Design Of Compliant Mechanisms Research Articles

Design and Experimental Investigation of XY Compliant Mechanism for Precision Applications

A XY compliant mechanism is designed for the precision application with higher range, precision, and accuracy. In earlier work, many researchers have used different methods to design compliant mechanism. In this paper, XY positioning stage is designed using blocks method. However, the model is monolithic in nature to avoid joints. By using wire EDM, the XY model is manufactured. Voice coil actuators are used for the displacement, which give larger range. Analytical modeling is carried out and is validated with MATLAB results. Finally, experimentation is done for performance analysis. The XY model gives ±6mm with motion direction. The XY model evaluates both static and dynamic performances.

Analytical model establishment and attitude calculation of a parallel leaf-spring carrying mechanism

Abstract. In this paper, a novel parallel leaf-spring carrying mechanism (PLCM) is investigated using a compliance-matrix-based approach. For the analytical modeling and attitude calculation, the geometric errors of the flexible arm, including the height and the top plane's direction, are considered, and the displacement method is used to calculate the equilibrium attitude. The influence of the equilibrium attitude at different heights and the initial tilts of the top planes are analyzed separately. The validity and effectiveness of the attitude calculation are illustrated by experimental verification. The laser triangulation coordinate method is used for attitude measurement. The deviations of the normal vector between the calculation results and measurement results are smaller than 2×10-4, which is small enough to satisfy practical requirements. This can be used to guarantee stable and accurate wafer transfer in a lithography machine. Therefore, it can be concluded that the methods employed for analytical model establishment and attitude calculation can be used as a reference for the analysis and design of a complex parallel compliant mechanism.

A curved-beam based quasi-constant force mechanism supporting large range and force-sensitive robotic manipulation

Emerging applications of force-sensitive manipulation with the requirements on grasping safety and efficiency pose significant challenges on the design of compliant constant-force mechanisms with large operating ranges. In this paper, we propose a novel curved-beam based quasi-constant force mechanism fully compatible with the additive manufacturing technology, which is configurable with appropriate arc-elements to achieve quasi-constant force output with a large motion stroke. We develop an analytical model to describe the static deformation behavior of the proposed mechanism and analyze the performance sensitivity of its structural parameters, with which we also propose the optimization formulation and general guidelines for the design of curved-beam based compliant quasi-constant force mechanisms to meet force and displacement requirements. Finite element analysis and experiments are also conducted to comprehensively evaluate the proposed design, demonstrating significant performance improvement over existing results.

Design and Optimization of a Large-Stroke Compliant Constant-Torque Mechanism

Compliant constant-torque mechanism (CTM) can produce an output torque that does not change within a prescribed input rotation range. This stability is maintained regardless of complicated sensorized control systems. Owing to the monolithic nature of the compliant mechanism, the device is more compact, lightweight, and portable, which is favorable to human joint rehabilitative devices or mobility-assisting devices. However, before approaching the stable range, the mechanism has to undergo a pre-loading range which usually accounts for one-third of the entire operational journey. In addition, the deformation of flexible segments is restricted due to the yield strength of the materials. This limited working range hampers other potential applications of compliant CTMs. This paper presents a novel design of a compliant 2-stage CTM with long-stroke by using serially connected curved beams that deform sequentially. The design process is implemented via a shape optimization scheme using genetic algorithm. Finite element analysis is used to characterize the constant-torque behavior of the CTM under static loading. A general design formulation is also proposed to synthesize this special kind of compliant mechanism. The results show that this CTM gets the stable torque range from 300 to 1100 over two stages with the deviation less than 4.3%.

Toward the Design of Kresling Tower Origami As a Compliant Building Block

Abstract In this paper, the use of the Kresling tower origami as a building block for compliant mechanism design is considered. To help building systems using this origami, models are derived to link the origami pattern geometry to the Kresling tower characteristics. This includes the position of stable configurations, the helical trajectory describing the motion and the orientation of panels during the tower deployment. The provided analytical expressions are helpful to adjust the tower geometry according to desired specification. In addition, an original modification of fold geometry is introduced to modify the tower stiffness. Material removal at specific locations, where maximum fold deformations occur, aims at reducing the actuation force without affecting the kinematics. Experimental evaluation is conducted to assess the relevance of the proposed models and evaluate the impact of fold line modification. The proposed simplified models are precise enough for the synthesis. The capacity to strongly reduce the actuation force, due to the fold line modification, is observed.

Hybrid explicit–implicit topology optimization method for the integrated layout design of compliant mechanisms and actuators

Increasing the working stroke of compliant mechanisms in a limited space has always been an important topic in mechanics. One effective method is to develop a more fundamental design model that considers the multi-physical coupling characteristics of compliant mechanisms and actuators. This paper presents a new method for the integrated design of compliant mechanisms and piezoelectric actuators, which incorporates the projective transformation-based moving morphable components method with the parametric level set method (PMMC-PLS), based on the use of explicit and implicit topology optimization methods to drive the layout evolution of the embedded actuator and host structure, respectively. The extended finite element method (XFEM) is adopted to accurately capture the boundary of the multi-component system, thereby increasing the accuracy of the structural response and sensitivity analysis. To circumvent defacto hinges and thin wall features, a global manufacturability constraint is proposed by applying the minimum length scale control to the host structure and a non-overlap constraint to embedded actuators. Moreover, the output stiffness is considered to enhance the mechanical performance of the mechanism. The effectiveness of the proposed method is verified considering numerical examples.

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom.

Compliant mechanisms are widely used in cutting-edge scientific and technological fields such as precision engineering, micro-/nano-manipulation, or microelectronics. Hence, the demand for multi-degree-of-freedom compliant mechanisms has increased sharply. The structure of compliant mechanisms becomes increasingly complex with the increase of degrees of freedom. Here, a compliant mechanism with six degrees of freedom is proposed based on curved beams. The compliant mechanism has the advantages of simple structure and multi-degree-of-freedom. Using the isogeometric analysis method, a model of the mechanism is constructed. Static analysis show that six degrees of freedom can be generated. The prototype of the mechanism is developed by 3D printing. A loading test in six degrees of freedom is carried out. The output and input have high linear relations and the structure has low inter-directional coupling. We trust that this study provides a pioneering step towards the design of compliant mechanisms based on curved beam elements.

A level set-based optimized design of multi-material compliant mechanisms considering stress constraints

This work presents a level set-based approach to design multi-material compliant mechanisms subject to local stress constraints. The inclusion of stress constraints can avoid non-realistic hinges formed by a single node or element often present in compliant mechanisms. This study proposes an optimization procedure capable of assigning multiple materials with distinct properties along the structure to obtain mechanisms that maximize the output displacement and satisfy stress constraints. For the level set topology description, the Multi-Material Level Set (MM-LS) model is adopted. Local stress constraints and volume constraints for the multiple material phases are included in the objective function via an augmented Lagrangian technique. The structural geometry is defined by an explicit level set method and the Ersatz material model. The proposed approach is presented in a generalized form that can be easily extended to any number of materials defined by the user. Two-dimensional numerical results demonstrate the efficacy of the proposed procedure.

Design of compliant mechanisms: An explicit topology optimization method using end-constrained spline curves with variable width

In this study, an approach using moving end-constrained spline (ECS) curves with variable widths is presented for the explicit topology optimization of compliant mechanisms. The proposed approach uses a series of spline curves to represent the topology of the compliant mechanism. Instead of using a fixed width, we let the width of such spline curves vary along the curve. The optimized design is obtained by optimizing the width of the spline curves and the position of the control points. To avoid infeasible solutions in the design process, the end points of several specific spline curves are constrained according to the design region. The validity of the proposed method is demonstrated using different types of splines, such as the Bézier curve and B-spline curve, for the design of a force inverter, a compliant gripper and a compliant orthogonal displacement amplification mechanism.

Configuration design of compliant mechanism by infill structure generation method

Part of the authors have proposed an infill structure generation method to obtain several suitable structural configurations, that is different from the structural optimization method that obtains a single optimal configuration. The method arranges the structural components fitted to the principal stress distributions for the grayscale optimum configuration obtained by SIMP method. This study applies the infill structure generation method to a compliant mechanism design problem. Through numerical examples, validity of the proposed method is demonstrated. Then, properties of several obtained structural configurations are compared.

Multi-material topology optimization considering joint stiffness using a two-step filtering approach

In this paper, a new method is presented to concurrently determine the structural layout and joint interface during the multi-material topology optimization (MMTO) process. Although the development of additive manufacturing techniques allows the fabrication of multi-material structures for soft materials with graded properties, joint materials for joining metals or composites are still needed. This paper proposes a novel material interpolation scheme for defining the joint area between dissimilar materials using a two-step filtering process. The general MMTO process is performed in the first filtering step. Furthermore, the filtered variables generate the joint area, and the filter radius controls the thickness of the area in the second filtering step. A modified discrete material optimization (DMO) approach is developed to control the different materials independently and to expand the applicability of the method to cases with more than two design materials. To demonstrate the performance of the proposed method, a compliance minimization problem is formulated for various volume constraints, joint thicknesses, material properties, mesh types, and number of materials. To show the scalability, 3-D design and compliant mechanism design examples are adopted. Based on numerical examples, it was confirmed that the proposed method performs well in various cases; moreover, the results demonstrate that the concurrent designing of the structural layout and joint interface leads to better performance than when joint stiffness is not considered.

Stiffness-Oriented Structure Topology Optimization for Hinge-Free Compliant Mechanisms Design

This paper presents a stiffness-oriented structure topology optimization (TO) method for the design of a continuous, hinge-free compliant mechanism (CM). A synthesis formulation is developed to maximize the mechanism’s mutual potential energy (MPE) to achieve required structure flexibility while maximizing the desired stiffness to withstand the loads. Different from the general approach of maximizing the overall stiffness of the structure, the proposed approach can contribute to guiding the optimization process focus on the desired stiffness in a specified direction by weighting the related eigen-frequency of the corresponding eigenmode. The benefit from this is that we can make full use of the material in micro-level compliant mechanism designs. The single-node connected hinge issue which often happened in optimized design can be precluded by introducing the eigen-frequency constraint into this synthesis formulation. Several obtained hinge-free designs illustrate the validity and robustness of the presented method and offer an alternative method for hinge-free compliant mechanism designs.

Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints.

This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

Correction to: Discrete variable topology optimization for compliant mechanism design via Sequential Approximate Integer Programming with Trust Region (SAIP-TR)

Correction to: Discrete variable topology optimization for compliant mechanism design via Sequential Approximate Integer Programming with Trust Region (SAIP-TR)

Analysis and design of spatial compliant mechanisms using a 3-D dynamic stiffness model

There have been a number of studies on the analysis and design of planar compliant mechanisms. However, it is more difficult to obtain an exact and concise description of the kinetostatics and dynamics for spatial compliant mechanisms. A general approach is herein presented for analyzing and designing spatial compliant mechanisms by combining a three-dimensional (3-D) dynamic stiffness model with the Pareto multi-objective optimization strategy. The investigation is devoted to small deformation providing a programmable solution for serial-parallel configurations with out-of-plane degrees of freedom (DOFs). Particularly, the 3-D dynamic stiffness model is well applicable to describe the kinetostatic and dynamic behaviors of spatial compliant mechanisms with both distributed and lumped compliance involving irregular-shaped rigid bodies. The Pareto optimal solution set in terms of concerned performances is provided and the optimum structural parameters can be straightforwardly determined. With the presented method, a new piezoelectric Z-θx-θy precision tilting manipulator is optimally designed. Experimental results show the strokes of 0.27 mm, 4.3 mrad, 4.3 mrad and the fundamental resonance frequencies of 470 Hz, 520 Hz and 520 Hz in the three motion DOFs.

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

Optimum design of two-material bending plate compliant devices

PurposeThe purpose of this study is to explore the optimum design of bending plate compliant mechanisms subjected to pure mechanical excitations using topological-derivative-based topology optimization. The main objective is to design the reinforcement in a plate of base material.Design/methodology/approachThe optimum design is performed by means of a level-set representation method guided by topological derivatives. Kirchhoff and Reissner–Mindlin models are used to solve the linear bending plate problem. A qualitative comparison has been carried out between the optimal obtained topologies for each model.FindingsThe proposed methodology was able to design reinforcement in a plate of the base material. The obtained reinforcements notably improve the device’s behavior. The shape and topology of the reinforcements vary depending on the mechanical plate model considered. In fact, in the Reissner–Mindlin solutions, very thin flexo-torsional hinges connecting big zones of the reinforcement material are designed.Originality/valueUp to date, the synthesis of ortho-planar mechanisms by means of continuum topology optimization was only boarded within a multi-physics context. In this work, the optimal design of pure ortho-planar compliance actuators is addressed. The best performance is found by analyzing the results for two classical mechanical plate models.

Design and modeling of a compact compliant stroke amplification mechanism with completely distributed compliance for ground-mounted actuators

This paper proposes a new compliant mechanism for the stroke amplification of piezoelectric actuators. Compared with the existing ones, this compliant stroke amplification mechanism (CSAM) has several advantages including lightweight, less stress concentration, large motion range, as well as ease of manufacture in macro- and micro-scales, mainly due to the completely distributed compliance and largely reduced moving mass. Kinetostatic models of the CSAM, with consideration of the payloads applied on the output stage, are derived for quick and insightful determinate analysis, which enables optimization of the associated parameters to achieve different objectives. The results obtained from the kinetostatic models are in reasonable agreement with the FEA simulation results, with less than 3.8% difference when the input displacement is less than 10 µm. An optimization method, based on the analytical models, is introduced and employed to increase the amplification ratio of the CSAM by up to 240%. The optimized CSAM is an excellent candidate for the stroke amplification of piezoelectric actuators, which is fabricated and experimentally tested. The optimization method is able to be extended to design other compliant mechanisms with optimized size, shape and topology configuration simultaneously.

Topology Optimization and Prototype of a Multimaterial-Like Compliant Finger by Varying the Infill Density in 3D Printing.

This study presents a multimaterial topology optimization method for design of multimaterial compliant mechanisms. Traditionally, the objective function in topology optimization for design of structures is to minimize the strain energy (SE). For synthesis of compliant mechanisms, the objective function is usually to maximize the mutual potential energy (MPE). To design an adaptive compliant gripper for grasping size-varied objects, a multicriteria objective function considering both the SE and MPE at two different output ports is proposed in this study. In addition, based on the fact that different infill densities in three-dimensional (3D) printing leads to prototypes with different equivalent mechanical properties, this article proposes that a multimaterial design can be approximated by varying the values of infill densities in different portions of a 3D-printed component, which enables the multimaterial designs to be prototyped using the general low-cost, single-material fused deposition modeling 3D printing machines. The proposed method is used to design and prototype a bi-material compliant finger which is 3D printed using a flexible thermoplastic elastomer with infill densities of 30% and 100%. The experimental results demonstrate that the bi-material finger is a better design in terms of reducing the driving force while increasing the output displacement at the fingertip comparing to the single-material finger design with the same volume and weight. Furthermore, a two-finger gripper with two identical multimaterial-like compliant fingers is prototyped and installed on a six-axis industrial robot. The experimental tests are performed to demonstrate the effectiveness of the presented design.

Design, analysis, and experimental investigation of micro-displacement amplification compliant mechanism for micro-transducers.

This paper presents experimental force and buckling analysis of a compliant micro-displacement amplification mechanism fabricated using the commercially available PolyMUMPs process. The proposed mechanism proficiently amplifies displacement, at two output ends, with an optimal amplification factor of 7.2. Buckling analysis revealed that an amplification factor ranging from 2.8 to 11 may be achieved for an input displacement varying from 0.1 to 7.5 µm. Based on the analysis, the optimal value of the amplification factor is found to be 7.2 with an input displacement of 3.5 µm at the operational force of 60 μN having a buckling load factor (BLF) >1. Critical load magnitude is 187 μN having BLF = 1. Buckling occurred when loading exceeded the critical load value, having BLF <1, and the mechanism failed to produce a significant amplification factor. Static analysis showed that stresses produced are within the safe region, and the structural integrity of the mechanism is not compromised having a factor of safety of 1.4. Modal analysis predicted that the natural frequency of the desired mode is 35.47 kHz. Dynamic simulations, under 15g dynamic load with a frequency range of 30-40 kHz, confirm the possibility of integrating the proposed mechanism with MEMS devices. Parametric optimization comprehends that length and angle are the two major geometric parameters that govern the working range, force, and amplification factor. For input displacements below 1 µm, the amplification factor is even higher, which is highly beneficial for amplifying small displacements. Static, modal, and dynamic analyses of the designed mechanism have been carried out using finite element method based commercial software IntelliSuite®. The experimental results showed that this mechanism can provide the same amplified displacement at two output points and is self-sufficient to be incorporated as an intermediate compliant mechanism for enhancing the output in the case of both static and dynamic micro-devices.