have the ability to move along the horizontal directions. In addition, analysis of vertical stage movement is few. This paper proposes a novel stick–slip nanopositioning stage capable of moving upwards and downwards with an excellent performance. An adjusting unit was developed and integrated into the stage to effectively change friction force which is the key to the vertical stage movement. Theoretical and numerical analysis show that many parameters including revised driving signal contributes to the upward movement of stick–slip nanopositioning stage. Experimental results show that the stage has the capability of traveling up to 22 mm with an upward positioning accuracy of 7.00 nm and a downward positioning accuracy of 5.00 nm, respectively. The maximum speed for maximum speeds of stage for upward and downward motion were measured to be 2.70 and 0.77 mm/s, respectively. The maximum load of stage in vertical direction is 72 g. This stage design has a huge potential in applications requiring vertical manipulation while requiring nanometer positioning accuracies, high travel stroke, compact structure, and large load.

Suppressing the backward motion of a stick–slip piezoelectric actuator by means of the sequential control method (SCM)

For stick–slip piezoelectric actuators working under the friction-inertia principle, the backward motion is nearly unavoidable especially at low driving frequency, which is detrimental to their driving performances. Accordingly, to suppress the backward motion of stick–slip piezoelectric actuators, this paper proposed a novel sequential control method (SCM). To verify the feasibility of SCM, an actuator prototype was designed and fabricated accordingly, and its output performances were tested experimentally. In this prototype, two flexure hinges and piezoelectric stacks were employed for driving and lifting, respectively. Before the generation of backward motion, the whole driving flexure hinge can be lifted up to separate from the mover by the lifting flexure hinge. Comparative experiments of the actuator working under the SCM and traditional stick–slip principle showed that backward motion could be significantly suppressed under the SCM, and the output displacement curve showed good stepping characteristics, proving the effectiveness of the proposed SCM.

Optimal Nonlinear PID Control of a Micro-Robot Equipped with Vibratory Actuator Using Ant Colony Algorithm: Simulation and Experiment

In this paper, an optimal nonlinear control scheme based on the application of ant colony optimization (ACO) is applied to a micro-robot equipped with vibratory actuators. Accordingly, two small vibrating motors are utilized to run the micro-robot and the motion principle of stick-slip is used for locomotion purpose. First, a dynamic model of the micro-robot is derived considering the stiffness of the robot’s legs. Then, the influences of robot mass and length of legs on micro-robot motion are studied using simulation. Next, an optimal linear PID control scheme is applied to the micro-robot system. However, it is found that this control method does not have an acceptable performance when friction is low or the system is under disturbance. Consequently, an ACO-based optimal nonlinear PID control is proposed to cope with the mentioned drawbacks as the main contribution of the paper. Afterwards, the performance of both control techniques is compared through simulation. Finally, the micro-robot is developed and experimentally evaluated. It is found that the experimental results are in a good agreement with some of the simulation outcomes through which the validity of the mathematical scheme as well as the feasibility of design is affirmed.

Design, Analysis, and Experiment on a Novel Stick-Slip Piezoelectric Actuator with a Lever Mechanism.

A piezoelectric actuator using a lever mechanism is designed, fabricated, and tested with the aim of accomplishing long-travel precision linear driving based on the stick-slip principle. The proposed actuator mainly consists of a stator, an adjustment mechanism, a preload mechanism, a base, and a linear guide. The stator design, comprising a piezoelectric stack and a lever mechanism with a long hinge used to increase the displacement of the driving foot, is described. A simplified model of the stator is created. Its design parameters are determined by an analytical model and confirmed using the finite element method. In a series of experiments, a laser displacement sensor is employed to measure the displacement responses of the actuator under the application of different driving signals. The experiment results demonstrate that the velocity of the actuator rises from 0.05 mm/s to 1.8 mm/s with the frequency increasing from 30 Hz to 150 Hz and the voltage increasing from 30 V to 150 V. It is shown that the minimum step distance of the actuator is 0.875 μm. The proposed actuator features large stroke, a simple structure, fast response, and high resolution.

A compact 2-DOF piezo-driven positioning stage designed by using the parasitic motion of flexure hinge mechanism

This paper presents a compact two-degrees of freedom piezo-driven positioning stage. To achieve large working stroke, the stick-slip principle was employed, and to make the stage compact, a lever-type flexure hinge mechanism (LFHM) with the L-shape structure was designed. The LFHM could tune the single-direction output displacement of the stacked piezoelectric (SPE) to be two directional motions, the main motion for stick-slip driving and the parasitic motion for the contact. The L-shape structure makes the SPE being parallel to the slider rather than vertical to it, and therefore, the stage could be compact. The positioning stage had a two-layer structure for realizing motions along x and y axes, and these two layers shared the same structure. The structure design and working principle of the stage were discussed in detail. A prototype was fabricated, and the effects of driving frequency and voltage on the output characteristics were evaluated, followed by measuring its loading capacity and frequency characteristic. Experimental results showed that the output displacement had very good linearity in both x and y axes and as well for both positive and negative motions. Especially, even for a relatively large displacement output being over 1600 μm achieved by stepping accumulation, the output displacement still maintained very good linearity, demonstrating good motion stability. Furthermore, the backward motion was quite small compared with some previous studies. In addition, the vertical load in the range of 0–2 N had quite weak effects on the output characteristics, and the first resonant frequency of the driving unit was over 1900 Hz. These results indicated that the designed x–y positioning stage not only had a compact structure but also possessed good performances, which were beneficial to its practical applications.

Evolution of one-stepping characteristics of a stick-slip piezoelectric actuator under various initial gaps

To investigate the effects of initial gap on the one-stepping characteristics of stick-slip piezoelectric actuators, a stick-slip piezoelectric rotary actuator with changeable initial gap was designed and fabricated. Its output characteristics were tested under various initial gaps. Experimental results indicated that the initial gap indeed significantly affected the output characteristics in one driving cycle, especially at the final stage when the driving voltage was decreased quickly. Gradually increasing the initial gap, an interesting phenomenon was observed that the one-stepping characteristics in the final stage transformed from the sudden return (the so-called backward motion) to a critical status (nearly smooth motion), and finally to sudden jump. By analyzing the practical driving waveform as well as the additional deformation of the actuator, the evolution of one-stepping characteristics was rationalized. These findings and discussion are expected to enhance our fundamental understanding of the stick-slip principle and actuators. In addition, this study suggests a method to suppress the backward motion by simply changing the initial gap.

A novel method of stick-slip vibration composite driving for improving the step displacement

The piezoelectric-actuated inertial stick-slip device (PAISSD) is widely used in the field of nanotechnology because of its high resolution and theoretically unlimited displacement. However, the small step displacement is an unavoidable issue of stick-slip driving technology. In this research, a stick-slip vibration composite driving method (SSVCDM) is proposed to increase the step displacement. The SSVCDM combines the principle of inertial stick-slip driving and the friction reduction under vibration. The friction is greatly affected by the vibration waveform when the PAISSD is in the buffer period. First, the SSVCDM is proposed, which includes a second order driving waveform, the step response of the waveform and the vibration waveform. Then the mechanism and the effect of friction reduction under vibration are studied based on the inertial stick-slip driving. Finally, the mechanism and the effect of friction reduction under vibration is validated and the effectiveness of the SSVCDM is demonstrated via experimental studies. The results provide an insight into the development of friction reduction technology by the inertial stick-slip driving.

Design and experiments of a miniature piezoelectric actuator using a multilayer PZT bimorph

ABSTRACTA miniature piezoelectric linear actuator based on stick-slip principle is proposed, with overall dimensions of only 3 mm * 3 mm * 4 mm. The actuator is comprised of a T-shape zirconia drive foot and a multilayer Lead Zirconate Titanate (PZT) bimorph. The bimorph consists of two parallel d33 stacks which are mechanically conjoined but electrically separated. The output step length and thrust of the actuator were about 1 μm and 0.23 N, respectively, under 50 V driving voltage and 0.25 N holding force. And the minimum step length was 0.17 μm at 10 V. The multilayer structure makes the miniature actuator produce a significant displacement at low driving voltage and non-resonant frequency, which are beneficial to drive and control. The tiny structure and easy-controllability of the actuator show huge superiority in precision micro-positioning systems.

Design and Experimental Research of a Novel Stick-Slip Type Piezoelectric Actuator

A linear piezoelectric actuator based on the stick-slip principle is presented and tested in this paper. With the help of changeable vertical preload force flexure hinge, the designed linear actuator can achieve both large travel stick-slip motion and high-resolution stepping displacement. The developed actuator mainly consists of a bridge-type flexure hinge mechanism, a compound parallelogram flexure hinge mechanism, and two piezoelectric stacks. The mechanical structure and motion principle of the linear actuator were illustrated, and the finite element method (FEM) is adopted. An optimal parametric study of the flexure hinge is performed by a finite element analysis-based response surface methodology. In order to investigate the actuator’s working performance, a prototype was manufactured and a series of experiments were carried out. The results indicate that the maximum motion speed is about 3.27 mm/s and the minimum stepping displacement is 0.29 μm. Finally, a vibration test was carried out to obtain the first natural frequency of the actuator, and an in situ observation was conducted to investigate actuator’s stick-slip working condition. The experimental results confirm the feasibility of the proposed actuator, and the motion speed and displacement are both improved compared with the traditional stick-slip motion actuator.