Flexure-based Compliant Mechanisms Research Articles

Bandgap tunability in pantographic metamaterials via flexure-based mechanisms

Inspired by flexure-based compliant mechanisms, we propose a novel pantographic system with broad, multiple bandgaps for wave and vibration control. This compliant mechanism embeds local inhomogeneities, such as flexure hinges, to achieve tunable bandgap properties. Using finite element analysis and Bloch’s theorem, we systematically study the bandgap properties of the pantographic lattice, including band structure diagrams, flexure hinge geometry effects, and vibration isolation in finite pantographic beam.

A Body-frame Beam Constraint Model

Compliant Mechanisms (CMs) have presented their inherently advantageous properties since the nature of CMs is to utilize elastic deformation of the built-in elementary flexible members to transfer motion, force and energy. To predict the performances of CMs and optimize their designs, modeling CMs turns out to be a major concern in this field, particularly, such as high-precision flexure-based CMs. Reported in the literature, the well-known Beam Constraint Model (BCM) expressed in Cartesian coordinate system serves as an effective tool to model the deflection of flexures. Inspired by BCM, in this paper, we take one step further to propose a Body-frame Beam Constraint Model (BBCM) to handle buckling and intermediate-range deflections under typical beam-end loading conditions. Numerical and analytical analysis also proves that BBCM can also provide reliable accuracy in complex loading conditions and complex beam geometries within small-to-intermediate-range deflections and may accurately characterize large deflections under some specific loading conditions as well.

Analytical Modeling and Application for Semi-Circular Notch Flexure Hinges

Flexure-based compliant mechanisms can be used to achieve bio-imitability and adaptability in the applications of biomedical engineering. However, a nonlinear load-displacement profile increases the design complexity of this type of compliant mechanism, especially when the cross-section of the flexure hinge is not constant. This paper proposes two general analytical models by analyzing the compliance and stress characteristics of the semi-circular notch flexure hinge undergoing large deflections, which is a typical variable cross-section of a flexure hinge, based on the Castigliano’s second theorem and the finite elements analysis method. As a case study for verification, three compliant four-bar linkage mechanisms are designed based on the proposed design approach, the design method proposed by Howell, and the equations proposed by Lobontiu, respectively. The results show that the design accuracy is improved 36% in comparison with designs from Howell and Lobontiu. Finally, a flexure-based artificial finger is designed and manufactured based on the proposed optimization approach. The performance test of the prototype shows that the artificial finger has good bio-imitability and adaptability with respect to joint movements.

RCM adjustment for a double-parallelogram based RCM mechanism used for MIS robots

The inevitable errors in the manufacturing, assembly, and testing of a remote center-of-motion (RCM) mechanism lead to the erroneous link parameters which deviate its geometry. Consequently, the motion, as well as the force, become non-zero at the entry port to the patient’s body which is undesirable. To address this issue, the current work first presents the accurate kinematic model of the RCM of an exemplary double-parallelogram-based RCM mechanism. Thereafter, it introduces the RCM adjustment concept and a flexure-based compliant mechanism to nullify/minimize the said deviation. For the analytical design of the flexure element, this paper makes the required design calculations and performs the finite element analysis. It is followed by the disclosure of the RCM Adjustment System and a systematized method of RCM adjustment for a mechanically constrained RCM device. The devised system is based on the prescribed compliant mechanism design and is advantageous, over the traditional RCM adjustments. The potential of the proposed concept lies in the fact that it is not limited to the adopted mechanism only rather, it is extendable to other mechanisms as well which was missing in the prior art. In addition, it offers a more simplified and economical design. Further, an initial prototype of the exemplary mechanism is manufactured using laser micromachining and rapid prototyping techniques. Both analytical as well as physical validations have been performed which proved the efficacy of the proposed kinematic modeling concept. Furthermore, the prototype of the introduced RCM Adjustment System is manufactured as a single-piece design which demonstrated its effectiveness. The preferred embodiment of the same is the said double-parallelogram-based RCM mechanism which is most widely used for robot-assisted minimally invasive surgery (RAMIS). It is designed in a SolidWorks environment and manufactured using Al6101-T6 and SS304 as link material, and a variety of standard elements.

Input coupling modeling method for a three-PRR flexure-based compliant stage

This paper presents the input coupling modeling method for a three-PRR flexure-based compliant stage. The input coupling modeling for planar compliant mechanisms is first established. The kinematic structure of a three-PRR compliant stage is then designed, and its input coupling is derived by using the proposed method. Subsequently, the validation and analysis are carried out by using finite element method (FEM). The relationships between two main parameters and the input coupling rate of the three-PRR compliant stage are discussed, and the decoupling region is then determined. Finally, its geometrical parameters are optimized, and the workspace calculated by the analytical method is compared with that obtained from FEM. It not only provides a new input coupling modeling method for flexure-based compliant mechanisms, but also provides a reference for the design of three-PRR mechanisms.

Mechanical and thermal stability of Bulk Metallic Glass alloys identified as candidates for space mechanism applications

Extraterrestrial environments expose engineering components to severe operating conditions for extended durations. Challenges of extreme temperature changes and high vacuum are being met by careful selection of available materials or by development of novel high-performance materials and processes. Bulk Metallic Glasses (BMGs) are amorphous alloys that exhibit very high strengths, hardness, strain energy storage, corrosion resistance, and the capacity for thermoplastic formability, and are of interest in space engineering design. Using criteria driven by the requirements of specific space-based mechanisms, BMG alloys were selected from the literature for processing and performance evaluation. Alloys particularly suited for gearing applications and flexure-based compliant mechanisms were identified and standard test specimens produced. Four Zr-based BMG alloys were selected for analysis: Zr53Al16Co23.25Ag7.75, Cu47Zr46Al5Y2, Zr49Ti1.96Cu37.24Al9.8Y2, and Zr60Ti2Nb2Al7.5Ni10Cu18.5, with compositions in at.%. Presented in this work are the results of compression testing, fatigue testing, and differential scanning calorimetry; previous results of wear and hardness testing have been presented elsewhere. A maximum space service temperature of 400 °C is considered. The alloys exhibited significant differences in processability and thermomechanical performance. The alloy Zr49Ti1.96Cu37.24Al9.8Y2 exhibited the best overall performance for gearing applications; and Zr60Ti2Nb2Al7.5Ni10Cu18.5 was the best alloy for compliant flexures.

The compliance matrix method for the kinetostatic analysis of flexure-based compliant parallel mechanisms: Conventions and general force–displacement cases

In this paper, we present the mathematical formulation of the Compliance Matrix Method (CMM) for the kinetostatic analysis of Flexure-Based Compliant Mechanisms (FBCM). The formulation is achieved by integrating the different approaches found in literature, as an attempt of unification of the CMM. The CMM is combined with inverse kinematics in an analytical process, to be used in the kinetostatic analysis of Flexure-Based Compliant Parallel Mechanisms (FBCPM) with multiple actuation forces where the output displacements are not coincident, neither are parallel, with the input forces. This analytical process allows the total compliance matrix of the FBCPM to be obtained, which relates the input forces (commonly applied on the legs) with the output displacements (commonly desired in the moving platform). The effectiveness of the analytical process presented here, is validated using two FBCPM with Two-Dimensional and Three-Dimensional architectures as examples. Then, the analytical results are validated with Finite Element Analysis by comparing the capability of the FBCPM to follow complex trajectories: circular and angular trajectories for the 2D-FBCPM, and a spherical spiral trajectory for the 3D-FBCPM, showing excellent agreement (less than 5%).

Redesigning a flexural joint for metal-based additive manufacturing

Traditional rigid mechanisms exhibit problems such as assembly difficulties, friction and lubrification. Flexure-based compliant mechanisms, instead, are monolithic and gain their mobility thanks to proper design and material deflection. Designing and producing a compliant mechanism accurately and conveniently is crucial. Thanks to its capabilities, additive manufacturing (AM) approach can provide optimal design and production and open the way to new, unexploited performances.This study investigates the redesign of a traditional cantilevered pivot. The redesign considers the performance improvements by exploiting the advantages of the AM based on laser powder bed fusion (L-PBF).The maximum tensile and compressive loads of the redesigned joint were identified. The structure was optimised by considering the most critical geometrical parameters in terms of mechanical performance. The geometrical factors comply with the design rules for L-PBF process, to maximise the dimensional and surface accuracies. The new approach to the flexural joint design presented in this paper provided higher mobility if compared with the traditional approach. Therefore, this study makes a major contribution to research on the production of precision alignment mechanisms and scientific instruments.

A Hybrid Computational Method of Desirability, Fuzzy Logic, ANFIS, and LAPO Algorithm for Multiobjective Optimization Design of Scott Russell Compliant Mechanism

Flexure-based compliant mechanisms are increasingly promising in precision engineering, robotics, and other applications, thanks to the excellent advantages of no friction, no backlash, no wear, and minimal assembly. However, their design and analysis are still challenging due to the coupling of kinematic-mechanical behaviors with large nonlinear deflections in comparison to their rigid-body counterparts. Optimal design is an important aspect in the field of compliant mechanisms and has attracted much attention during the last decades. Especially, when considering a multiobjective optimization design for compliant mechanisms, the problem is becoming more complicated. Thus, this article presents a new efficient hybrid computational method to resolve multiobjective optimization design of compliant mechanisms. A Scott Russell compliant mechanism is employed as the design example and to show the advantages of the proposed optimizing method. The proposed method is developed by hybridizing the desirability function approach, fuzzy logic system, adaptive neuro-fuzzy inference system (ANFIS), and lightning attachment procedure optimization (LAPO). First of all, a 3D finite element model is created and central composite design is employed to build a numerical matrix. First, design variables are refined by using analysis of variance and Taguchi approach in terms of considerably eliminating space of design variables. Subsequently, desirability values of two objective functions are determined and transferred into the fuzzy logic system. The output of the fuzzy logic system is considered as a single combined objective function. Next, modeling for fuzzy output is established via developing the ANFIS model. At last, the LAPO algorithm is adopted for solving the multiobjective optimization problem for the mechanism. Three numerical examples are investigated to validate the feasibility and the effectiveness of performance efficiency of the proposed methodology. The results find that the proposed methodology is more efficient than traditional Taguchi-based fuzzy logic. Besides, the performance efficiency of the proposed approach outperforms the Jaya algorithm and TLBO algorithm through the Wilcoxon signed rank test and Friedman test. The results of this article give a useful approach for complex optimization problems.

Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

Abstract Flexure-based compliant mechanisms are becoming increasingly promising in precision engineering, robotics, and other applications due to the excellent advantages of no friction, no backlash, no wear, and minimal requirement of assembly. Because compliant mechanisms have inherent coupling of kinematic-mechanical behaviors with large deflections and/or complex serial-parallel configurations, the kinetostatic and dynamic analyses are challenging in comparison to their rigid-body counterparts. To address these challenges, a variety of techniques have been reported in a growing stream of publications. This paper surveys and compares the conceptual ideas, key advances, and applicable scopes, and open problems of the state-of-the-art kinetostatic and dynamic modeling methods for compliant mechanisms in terms of small and large deflections. Future challenges are discussed and new opportunities for extended study are highlighted as well. The presented review provides a guide on how to select suitable modeling approaches for those engaged in the field of compliant mechanisms.

CLOSED-FORM TORSIONAL COMPLIANCE OF TWO-AXIS FLEXURE HINGES

This paper focuses on closed-form equations of torsional compliance for two-axis flexure hinges with variable rectangular cross-section (VRC) which can serve as the alternatives of flexure spherical hinges in flexure-based spatial compliant mechanisms.

A novel method for testing accelerometer transverse sensitivity.

This paper presents a flexure-based compliant mechanism for testing accelerometer transverse sensitivity. The definition of transverse sensitivity is first described. Subsequently, the detailed structure of the developed mechanism is introduced. The principle of this method and the corresponding theoretical model are analyzed. Based on the principle, a prototype is manufactured and an experimental platform is set up. The circular trajectory tests are carried out to verify the feasibility of this method. It shows that the precision of the circular trajectory can be guaranteed. Finally, a three-axis piezoelectric accelerometer is tested. The maximum transverse sensitivity is below 5%, and its maximum measurement uncertainty is 0.15%, while the maximum measurement uncertainty of the corresponding direction angle is 0.79°. It demonstrates that the proposed method is reasonable and accurate.

Design, Analysis and Testing of a New Compliant Compound Constant-Force Mechanism

This paper presents the design and testing of a novel flexure-based compliant compound constant-force mechanism (CCFM). One uniqueness of the proposed mechanism lies in that it achieves both constant-force input and constant-force output, which is enabled by integrating two types of sub-mechanisms termed active and passive constant-force structures, respectively. Unlike conventional structures, the active constant-force structure allows the reduction on input force requirement and thus the enlargement of motion stroke provided that the maximum stress of the material is within allowable value. While the passive one offers a safe environmental interaction during the contact process. Analytical model of the proposed CCFM is derived which is verified by simulation study with finite element analysis (FEA). A prototype mechanism is fabricated by a 3D printer to demonstrate the performance of the proposed CCFM design. Experimental results reveal the effectiveness of the reported CCFM.

Dynamic stiffness matrix for free vibration analysis of flexure hinges based on non-uniform Timoshenko beam

As a typical non-uniform beam with complex varying cross-section and large curvature, free vibration analysis of flexure hinges in the state-of-the-art compliant mechanisms is challenging due to their complicated and even unsolvable governing differential equation. Investigation on the free vibration analysis of non-uniform beams was attractive in the past but still with a few types of specific beams or approximate solutions. The contribution of this paper is to formulate the dynamic stiffness matrix for generic non-uniform beams and applied for the first time to the free vibration analysis of flexure hinges. Firstly, the vibration solution of general non-uniform Timoshenko beam is derived by using a recursive integral in power series of circular frequency but not the traditional way in the well-known method of Frobenious. Then, the dynamic stiffness matrix of non-uniform Timoshenko beam is derived based on the variational principle. At last, the new method is applied for the free vibration analysis of flexure hinges and flexure-based compliant mechanisms. Several case studies demonstrate the advantage of the proposed approach in terms of high accuracy, generality and high efficiency (only one element is needed). The obtained results are useful for dynamic design of flexure hinges and can serve as a benchmark to examine the accuracy of other numerical solutions. Due to the closed form and universality of the proposed method, it is also of benefit for free vibration analysis of other non-uniform beams with all kinds of varying cross-section or functionally graded beams.

A general approach for generating kinetostatic models for planar flexure-based compliant mechanisms using matrix representation

Kinetostatic modeling of a flexure-based compliant mechanism (FCM) is always a complicated and error-prone process because it involves not only the formulation of the geometric compatibility but also the formulation of the load equilibrium of the mechanism. In this paper, we propose a general approach for automatically generating kinetostatic models for FCMs based on their matrix representation. The approach utilizes virtual flexure hinges, link-flexure incidence matrices and path matrices to unify and simplify the formulation of the kinetostatic equations of FCMs. Four case studies are provided to demonstrate the use of the proposed method for modeling various FCMs.

A Generic Compliance Modeling Method for Two-Axis Elliptical-Arc-Filleted Flexure Hinges.

As a kind of important flexible joint, two-axis flexure hinges can realize in-plane and out-of-plane motions and can be used for constructing flexure-based spatial compliant mechanisms. The paper introduces a common two-axis elliptical-arc-filleted flexure hinge that is generated by two different elliptical-arc-filleted cutout profiles and that provides some new hinge types. The analytical compliance equations of both half-segments of the two-axis elliptical-arc flexure hinges are firstly formulated, and then, based on a generic compliance modeling method of a flexure serial chain, the closed-form compliance and precision matrices of two-axis elliptical-arc-filleted flexure hinges are established and validated by the finite element method. Some numerical simulations are conducted to compare the effect of different design geometric parameters on the performance of the two-axis flexure hinges.

Addressable wireless actuation for multijoint folding robots and devices.

"Printing" robots and other complex devices through a process of origami-like folding is an emerging and promising manufacturing method due to the inherent simplicity and low cost of folding-based assembly. Folding is used in this class of device to create both complex static structures and flexure-based compliant mechanisms. Dependency on batteries to power these folds with no external wires is a hurdle to giving small-scale folding robots and devices functionality. We demonstrate a battery-free wireless folding method for dynamic multijoint structures, achieving addressable folding motions-both individual and collective folding-using only basic passive electronic components on the device. The method is based on electromagnetic power transmission and resonance selectivity for actuation of resistive shape memory alloy actuators without the need for physical connection or line of sight. We demonstrate the utility of this approach using two folded devices at different sizes using different circuit approaches.

Analytical Compliance Modeling of Serial Flexure-Based Compliant Mechanism Under Arbitrary Applied Load

Analytical compliance model is vital to the flexure- based compliant mechanism in its mechanical design and motion control. The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the external loads are applied on the flexure members. Concise and explicit analytical compliance models of the serial flexure-based compliant mechanisms under arbitrary loads are derived by using the matrix method. An equivalent method is proposed to deal with the situation when the external loads are applied on the flexure members. The external loads are transformed to concentrated forces applied on the rigid links, which satisfy the equations of static equilibrium and also guarantee that the deformations at the displacement output point remain unchanged. Then the matrix method can be still adopted for the compliance analysis of the compliant mechanism. Finally, several specific examples and an experimental test are given to verify the effectiveness of the compliance models and the force equivalent method. The research enriches the matrix method and provides concise analytical compliance models for the serial compliant mechanism.

A compact stepper motor actuated disposable microgripper

This paper describes the design, modeling and experimental testing of a disposable microgripper for manipulation of micro particles and objects. We utilize a CO2 laser cutter to fabricate acrylic microgripper capable of handling objects less than 300 μm in size. The microgripper forms a flexure-based compliant mechanism which is actuated with a radial cam driven by a miniature stepper motor. Finite element analysis is used to optimize the selected design for optimal stress distribution and tip displacement in response to the applied force on the legs of the mechanism. The gripper fits on an ergonomically designed holder that contains the stepper motor and a microstepping driver to control the motor. A push of a button on the holder opens and closes the microgripper, thus, making it very easy to operate. We demonstrate the utility of the microgripper through various pick and place experiments. The experimental results exhibit a high level of integrity in the design of the microgripper to manipulate a variety of microparticles.

Theoretical modeling of attenuated displacement amplification for multistage compliant mechanism and its application

With the merits of multiplying displacement amplification ratio and compact structure, flexure-based multistage compliant mechanisms have been widely proposed in recent ten years. Experimental output displacement, however, is attenuated more or less in various designs and is even reduced to less than 10% of the original ambitious design in some prototypes. In this paper, the issue on attenuated displacement amplification of multistage compliant mechanisms is theoretically investigated. A formula of displacement amplification ratio is established based on the elastic beam theory and by defining an impedance factor, which describes the hindering effect of the second layer on the preceding layer. The high accuracy of the model is verified by finite element analysis with no more than 5% deviations. It allows a designer to quickly get an intuitional sense of why the output displacement is attenuated and how each parameter affects the mechanisms’ performance. Thanks to the theoretical guidance, a new planar two-stage compliant mechanism with relatively high frequency response and large range as well as no assembly error is designed and tested. Experiments show a natural frequency of 3.3kHz in the output direction and displacement of 198μm, which agrees with the theoretical prediction.