Parallel-Kinematic Nanopositioning Stages Based on Roberts Mechanism

Piezoelectric actuators (PEAs) and compliant parallel mechanisms (CPMs) are advantageous for designing nanopositioning stages (NPSs) with multiple degrees of freedom (multi-DOFs). This paper proposes a new NPS that uses PEAs and CPMs with multiple spatial DOFs. First, the design of the mechanism is introduced. Six parallel kinematics revolute-revolute-revolute-revolute (RRRR) branched chains were used to create a 6-RRRR CPM for superior mechanical performance. Three in-plane and three out-of-plane chains were combined using a two-in-one structure to ensure fabrication feasibility. A two-in-one 6-RRRR CPM was employed to build the proposed NPS. Second, the mechanical performance was analyzed. High-efficiency finite-element modeling approaches were derived using the compliance-based matrix method (CMM) and a pseudo-rigid body model (PRBM). The model included both 6-RRRR CPM and NPS. The simulation results validated the static and dynamic performance, and the experimental results verified the kinematics. Based on the newly designed mechanism and verified mechanical performance, the proposed 6-RRRR NPS contributes to the development of spatial multi-DOF NPSs using PEAs and CPMs.

The design of the canopy utilizes the conventional rigid body mechanisms which is vulnerable to the presence of backlash, friction of joints or wearing of mechanical parts which lead to short product life. Compliant mechanisms are employed to reduce these mechanical problems, owing to their zero-joint and monolithic structure. A reference design for the conventional canopy was chosen and modified through reviewing different patent designs. Six different configurations of the pseudo-rigid-body model (PRBM) were constructed, and the best configuration was selected. Kinematic synthesis with function generation was performed for the chosen PRBM using MATLAB. The obtained results from the kinematic synthesis were then used to calculate the dimensions and stresses of the flexural pivots for the compliant stretcher mechanism. Finite Element Analysis (FEA) simulation was then performed on each of the models and the obtained flexural pivot stresses were compared with that of the PRBM. This research successfully replaces all the rigid joints and links of the stretcher mechanism of the conventional canopy to form a monolithic structure of compliant stretcher mechanism.

This work introduces an interior contact-aided rolling element (I-CORE) compliant mechanism that draws upon the concepts used for the contact-aided rolling element, cross-axis flexural pivot, and pre-curved flexible beam. The I-CORE incorporates a bilinear compressive stiffness response with an initial tailorable stiffness governed by the flexural geometry, followed by a stiffness curve governed by the material stiffness at the contact point. The I-CORE mechanism can achieve one or two degrees of rotational freedom as well as a single degree of translational freedom. The purpose of the present work was to introduce the I-CORE mechanism, as well as a pseudo-rigid-body replacement model (PRBM) of the I-CORE mechanism which was subsequently validated using both finite element analysis and benchtop mechanical testing. A pseudo-rigid body model was created for the I-CORE to simplify the rapid adaptation of this mechanism to different design applications. This model was validated using both finite element analysis and benchtop mechanical testing under both compression and rotation loading conditions. Additionally, multiple configurations of the device were created and evaluated in order to test its sensitivity to certain design features including the flexure width, flexure thickness, and the radius of the rounded contact surfaces. It was found that the model is sensitive to the thickness of the flexures and that despite some limitations, the pseudo-rigid body model is sufficiently accurate for initial design work. Some possible applications of the mechanism are proposed.

A new 2-degrees of freedom compliant parallel micromanipulator (CPM) utilizing flexure joints is proposed for two-dimensional nanomanipulation in this paper. By a proper selection of actuators, flexure hinges, and materials, this system is constructed and analyzed by a pseudorigid-body model, architectural optimization, and finite-element analysis. Both the position and velocity kinematic modelings are established, and afterwards, statics analysis is performed. In view of the physical constraints imposed by pizeo-actuators and flexure hinges, the CPM's workspace area is determined. And in order to achieve a maximum workspace subjected to the given dexterity indices, kinematic optimization of the design parameters is carried out, which results in a manipulator satisfying the operational requirements. Furthermore, the finite-element analysis has been undertaken to validate the analytical modeling, and the influence of architectural parameters on CPM performance has been evaluated as well. Note to Practitioners-This paper is motivated by the problem of designing a nanomanipulator for two-dimensional (2-D) assembly of nanoscale objects via nanomanipulation. A novel planar parallel mechanism incorporating compliant mechanisms is designed for such a purpose. Since the application of the manipulator depends significantly on the kinematic mathematical models, the designed compliant parallel micromanipulator (CPM) is analyzed by the established pseudorigid-body (PRB) model. The architectural optimization leads to a CPM satisfying the workspace and resolution requirements of this work. Moreover, finite-element analysis is performed to verify the accuracy of the developed PRB model, and simulation results illustrate the efficiency of the PRB model in designing and analyzing the CPM. Since the designed CPM is composed solely of flexural elements which are known to be competent in high precise applications, it is reasonable to expect that the CPM could find its way into 2-D manipulation of nanoscale components.

Compliant Mechanisms (CMs) are currently employed in several engineering applications requiring high precision and reduced number of parts. For a given mechanism topology, CM analysis and synthesis may be developed resorting to the Pseudo–Rigid Body (PRB) method, in which the behavior of flexible members is approximated via a series of rigid links connected by spring-loaded kinematic pairs. From a CM analysis standpoint, the applicability of a generic PRB model requires the determination of the kinematic pairs’ location and the stiffness of a set of generalized springs. In parallel, from a design standpoint, a PRB model representing the kinetostatic behavior of a flexible system should allow to compute the flexures’ characteristics providing the desired compliance. In light of these considerations, this paper describes a Computer-Aided Design/Engineering (CAD/CAE) framework for the automatic derivation of accurate PRB model parameters, on one hand, and for the shape optimization of complex-shape flexures comprising out-of-plane displacements and distributed compliance. The method leverages on the modelling and simulation capabilities of a parametric CAD (i.e. PTC Creo) seamlessly connected to a CAE tool (i.e. RecurDyn), which provides built-in functions for modelling the motion of flexible members. The method is initially validated on an elementary case study taken from the literature. Then, an industrial case study, which consists of a spatial crank mechanism connected to a fully-compliant four-bar linkage is discussed. At first, an initial sub-optimal design is considered and its PRB representation is automatically determined. Secondly, on the basis of the PRB model, several improved design alternatives are simulated. Finally, the most promising design solution is selected and the dimensions of a flexure with non-trivial shape (i.e. hybrid flexure) is computed. This technique, which combines reliable numerical results to the visual insight of CAD/CAE tools, may be particularly useful for analyzing/designing spatial CMs composed of complex flexure topologies.

This paper presents a novel piezoelectric XY micro-displacement scanning stage (MDSS), which features a parallel structure based on compliant mechanisms and has a compact configuration. Since the coupling problem between two motion axes, an innovative elliptical compliant restraint mechanism (ECRM) with a compact layout is proposed and utilized in XY MDSS to obtain high motion accuracy. And the XY MDSS can realize compact structure and lower input stiffness for a large workspace owing to the ECRM simultaneously. Due to the limited displacement of the piezoelectric stack actuator, compliant amplification mechanism is applied to achieve a large stroke. In order to estimate the static and dynamic characteristics theoretically, Castigliano’s second theorem and Lagrange’s method are utilized to establish the analytical models of the newfangled ECRM, compliant amplification mechanism, and XY MDSS. The finite element analysis and experimental tests are carried out to evaluate the performances of XY XDSS, and the results are all in correspondence with analytic solutions, which further validate the correctness of the analytical modeling methodologies. Experimental results show that the XY MDSS can realize a workspace of 58.8 μm × 51.5 μm with a resonance frequency of 576.5 Hz and nanometer-level resolution. The effectiveness of the designed ECRM is also proved simultaneously, which could well limit the coupling motion. The theoretical studies, finite element analysis, and experimental testing all demonstrate that the designed XY MDSS with ECRM has good performance while having a compact structure.

摘要: 基于伪刚体模型,综合考虑平面柔顺机构中柔性杆件的横向变形和轴向变形影响,提出具有移动副的两自由度伪刚体新模型。分别用移动副和转动副描述柔顺杆件的轴向位移和横向位移,模拟末端受力和力矩复合载荷作用时柔顺杆的变形,建立平面柔顺机构的PR伪刚体模型,通过三维搜索得出了模型的最优特征半径系数,应用线性回归方法得到了模型的刚度系数。通过与1R、2R伪刚体模型以及柔顺杆的数值算例对比,说明了PR伪刚体模型的优越性。

This paper discusses one type of commonly used parallel manipulator mechanism for the generation of micro-motion. This mechanism is designed as a compliant mechanism. The design and control of such a compliant mechanism is an important issue. This paper focuses on kinematic issues with consideration of future real-time control of the system. In particular, a constant-Jacobian method to approximate the kinematics, which is based on a pseudo rigid body model of the compliant mechanism, is further validated. This validation is based on the difference between this approximate method and the finite element method to the actual device, for an actuator range of 0–15 μm. The computational time with this approximate method is nearly 50 times less than that with the finite element method. It is expected that this approximation method will be far superior to the finite element method in terms of real-time control.

Kinetostatic modeling of complex compliant mechanisms with serial-parallel substructures: A semi-analytical matrix displacement method

Analysis and synthesis of compliant mechanisms has recently been the subject of significant study in the research community. This focus has led to a number of design approaches for developing compliant mechanisms. This paper describes the value of using the Pseudo-Rigid-Body Model (PRBM) to design compliant mechanisms for commercial products. Application of the PRBM is illustrated through the development of two parallel mechanisms: a bicycle derailleur and parallel-motion bicycle brakes. The PRBM allows compliant mechanisms to be modeled and analyzed as rigid-body mechanisms and significantly reduces the complexity of analysis. Mechanisms with straightforward properties are used to demonstrate the use of the PRBM to design commercially viable compliant mechanisms for required motion and force-deflection characteristics.

The design of an effective hand-exercising device is based on an existing study of the force-deflection behavior of the human hand. This paper presents a design methodology using a compliant mechanism construct, for generating the desired force-deflection profile as the output. This is made possible by the integration of a rigid cam profile segment. The compliant segments serve as the followers, and their material and geometric properties serve as design variables. The force-deflection profile utilized was developed through experimental studies conducted on the human hand, along with a mathematical model that predicts the maximum grip force as a function of the handle’s diameter. A procedure is proposed herein that would allow the use of various force-deflection profiles, to be able to change the resistance level in order to meet individual requirements. The synthesis results obtained are investigated for cam-follower non-interference using a novel pseudo-rigid-body model (PRBM) approach and verified by finite element analysis. The exercise devices generally ignore in their conceptualization and design the anatomical mechanical advantage. This methodology, owing to the nature of the experiment, duly regards the variable mechanical advantage characteristic of the hand in different positions naturally.

This paper presents a completely decoupled XY micro-motion stage which is a compliant parallel mechanism based on flexure hinges and driven by piezoelectric actuators (PZT). Simplified matrix method is employed to derive the compliance model. Then the workspace is analyzed by considering the output reduction of PZT, stress in the flexure hinges and buckling phenomenon. Finally, the stage dimensions are optimized using particle swarm optimization (PSO) algorithm in order to achieve maximum natural frequencies, and finite element analysis (FEA) is carried out to simulate the performance of the optimized stage. The FEA result indicates that the XY stage has an ideal decoupling property.

While nonlinear-elastic materials demonstrate potential in enhancing the performance of compliant mechanisms, their behavior still needs to be captured in a generalized mechanical model. To inform new designs and functionality of compliant mechanisms, a better understanding of nonlinear-elastic materials is necessary and, in particular, their mechanical properties that often differ in tension and compression. In the current work, a beam-based analytical model incorporating nonlinear-elastic material behavior is defined for a folding compliant mechanism geometry. Exact equations are derived capturing the nonlinear curvature profile and shift in the neutral axis due to the material asymmetry. The deflection and curvature profile are compared with finite element analysis along with stress distribution across the beam thickness. The analytical model is shown to be a good approximation of the behavior of nonlinear-elastic materials with tension–compression asymmetry under the assumptions of the von Kármán strain theory. Through a segmentation approach, the geometries of a semicircular arc and folding compliant mechanism design are defined. The deflection of the folding compliant mechanism due to an applied tip load is then evaluated against finite element analysis and experimental results. The generalized methods presented highlight the utility of the model for designing and predicting the behavior of other compliant mechanism geometries and different nonlinear-elastic materials.

The piezo-actuated micro-/nanopositioning stages are often used in the current precision engineering applications, and the coupling deformation under the gravity of the stage is critical to error analysis. Considering the torsional deformation and bending deformation of the flexure hinges, the coupling error’s analytical model of the positioning stage along the Z-axis is derived by using the virtual work principle and the elastic beam theory. The performance of the proposed theoretical model is analyzed and verified by the comparison between two common materials, and the quantities of the piezoelectric actuators are also analyzed with the impact on the coupling deformation of the stage along the Z-axis. Through the comparison and analysis of theoretical results, simulation results and experimental results, the maximum error between finite element analysis and experimental results is 11.43%, with the rest fluctuates within 10%, which proves the correctness of the theoretical model. It is concluded that gravity generated by the workload and the stage does have an influence on the coupling deformation along the Z-axis of the micro-/nanopositioning stage. It cannot be ignored in the analysis and consideration of the positioning stage.

We report on the accuracy of the pseudo-rigid-body model (PRBM) in predicting the behavior of a nanoscale parallel-guiding mechanism (nPGM) that uses two single-walled (5,5) carbon nanotubes (CNTs) as the flexural guiding elements. The nPGM has two regions of behavior: region 1 is governed by the bulk deformation of the nanotubes, and region 2 is characterized by hingelike flexing of four “kinks” that occur due to buckling of the nanotube walls. PRBM parameters for (5,5) CNTs are proposed. Molecular simulation results of region 1 behavior match PRBM predictions of (1) kinematic behavior with less than 7.3% error and (2) elastomechanic behavior with less than 5.7% error. Although region 1 is of more interest because of its well-defined and stable nature, region 2 motion is also investigated. We show that the PRBM parameters are dependent on the selection of the effective tube thickness and moment of inertia, the lesson being that designers must take care to consider the thickness and moment of inertia values when deriving PRBM constants.