Parasitic Motion Research Articles

Development and analysis of a dynamic model for parasitic motion principle piezoelectric actuator

The main goal of this paper is studying characteristics of the parasitic motion principle (PMP) piezoelectric actuator and providing a dynamic model for possible control and optimization in future. Through analyzing motion principle of the PMP piezoelectric actuator and considering elastic deformation between the mover and the flexible mechanism, this paper first presents a dynamic model which is verified to be feasible through fitting experiment data. Then the model is used to analyze influence of the coupling angle, the driving signal symmetry, the mover mass and the preload force on performance of the PMP piezoelectric actuator, including the step length, the backlash ratio and the maximum output force. This research contributes to enhance the understanding of the PMP and provide a guidance for design of the PMP piezoelectric actuators.

Design and test of a compact compliant gripper using the Scott–Russell mechanism

This paper presents the design, modeling, fabrication, and test of a monolithic compliant gripper for micro-manipulation applications. A compact compliant mechanism that enables in-principle straight-line parallel jaw motion is obtained, by combining the Scott–Russell mechanism and the parallelogram mechanism. The right-circular corner-filleted (RCCF) flexure hinge is adopted to achieve a large displacement of lumped-compliance joints. A pseudo-rigid-body model (PRBM) method with the help of the virtual work principle is performed to obtain parametric analytical models including the amplification coefficient and kinetostatics. Finite element analysis (FEA) is conducted to validate the analytical model and capture adverse parasitic motions of jaws. A monolithic prototype was fabricated, the test results of which show satisfactory performances.

Development and analysis of a stick-slip rotary piezoelectric positioner achieving high velocity with compact structure

A high-velocity rotary stick-slip piezoelectric positioner working in non-resonant condition driven by piezo-stacks is proposed in this paper. For improving working performance through the parasitic motion principle, a compact flexible mechanism with rotational symmetric structure is designed. Its special structure can realize self-centering function, thus there is no need to adopt a bearing for the rotor. And in order to reduce the amounts of needed piezo-stacks and achieve synchronous action of four driving feet, a connecting ring is designed to connect four driving feet. A prototype is manufactured and corresponding experiments are carried out, experimental results show the proposed positioner has a good working performance. Its maximum velocity reaches 151.4 mrad/s, which is greater than most existing non-resonant stick-slip piezoelectric positioners driven by piezo-stacks. And a dynamic model is established and calculated in MATLAB/Simulink, a series of simulation are carried out to further investigate influential factors of the proposed positioner.

A linear piezoelectric actuator with high flexibility flexible mechanism designed by the bidirectional parasitic motion principle.

This paper proposes a piezoelectric actuator based on the parasitic motion principle which overcomes the disadvantage that piezoelectric actuators designed by the parasitic motion principle always sacrifice reverse directional performance for improving forward directional performance. The parasitic motion principle based piezoelectric actuator can use two flexible mechanisms to achieve bidirectional motion, but more assembly errors will be introduced. Therefore, the proposed actuator is designed to output bidirectional motion through one flexible mechanism. To this end, two mounting slots with high flexibility are specially designed for improving output displacement. The working principle and design process are elaborated, and experiments are conducted to prove the feasibility of the proposed actuator. The fabricated prototype can achieve a maximum velocity of 1.563 mm/s and 1.054 mm/s, a displacement resolution of 5.8 µm and 6 µm, an operating bandwidth of 1600 Hz and 1200 Hz, and a vertical load capacity larger than 500 g in forward and reverse directions.

Design, analysis, and experimental investigation of a single-stage and low parasitic motion piezoelectric actuated microgripper

The demand for high precision micro/nano manipulation is increasing for advanced manufacturing technology. The precise motion of the microgripper jaw is required to achieve high performance micromanipulation tasks. The parasitic motion of the microgripper reduces placement accuracy during pick and place tasks. This paper presents an asymmetric design of piezoelectric actuated microgripper. It investigates key characteristics including parasitic motion, output displacement, and displacement amplification ratio. The microgripper is designed with a single-stage displacement amplification mechanism to form a compact layout. The design of the microgripper integrates the bridge-type mechanism and the parallelogram mechanisms. The bridge-type mechanism amplifies the piezoelectric actuator output and the parallelogram mechanisms offer linear motion of the gripper jaw. The analytical modeling and finite element analysis were conducted to evaluate the characteristics of the microgripper. The design parameters of the microgripper were optimized through several finite element analysis. Further, experimental studies were conducted to verify the characteristics of the microgripper. The parasitic motion of the jaw was obtained as less than 0.18% of the microgripper jaw motion in the x-direction. The mechanism of the microgripper also achieves a high positioning accuracy. Further, a high displacement amplification ratio and large output displacement can be achieved.

Primary accelerometer calibration by scanning laser Doppler vibrometry

A primary calibration system for vibration transducers based on laser Doppler vibrometry was complemented by a commercial scan unit. The data acquisition and analysis were optimized for accuracy and a novel procedure to visualize and compensate parasitic rigid-body motion was developed. Additionally, effects related to drift during the calibration process were explicitly taken into account and compensated, thereby allowing an automated measurement of spatial sensitivity distributions at hundreds of measurement positions with the same accuracy as a single-point primary calibration. The system was applied to study the influence of rocking and deforming motion on the apparent sensitivity of back-to-back vibration transducers during the calibration process. New insights were gained by interpreting the measured spatial sensitivity distributions as operational deflection shapes.

Modeling, Optimization, and Experimentation of the ParaGripper for In-Hand Manipulation Without Parasitic Rotation

Recently, underactuated robotic hands have been exploited for dexterous in-hand manipulation, after having been proven efficient in performing versatile adaptive grasps. However, the reported in-hand manipulation skills are usually associated with parasitic motion, which may complicate control and application of the hand. This paper presents the modeling, optimization and experimentation of the ParaGripper, an underactuated gripper capable of performing in-hand manipulation without parasitic rotation. The underactuated finger uses two serially connected parallelograms to ensure pure translation of the fingertips. If the object remains stationary within the fingertips, the gripper can translate the object without parasitic rotation. The kinematics and kinetostatics of the hand–object system are derived and the manipulation workspace is optimized. The ParaGripper is designed and fabricated according to suitable optimal parameters. Experiments show that the ParaGripper could perform non-parasitic in-hand manipulation and versatile adaptive grasps.

Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy.

In this paper the dynamics of a submerged axi-symmetric wave energy converter are studied, through mathematical models and wave basin experiments. The device is disk-shaped and taut-moored via three inclined tethers which also act as a power take-off. We focus on parasitic yaw motion, which is excited parametrically due to coupling with heave. Assuming linear hydrodynamics throughout, but considering both linear and nonlinear tether geometry, governing equations are derived in 6 degrees of freedom (DOF). From the linearized equations, all motions, apart from yaw, are shown to be contributing to the overall power absorption. At higher orders, the yaw governing equation can be recast into a classical Mathieu equation (linear in yaw), or a nonlinear Mathieu equation with cubic damping and stiffness terms. The well-known stability diagram for the classical Mathieu equation allows prediction of onset/occurrence of yaw instability. From the nonlinear Mathieu equation, we develop an approximate analytical solution for the amplitude of the unstable motions. Comparison with regular wave experiments confirms the utility of both models for making relevant predictions. Additionally, irregular wave tests are analysed whereby yaw instability is successfully correlated to the amount of parametric excitation and linear damping. This study demonstrates the importance of considering all modes of motion in design, not just the power-producing ones. Our simplified 1 DOF yaw model provides fundamental understanding of the presence and severity of the instability. The methodology could be applied to other wave-activated devices.

A parasitic type piezoelectric actuator with the asymmetrical trapezoid flexure mechanism

With the help of the parasitic motion of the asymmetrical trapezoid flexure mechanism, a piezoelectric actuator which could achieve linear motion with large working stroke has been presented and inspected. The structure of the asymmetrical trapezoid flexure mechanism and the motion principle of the proposed piezoelectric actuator are introduced and investigated in details. Finite Element Method (FEM) has been exploited, and an experimental system has been built up to study the working performance of the proposed piezoelectric actuator. Simulation results confirm that the parasitic motion could be achieved by the asymmetrical trapezoid flexure mechanism. Additionally, the dynamic model has been proposed for the investigation. Experimental results show that the presented actuator could obtain continuous linear motion with large working stroke by the parasitic motion of the proposed asymmetrical trapezoid flexure mechanism. The minimum stepping displacement of the proposed actuator is 0.68 μm; the maximum speed is 4676 μm/s; the output force could be as large as 91.3 g. This study shows a meaningful idea of the utilization of the asymmetrical trapezoid flexure mechanism for the design of novel piezoelectric actuators.

Kinematic Design of a 2R1T Robotic End-Effector With Flexure Joints

This paper focuses on the kinematic design issues for a three degrees-of-freedom (DOFs), i.e., two-rotational and one-translational (2R1T) end-effector to perform continuous contact operations, such as deburring, grinding, and polishing. The proposed end-effector design employs a 3-legged prismatic-prismatic-spherical (3-PPS) parallel mechanism due to its desired kinematic characteristics and dynamic behavior. As the 3-PPS parallel mechanism is featured with zero-torsion motion characteristic, the orientation of its moving platform can be always represented by a rotation about an axis parallel to its base platform plane. Through analysis of the rotation matrix of the moving platform, closed-form linear solutions for both forward and inverse displacement analyses are readily derived. Other critical design issues, such as passive prismatic joint displacement, parasitic motion, velocity, and singularity analyses, are addressed. For a specific dimension design of the 3-PPS parallel mechanism, the workspace analysis indicates that the proposed design can achieve a singularity-free $\pm 12 ^\circ \times \pm 12^\circ \times 25$ mm workspace. Furthermore, as the displacements of the passive prismatic joints are within 2.63mm, light-weight flexure-based prismatic joints are designed to replace the conventional heavy linear guides. The flexure-rigid structure of the 3-DOF 2R1T end-effector significantly improves the dynamic performance of the system. A prototype of the 3-DOF 2R1T robotic end-effector is designed and fabricated to verify the proposed design.

A Review on the Flexure-Based Displacement Amplification Mechanisms

Multifarious flexure-based displacement amplifiers have been proposed and studied in the past decades, showing importance in many industrial fields, such as bioengineering, optical instruments, and semiconductor technology. Displacement amplifiers provide precise motion and large stroke through a simple and low-cost way compared with other piezoelectric actuators. Those merits have opened a door for new and advanced micro devices with unprecedented performance. This paper aims to proffer a comprehensive review on the design, modeling, characteristics, and applications of flexure-based displacement amplifiers, following by pointing out the inherent drawbacks in this research area such as amplification ratio limit, parasitic motion, low lateral stiffness, low natural frequency, and discussing existing solutions and some potential research directions in those topics. Finally, a summary is concluded and the future development perspectives of the displacement amplifiers are discussed. This review contributes to giving a comprehensive understanding of the displacement amplifier, which provides guidance on designing new displacement amplifiers for improving their mechanical output performance. It is also expected to be instrumental for related researchers to understand displacement amplifiers, and to successfully select and design for specific applications.

Kinematic design of a hybrid planar-tripod mechanism for bone reduction surgery

In the most severe cases of longitudinal bone fractures such as femur, tibias, humerus etc., the bone can be completely separated into two fragments. In order to guarantee the re-ossification of the bone, it is required to reposition the bone fragments together. This process requires a delicate surgery called “bone reduction surgery”. The most advanced technique relies on the use of a robotic manipulator to reposition the bone fragments with higher precision and stability than manual surgeries. The present work introduces the kinematic design of a new hybrid mechanical architecture to perform this task. It is composed of a 3-PRP planar mechanism attached with a 3-RPS tripod mechanism. The kinematic analysis of this mechanism is provided while taking account the tripod parasitic motion. Kinematic simulations using Matlab and Adams are performed to validate the kinematic and velocity models and the parasitic motion compensation provided by the planar mechanism. The workspace of this hybrid mechanism is then compared to the standard hexapod mechanism that is widely used in bone reduction surgery. It reveals that the proposed mechanism can generate a larger workspace with the same linkage dimensions.

Nonunion - consensus from the 4th annual meeting of the Danish Orthopaedic Trauma Society.

Nonunions are a relevant economic burden affecting about 1.9% of all fractures. Rather than specifying a certain time frame, a nonunion is better defined as a fracture that will not heal without further intervention.Successful fracture healing depends on local biology, biomechanics and a variety of systemic factors. All components can principally be decisive and determine the classification of atrophic, oligotrophic or hypertrophic nonunions. Treatment prioritizes mechanics before biology.The degree of motion between fracture parts is the key for healing and is described by strain theory. If the change of length at a given load is > 10%, fibrous tissue and not bone is formed. Therefore, simple fractures require absolute and complex fractures relative stability.The main characteristics of a nonunion are pain while weight bearing, and persistent fracture lines on X-ray.Treatment concepts such as ‘mechanobiology’ or the ‘diamond concept’ determine the applied osteosynthesis considering soft tissue, local biology and stability. Fine wire circular external fixation is considered the only form of true biologic fixation due to its ability to eliminate parasitic motions while maintaining load-dependent axial stiffness. Nailing provides intramedullary stability and biology via reaming. Plates are successful when complex fractures turn into simple nonunions demanding absolute stability. Despite available alternatives, autograft is the gold standard for providing osteoinductive and osteoconductive stimuli.The infected nonunion remains a challenge. Bacteria, especially staphylococcus species, have developed mechanisms to survive such as biofilm formation, inactive forms and internalization. Therefore, radical debridement and specific antibiotics are necessary prior to reconstruction.Cite this article: EFORT Open Rev 2020;5:46-57. DOI: 10.1302/2058-5241.5.190037

Structure dependence of the output performances of a self-deformation driving (SDD) piezoelectric actuator

Pre-loading the driving compliant mechanism is an effective method to improve the self-locking ability of the parasitic motion principle (PMP) piezoelectric actuators, but it may also change the motion mode from the normal PMP to the self-deformation driving (SDD). When the self-deformation is distributed along the whole driving compliant mechanism, the structure design and analysis would be difficult. To facilitate the design and analysis of SDD piezoelectric actuators, following our previous study, an additional flexible hinge was introduced to the lever-amplification compliant mechanism, and thus the self-deformation would be concentrated in the introduced flexible hinge. The maximum one-step displacement of the proposed SDD piezoelectric actuator was analyzed by pseudo-rigid-body method, and the effects of the radius of the introduced right-circular flexible hinge on its compliance were theoretically analyzed. Output performances of the SDD actuator under various radiuses were characterized by experiments. The results showed that the introduced flexible hinge could not only increase the peak motion speed but also increase the adjustable initial gap, i.e. reducing the assembly requirements. Furthermore, when reducing the initial gap to be over the one corresponding to the peak motion speed, the backward motion would become remarkable; however, it would also bring an important advantage, improving the self-locking ability (also the loading capability). These results are expected to provide useful information for the design and application of SDD piezoelectric actuators.

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

Abstract. In severe fracture cases, a bone can be separated into two fragments and it is mandatory to reposition the bone fragments together. This type of surgery is called “bone reduction surgery”. Originally, the operation consisted in manipulating the bones fragments by hand in open surgery. The most advanced technique relies on robotic manipulators providing higher precision and stability. A new mechanical architecture is proposed based on a 3-RPS tripod parallel mechanism combined with a Double Triangular Planar parallel mechanism. Its kinematic and velocity models are calculated and the parasitic motion generated by the tripod mechanism is considered in the final result. The workspace it can generate is compared to the Stewart manipulator, which is a classical mechanism for the targeted application. The use of a robotic manipulator is due to be part of an entire surgical procedure involving a pre-operative simulation software dedicated to pre-planning reduction surgery, namely PhysiGuide. It is used to measure the kinematic associated with bone fragments manipulation and transfer it to the robot during the intra-operative phase. Simulations are then performed based on a real patient's fracture images showing the suitability of the present mechanism with bone reduction surgery.

Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

Abstract The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.

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.

A linear piezoelectric actuator with the parasitic motion of equilateral triangle flexure mechanism

A parasitic type piezoelectric actuator with an equilateral triangle flexure mechanism is proposed and investigated to achieve large-stroke linear motion. Right-circular flexure hinges with different thicknesses (t1 and t2) are utilized in the design of the equilateral triangle flexure mechanism which is able to generate parasitic motion. The working principle is analyzed and illustrated by the theoretical simulation and finite element method (FEM) simulation. A prototype is manufactured to study the performance of proposed parasitic type actuator, together with an experimental system. Experiments indicate that the maximum stepping displacement is ΔL = 9.00 μm in the case that input voltage Ue = 150 V; the minimum stepping displacement ΔL = 0.24 μm is achieved under Ue = 60 V; the maximum speed is Vs = 180 μm s−1; the largest output force is F = 106.3 g under that input frequency f = 1 Hz and Ue = 100 V. This study demonstrates the feasibility of symmetrical triangle flexure mechanisms in the design of parasitic type piezoelectric actuators with large working stroke.

Active suppression of the backward motion in a parasitic motion principle (PMP) piezoelectric actuator

In the piezoelectric driving field, backward motion commonly exists in output displacement curves of the actuators designed by various driving principles, which deteriorates the output performances and increases difficulty in subsequent control. To suppress the backward motion, a synergic motion principle (SMP) was proposed in this paper, which employed two piezoelectric stacks (PESs), one for driving and the other for lifting. By synergic driving of these two PESs, the contact force during the driving process could be effectively controlled and thus the backward motion could be actively suppressed. To verify the feasibility, an actuator prototype was designed and fabricated, and an experimental system was established to test its output performances. By theoretical analysis and experiments, the relationship of the driving voltages for these two PESs was determined. Under the optimized experimental conditions, it showed that the actuator could output stepping displacement without backward motion when working under the SMP. By comparing the results with those obtained when the actuator worked under the parasitic motion principle (PMP), the feasibility and validity of the proposed SMP for suppressing the backward motion were further confirmed.

Kinematic analysis of a novel 2-PrRS-PR(P)S metamorphic parallel mechanism

Lower mobility parallel mechanisms have been developed in different structures and widely applied in industry, but still have disadvantages in various tasks and functional requirements. A 2-PrRS-PR(P)S metamorphic parallel mechanism with two working configurations and a transiting configuration is presented. First, the architecture and the way of metamorphosis about the mechanism are described in detail. The mobility of the metamorphic parallel mechanism is obtained with screw theory. Furthermore, the parasitic motions in different configurations are derived based on the geometry constraint conditions. Both the inverse kinematic problem and forward kinematic problem of the mechanism are investigated by the closed-loop equation and validated via numerical examples. Then, the velocity and acceleration in two working configurations are obtained by the derivation of the inverse kinematic problem. Finally, the reachable orientation workspaces are discussed using the three-dimensional search method in different configurations. A comparison with the 3-PRS PM without metamorphic mechanism in workspace is presented and an example of the metamorphic parallel mechanism in robotic supporting leg is presented. The above analyses provide theoretical foundations for application of this mechanism.