Compliant Parallel Mechanism Research Articles

An Analytical Model for Calculating the Workspace of a Flexure Hexapod Nanopositioner

This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms.

Towards the design of monolithic decoupled XYZ compliant parallel mechanisms for multi-function applications

Abstract. This paper deals with the monolithic decoupled XYZ compliant parallel mechanisms (CPMs) for multi-function applications, which can be fabricated monolithically without assembly and has the capability of kinetostatic decoupling. At first, the conceptual design of monolithic decoupled XYZ CPMs is presented using identical spatial compliant multi-beam modules based on a decoupled 3-PPPR parallel kinematic mechanism. Three types of applications: motion/positioning stages, force/acceleration sensors and energy harvesting devices are described in principle. The kinetostatic and dynamic modelling is then conducted to capture the displacements of any stage under loads acting at any stage and the natural frequency with the comparisons with FEA results. Finally, performance characteristics analysis for motion stage applications is detailed investigated to show how the change of the geometrical parameters can affect the performance characteristics, which provides initial optimal estimations. Results show that the smaller thickness of beams and larger dimension of cubic stages can improve the performance characteristics excluding natural frequency under allowable conditions. In order to improve the natural frequency characteristic, a monolithic decoupled configuration that is achieved through employing more beams in the spatial modules or reducing the mass of each cubic stage mass can be adopted. In addition, an isotropic variation with different motion range along each axis and same payload in each leg is proposed. The redundant design for monolithic fabrication is introduced in this paper, which can overcome the drawback of monolithic fabrication that the failed compliant beam is difficult to replace, and extend the CPM's life.

A Compliant-Parallel Mechanism with Bio-Inspired Compliant Joints for High Precision Assembly Robot

In this paper, we describe a study on compliant-parallel (C-P) mechanism with high precision and wide range of working area using bio-inspired compliant joints. C-P mechanism is a parallel mechanism in which all of joints are composed by wide deformable compliant joints. In the integration of the compliant joint and the parallel mechanism, a deformation of the compliant joint can be guided by mechanical constraints from the parallel mechanism; thus C-P mechanism can be precisely driven. C-P mechanism has no back-lash, requires no lubrication, and is free from machine noise and abrasion power. And, unlike conventional mechanisms, C-P mechanism can be integrated into compact, lightweight, and simple structure. From these backgrounds, we developed a widely deformable circular compliant joint inspired by Drakaea, which is an orchidaceous species. The circular compliant joint was implemented on a 3-DOF (rotational 2 and translational 1 DOF) parallel mechanism as a first prototype. Then, our second prototype was developed to realize further wide range of working area. A serially layered-flat spring compliant joint was developed based on the bio-inspired circular compliant joint, and was implemented on a traditional 3-DOF DELTA mechanism, as the second prototype. From the evaluation tests of these prototypes, the feasibility of C-P mechanism was shown positive to be applied to a high precision assembly robot within a wide range of working area.

2A2-K02 高精度位置決め装置のための広動作域な5自由度を有する柔軟パラレルメカニズム(パラレルロボット・メカニズム)

2A2-K02 高精度位置決め装置のための広動作域な5自由度を有する柔軟パラレルメカニズム(パラレルロボット・メカニズム)

Modelling and analysis of a rigid–compliant parallel mechanism

This paper presents a two-staged parallel mechanism composed by a rigid platform in a serial connection with a compliant platform, and concentrates on its configuration and interrelation. The analysis starts with the operator of a 3UPU configuration with a central strut being derived. Configuration and displacement formulas of the compliant platform are demonstrated, leading to the analytic equations of the relationship between the actuated angles of the operator and the position parameters of the end-effector. The numerical evaluation of workspace of the two-staged parallel mechanism is then followed.

A compliant parallel mechanism with flexure-based joint chains for two translations

A compliant parallel mechanism for two translations is proposed and applied to a XY fine motion stage driven by piezo actuators. Four flexure-based prismatic-prismatic joint chains are arranged in four sides of a target platform to implement the compliant parallel mechanism. Among others, two are passive joint chains for only motion guidance, and the others are active joint chains for motion guidance merging the function of the displacement amplification of a piezo actuator. Due to the active joint chains, the proposed mechanism has more compact structure than the others which have the separated mechanisms of the motion guidance and the displacement amplification. In addition, the compliant mechanism has a monolithic structure not to be assembled. The compliant mechanism is designed, verified to satisfy some design constraints using Finite element Analysis, and then combined with piezo actuators and capacitance sensors. The characteristics and the performance of the piezo-driven compliant parallel mechanism are demonstrated by experiments.

3自由度精密定位平台的运动特性和优化设计

To achieve the precise motion of a 3-RRR compliant parallel precision positioning stage,a closed-form exact motion model was established and the optimized design of structure parameters was investigated.The Castigliano's second theorem was applied to establishment of the closed-form compliance model for the precision positioning stage.According to the structural characteristics of compliant parallel mechanisms,the system was divided into three symmetrical motion sub-chains.Combining the compliance equations of flexure hinge with the force transmission relations of mechanisms,the stiffness model of each sub-chain was obtained,and the stiffness of the entire system was calculated by summing the stiffness of three sub-chains in the same coordinate system.The proposed stiffness model took the hinge flexibility as the independent variables in the closed form.According to the flexibility matrix,the Jacobian matrix to reflect the relationship between input displacement and output one could be derived.By comparing the kineamatic model between theoretical analysis and FEA,the results show that the errors are within 1.0%~9.5%,which illurastrates that the proposed kinematic model is correct and precise.According to the closed-form Jacobian matrix,its sensitivity to structureal parameters was analyzed,then the design variables with greater impact on the kinematic properties were chosen.By taking the maxmium workspace as a target and the hinge strength,maxmium input forces,geometric dimensions and input coupling as the constrains,an optimal model was proposed.The results show that the optimized structural parameters can obtain more output displacements,and the proposed model can meet the design requirement.

Vibration Analysis of a New Type of Compliant Mechanism with Flexible‐Link, Using Perturbation Theory

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped‐clamped boundary conditions. Comparing perturbation method with Runge‐Kutta‐Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed.

A unified approach to type synthesis of both rigid and flexure parallel mechanisms

Type synthesis of both rigid and compliant parallel mechanisms has become a hot issue in the field of mechanisms and robotics research in recent years. A unified approach to type synthesis of the two classes of mechanisms, however, has not been referred and investigated up to date. Based on the state-of-art analysis for several major type synthesis approaches related to rigid and compliant mechanisms, respectively, it proves feasible to establish a unified methodology for type synthesis of these two classes of mechanisms. That is a synthesis philosophy in terms of the hierarchy mapping between mathematic, physical, and mechanical building blocks in the framework of screw theory, as addressed in this paper. The key point of the proposed method lies in establishing the mapping among three different building blocks (i.e. geometric building block, kinematic or constraint building block, and mechanical building block). As a result, it makes the whole type synthesis process simple and visible. By using the proposed method, two examples are taken to verify the effectiveness for the type synthesis of both rigid and flexure mechanisms. The content of this paper may provide a theoretical frame for constructing a visualized algorithm or software about the unified type synthesis (or conceptual design) of both rigid and flexure parallel mechanisms.

A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

Abstract This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear–analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear–analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms.

Kinematostatic modeling of compliant parallel mechanisms

The benefits of compliant mechanisms in terms of precision are not easy to exploit because of the limitations of the existing kinematic models used to analyze them. In practice, compliant mechanisms are more sensitive to external wrenches than conventional mechanisms. In this paper, based on the kinematic constraints and the static equilibrium between the joint coordinates and the external wrenches, a general kinematostatic model of compliant parallel mechanisms is presented. Then, this model is differentiated to provide a quasi-static model that makes it possible to calculate the variation of the pose as a linear function of the motion of the actuators and the variation of the external loads through two new matrices: the quasi-static Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism.

Stiffness Modeling and Analysis of Passive Four-Bar Parallelogram in Fully Compliant Parallel Positioning Stage

In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair are studied based on the developed model. The relative geometric parameters are changed to show the rules of the stiffness variation and to obtain the demands for simplification in the stiffness modeling of the prismatic pair. Furthermore, the finite element analysis has been conducted to validate the analytical model.

Design, analysis and fabrication of a multidimensional acceleration sensor based on fully decoupled compliant parallel mechanism

Parallel mechanism has become an alternative solution when designing the mechanical component of physical sensors. Previous work was focused on the six degree-of-freedom (DOF) force/torque sensor with the aid of the traditional Gough–Stewart platform. In this paper, a multidimensional acceleration sensor is proposed for kinetic information acquisition through the novel architecture of a 3RR PRR fully decoupling parallel mechanism. The translational elements of three perpendicular legs are served as elastic bodies which are manufactured by aluminum alloy. The structural evolution and mechanism kinematics is first introduced, followed by the modeling of performance atlas including isotropy and sensitivity. Compliance comparison between multi-spring model and finite-element analysis is conducted. The prototype is fabricated for deep investigation on the actual performances. A self-developed calibration platform is utilized for the static calibration to verify its sensitivity and linearity. Consequently, two trial experiments for measuring human motions are implemented to validate the feasibility and effectiveness of the parallel-legged accelerometer.

Six-DOF micro-manipulator based on compliant parallel mechanism with integrated force sensor

This paper describes the design of a micro-scale manipulator based on a six-DOF compliant parallel mechanism (CPM), which is featured by piezo-driven actuators and integrated force sensor capable of delivering six-DOF motions with high precision and providing real-time force information for feedback control. Particularly, the position and screw-based Jacobian analyses of the CPM are presented. Then, the compliance model and the workspace evaluation of the CPM are proposed in order to account for the compliance and obtain design guidelines. Finally, the integrated sensor is introduced. The static features of such a mechanism include high positioning accuracy, structural compactness and smooth and continuous displacements.

Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

Experimental investigations of the large deflection capabilities of a compliant parallelmechanism actuated by shape memory alloy wires

This experimental study investigates the coupled effect of the force developed by the shapememory alloy (SMA) actuators and the force required for the large deflection of an elasticamember in a compliant parallel mechanism. The compliant mechanism developed in houseconsists of a moving platform mounted on a superelastic pillar and three SMA wireactuators to manipulate the platform. A three-axis MEMS accelerometer has been mountedon the moving platform to measure its tilt angle. Three miniature force sensors have beendesigned and fabricated out of cantilever beams, each mounted with a pair of strain gauges,to measure the force developed by the respective actuators. The force sensors are highlysensitive and cost effective compared to commercially available miniature forcesensors. Calibration of the force sensors has been accomplished with known weights,and for the three-axis MEMS accelerometer a rotary base has been consideredwhich is usually used in optical applications. The calibration curves obtained, withR-squared values between 0.9997 and 1.0, show that both the tilt and force sensorsconsidered are most appropriate for the respective applications. The mechanism fixed withthe sensors and the drivers for the SMA actuators is integrated with a NationalInstrument’s data acquisition system. The experimental results have been compared withthe analytical results and it was found that the relative error is less than 2%. This is apreliminary study in the development of a mechanism for eye prosthesis and similarapplications.

Modelling and simulation of a novel shape memory alloy actuated compliant parallel manipulator

This paper presents the non-linear analysis of a shape memory alloy (SMA) actuated fully compliant spatial parallel mechanism. A compliant mechanism made of SMA wires as its actuators and SMA pipe as its structural member that exploits both the shape memory and superelastic effects is proposed and its static analysis using ANSYS is presented in this study. Finite element analysis in a multi-physics environment considering geometric and material non-linearities helps the user to analyse complex behaviour of a system. For the proposed mechanism, simulation results show: (a) 4 per cent strain for SMA actuation is optimal considering the geometric non-linearity of the proposed mechanism for obtaining maximum displacement; (b) buckling effect is less predominant while implementing the superelastic behaviour; and (c) the mechanism can be designed as a compliant device with one or more inflexion points by exploiting the superelasticity of the SMA pipe. The knowledge obtained from the simulation study could help in further miniaturization of the manipulator.

Stiffness mapping of compliant parallel mechanisms in a serial arrangement

Stiffness mapping of compliant parallel mechanisms in a serial arrangement

Stiffness research on a high-precision, large-workspace parallel mechanism with compliant joints

Parallel-structure mechanisms, especially the non-backlash compliant parallel mechanisms, excel serial-structure ones in many indexes. This paper explores a novel six-strut compliant parallel mechanism based on the development of wide-range flexure hinges, and in this system the repeatability and resolution of sub-micron scale can be achieved over cubic centimeter motion range. The system stiffness, as a very important performance for compliant parallel mechanisms, directly influences the workspace, load-carrying capacity and driving-load capacity, etc. The system stiffness depends on the parallel mechanism's geometric dimensions and spatial layout, which is discussed in detail in this paper. The stiffness equation of individual flexure hinge is established firstly, and then the stiffness of the whole mechanism is modeled via assembling stiffness matrices and formulating constraint equations. Finally, the system stiffness influence plots are presented and discussed. The stiffness research on the six-strut compliant parallel mechanism provides further theoretical principles for designing and developing this kind of precision parallel devices.