Showing papers on "Compliant mechanism published in 2001"

Topology synthesis of large‐displacement compliant mechanisms

Abstract: This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the method of moving asymptotes. Procedures to circumvent some numerical problems are discussed. Copyright © 2001 John Wiley & Sons, Ltd.

Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme

Abstract: In the topology optimization of structures, compliant mechanisms or materials, a density-like func- tion is often used for material interpolation to overcome the computational difficulties encountered in the large "0-1" type integer programming problem. In this paper, we illustrate that a gradually formed continuous peak function can be used for material interpolation. One of the advantages of introducing the peak function is that multiple materials can easily be incorporated into the topology optimization without increasing the number of design variables. By using the peak function and the op- timality criteria method, we synthesize compliant mech- anisms with multiple materials with and without the ma- terial resource constraint. The numerical examples in- clude the two-phase, three-phase, and four-phase materi- als where void is treated as one material. This newdesign method enables us to optimally juxtapose stiff and flex- ible materials in compliant mechanisms, which can be built using modern manufacturing methods.

Design of Compliant Mechanisms: Applications to MEMS

Abstract: Compliant mechanisms are single-piece flexible structures that deliver the desired motion by undergoing elastic deformation as opposed to jointed rigid body motions of conventional mechanisms. Compliance in design leads to jointless, no-assembly (Fig. 1), monolithic mechanical devices and is particularly suited for applications with small range of motions. The compliant windshield wiper shown in Fig. 1 illustrates this paradigm of no-assembly. Conventional flexural mechanisms employ flexural joints that connect relatively rigid links as depicted in Fig. 2. Reduced fatigue life, high stress concentration and difficulty in fabrication are some of the drawbacks of flexural joints. Our focus is on designing compliant mechanisms with distributed compliance which employs flexural links (see Fig. 3) and have no joints (neither pin nor flexural joints) for improved reliability, performance, and ease of manufacture. Distributed compliant mechanisms derive their flexibility due to topology and shape of the material continuum rather than concentrated flexion at few regions. This paper focuses on the unique methodology employed to design jointless mechanisms with distributed compliance. The paper also illustrates a compliant stroke amplification mechanism that was recently designed, fabricated and tested for MEMS application.

Topology optimization of elastic continua using restriction

Abstract: This is a study of restriction methods in topology optimization of linear elastic continua. An ill-posed optimization problem is transformed into a well-posed one by restricting the feasible set, hence the term restriction. A number of restriction methods are presented and compared, of which some have been treated previously in the literature and some are new. Advantages and drawbacks of the methods are discussed from a theoretical as well as a numerical point of view. The problems of minimizing compliance and designing compliant mechanisms constitute the base for these discussions and several numerical examples are presented that illustrate features of the various restriction methods.

Synthesis of Planar, Compliant Four-Bar Mechanisms for Compliant-Segment Motion Generation four-bar mechanisms treated in previous works consisted of at least one rigid

Abstract: moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliantsegment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example. @DOI: 10.1115/1.1416149#

Synthesis of planar, compliant four-bar mechanisms for compliant-segment motion generation

Abstract: Compliant four-bar mechanisms treated in previous works consisted of at least one rigid moving link, and such mechanisms synthesized for motion generation tasks have always comprised a rigid coupler link, bearing with the conventional definition of motion generation for rigid-link mechanisms. This paper introduces a new task called compliant-segment motion generation where the coupler is a flexible segment and requires a prescribed shape change along with a rigid-body motion. The paper presents a systematic procedure for synthesis of single-loop compliant mechanisms with no moving rigid-links for compliant-segment motion generation task. Such compliant mechanisms have potential applications in adaptive structures. The synthesis method presented involves an atypical inverse elastica problem that is not reported in the literature. This inverse problem is solved by extending the loop-closure equation used in the synthesis of rigid-links to the flexible segments, and then combining it with elastic equilibrium equation in an optimization scheme. The method is illustrated by a numerical example.

Topology optimization of compliant mechanisms with strength considerations

Abstract: Multicriteria formulations that have been reported previously in topology design of compliant mechanisms address flexibility and stiffness issues simultaneously and aim to attain an optimal balance between these two conflicting attributes. Such techniques are successful in indirectly controlling the local stress levels by constraining the input displacement. Individual control on the conflicting objectives is often difficult to achieve with these flexibility-stiffness formulations. Resultant topologies may sometimes be overly stiff, and there is no guarantee against failure. Local stresses may exceed the permissible yield strength of the constituting material in such designs. In this article, local failure conditions relating to stress constraints are incorporated in topology optimization algorithms to obtain compliant and strong designs. Quality functions are employed to impose stress constraints on retained material, ignoring nonexisting regions in the design domain. Stress constraints are further relax...

A Pseudo-Rigid-Body Model for Initially-Curved Pinned-Pinned Segments Used in Compliant Mechanisms

Abstract: The pseudo-rigid-body model concept allows compliant mechanisms to be analyzed using well-known rigid-body kinematics. This paper presents a pseudo-rigid-body model for initially curved pinned-pinned segments that undergo large, nonlinear deflections. The model approximates the segment as three rigid members joined by pin joints. Torsional springs placed at the joints model the segment's stiffness. This model has been validated by fabricating several such segments from a variety of different materials. Testing of the force-deflection behavior of these segments verified the accuracy of the model.

Two-stage compliant microleverage mechanism optimization in a resonant accelerometer

Abstract: Compliant microleverage mechanisms can be used in micro-electro-mechanical systems (MEMS) to transfer an input force/displacement to an output to achieve mechanical/geometrical advantages. By stacking multiple stages of microlevers together, a compound microleverage mechanism is obtained with a higher amplification factor. This paper presents the analysis and optimization of a two-stage microleverage mechanism in a resonant output micro-accelerometer for force amplification. It is found that the compliance of the two-stage mechanism needs to be appropriately distributed in order for both stages to have the desired amplification effect.

Technical Briefs A Pseudo-Rigid-Body Model for Initially-Curved Pinned-Pinned Segments Used in Compliant Mechanisms

Abstract: The pseudo-rigid-body model concept allows compliant mechanisms to be analyzed using well-known rigid-body kinematics. This paper presents a pseudo-rigid-body model for initially curved pinned-pinned segments that undergo large, nonlinear deflections. The model approximates the segment as three rigid members joined by pin joints. Torsional springs placed at the joints model the segment’s stiffness. This model has been validated by fabricating several such segments from a variety of different materials. Testing of the force-deflection behavior of these segments verified the accuracy of the model. @DOI: 10.1115/1.1376396#

Single-stage microleverage mechanism optimization in a resonant accelerometer

Abstract: Microleverage mechanisms have potentially wide applications in Micro-Electro-Mechanical Systems (MEMS) for achieving mechanical or geometrical advantages. Constrained by micro-fabrication technology, microleverage mechanisms are formed by planar flexures and referred to as compliant mechanisms. In this paper, the analysis and optimization of a single-stage compliant microleverage mechanism is presented, with double-ended tuning fork (DETF) as the output system in a resonant accelerometer to address design issues. It is found that the axial and rotational spring constants of the output system can significantly influence the amplification factor and need to match those of a pivot (with high axial spring constant and low rotational spring constant being desirable) in order to achieve maximum force amplification. This compliance-match theory is very important for the design of both single-stage and multiple-stage microleverage mechanisms.

Compliant bistable micromechanism

Abstract: A method for designing and optimnizing compliant mechanisms is provided, in addition to bistable compliant mechanism designs. According to the method, a selected compliant structure may be modeled analytically, and the characteristics of the analytical model may be optimized. Multiple recursive optimization algorithms may be used, for example, to determine the general location of a global optimum, and then to determine the values of the analytical model characteristics that obtain the global optimum or a feasible configuration for the selected compliant structure. Geometric characteristics of the selected compliant structure may be derived from the values of the analytical model characteristics. Bistable compliant designs may have a shuttle disposed between a pair of base members. The shuttle (20) may be linked to the base members (22, 24) by a pair of legs (30, 32), via flexural pivots. The base members may have cantilevered mounting beams to create deformable mounts that receive and store potential energy. The stable configurations are those in which the stored potential energy is at a relative minimum.

Delta3: design and control of a flexure hinge mechanism

Abstract: In the fields of micro positioning, micromanipulation and micro machining, the required motion precision is continuously increasing. The demand also increases for high dynamic performances (large bandwidth, high closed loop stiffness.). In many cases an inappropriate mechanical structure prevents to achieve these objectives. For example backlash or friction have to be reduced as much as possible. In this paper, we propose backlash-free and friction-free manipulators using flexure hinges and direct drive actuators. A three degrees of freedom (dof) parallel robot (X, Y, Z) that is a transposition in a flexible structure of the Delta robot kinematics is presented. We focus on the design and control of the robot. A simple dynamic model is proposed and compared with measurements. The system is characterized and we propose solutions to improve performances. These solutions are tested on a linear stage.

Large deformation behavior of compliant mechanisms

Abstract: This paper presents a non-linear formulation for size and shape ∗ optimization of compliant mechanisms using tapered beam elements. Designs based on linear and nonlinear formulations are compared using a stroke amplification mechanism example. Also, the scaling effect of the compliant mechanism is investigated.

Convex analysis for topology optimization of compliant mechanisms

Abstract: This paper analyses the convexity of the problem formulations for topological optimization of compliant mechanisms. In this context, a ground structure is assumed to consist of membranes with variable thickness or trusses with variable cross-sectional area. It is proven that the objective function of maximum mechanical or geometrical advantage may not be convex even though the constraints for the problem formulations give rise to a convex set. The constraints include volumetric constraint and a bound on input displacement. The nonconvex objective functions are shown analytically with two examples using truss elements. Also, it is illustrated numerically with an example using bilinear quadrilateral elements. It is concluded that nonconvex objective functions also attribute to difficulties in arriving at the globally optimal topology of compliant mechanisms, in addition to the number of design variables and constraints. As the problem is more complicated, the solution of the problem requires robust and reliable optimization techniques.

Predicting the Effects of Dimensional and Material Property Variations in Micro Compliant Mechanisms

Abstract: PREDICTING THE EFFECTS OF DIMENSIONAL AND MATERIAL PROPERTY VARIATIONS IN COMPLIANT MECHANISMS Jonathan W. Wittwer Department of Mechanical Engineering Master of Science Surface micromachining of micro-electro-mechanical systems (MEMS), like all other fabrication processes, has inherent variation that leads to uncertain material and dimensional parameters. To obtain accurate and reliable predictions of mechanism behavior, the effects if these variations need to be analyzed. This thesis expands already existing tolerance and uncertainty analysis methods to apply to micro compliant mechanisms. For simple compliant members, explicit equations can be used in uncertainty analysis. However, for a nonlinear implicit system of equations, the direct linearization method may be used to obtain sensitivities of output parameters to small changes in known variables. This is done by including static equilibrium equations and pseudo-rigid-body model relationships with the kinematic vector loop equations. Examples are used to show a comparison of this method to other deterministic and probabilistic methods and finite element analysis.

Compliant apparatus and method

Abstract: A method for designing and optimizing compliant mechanisms is provided, in addition to bistable compliant mechanism designs. According to the method, a selected compliant structure may be modeled analytically, and the characteristics of the analytical model may be optimized. Multiple recursive optimization algorithms may be used, for example, to determine the general location of a global optimum, and then to determine the values of the analytical model characteristics that obtain the global optimum or a feasible configuration for the selected compliant structure. Geometric characteristics of the selected compliant structure may be derived from the values of the analytical model characteristics. Bistable compliant designs may have a shuttle disposed between a pair of base members. The shuttle (20) may be linked to the base members (22, 24) by a pair of legs (30, 32), via flexural pivots. The base members may have cantilevered mounting beams to create deformable mounts that receive and store potential energy. The stable configurations are those in which the stored potential energy is at a relative minimum.

An investigation of compliant micro-half-pantographs using the pseudorigid body model

Abstract: Many microelectromechanical systems (MEMS) require a mechanism that amplifies motion. This article investigates the use of the pseudorigid body model (PRBM) to design fully compliant micro-half-pantographs for this purpose. The results demonstrate the ability to amplify motion with a compliant mechanism with no assembly or pin joints. The PRBM was used to develop equations for input-output displacement, force-deflection, and maximum nominal stress-deflection predictions. Predictions compared favorably to finite-element and experimental results. This work emphasizes further that the traditional method of trial-and-error design can be substituted by the pseudorigid body model approach. *Communicated by B. Gilmore.

Compliant parallel robot with 6 DOF

Abstract: In this paper a patented parallel structure will be presented in which conventional bearings are replaced by flexure hinges made of pseudo-elastic shape memory alloy. The robot has six degrees of freedom and was developed for micro assembly tasks. Laboratory tests made with the robot using conventional bearings have shown that the repeatability was only a couple of 1/100 mm instead of the theoretical resolution of the platform of < 1 micrometers . Especially the slip-stick effects of the bearings decreased the positional accuracy. Because flexure hinges gain their mobility only by a deformation of matter, no backlash, friction and slip-stick-effects exist in flexure hinges. For this reason the repeatability of robots can be increased by using flexure hinges. Joints with different degrees of freedom had to be replaced in the structure. This has been done by a combination of flexure hinges with one rotational degree of freedom. FEM simulations for different designs of the hinges have been made to calculate the possible maximal angular deflections. The assumed maximal deflection of 20 degree(s) of the hinges restricts the workspace of the robot to 28x28 mm with no additional rotation of the working platform. The deviations between the kinematic behavior of the compliant parallel mechanism and its rigid body model can be simulated with the FEM.

Techniques to suppress intermediate density in topology optimization of compliant mechanisms

Abstract: Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Such practice prevails because large-scale discrete 0–1 mathematical programming is not generally available. Although the relaxed problems become tractable, they may cause the appearance of intermediate density in the optimum topologies, especially those of structures and compliant mechanisms. Various penalty schemes have been proposed to suppress the intermediate density. Most of the past works assumed that the same penalty schemes could be effectively applied to both problems of stiffest structure design and compliant mechanism design. Differences in nature between the problems are generally neglected. This work distinguished the two problems, and observed that complaint mechanism (CM) problem does not suffer intermediate density as seriously as minimum compliance (MC) problem does. Besides allocating more material, explicit and implicit penalties were pursued to suppress intermediate density. To ensure mesh-independence and not to complicate the nonconvex objective function in CM problem, a new technique using a constraint of explicit penalty with variable bound is proposed to suppress intermediate density in topology optimization of compliant mechanisms. Together with a perimeter constraint, the new technique is also applied to MC problem.

Compliant removable battery support

Abstract: This invention includes a compliant removable battery support for configuring a pocket to accommodate devices of varying size. In one preferred embodiment, a charger is provided having a pocket capable of receiving an electronic apparatus, like a cellular phone for instance. The electronic apparatus is capable of having different sized batteries attached. The pocket size is adjusted by inserting the compliant removable battery support into a guide slot that corresponds to the desired battery size. In a preferred embodiment, the compliant removable battery support has a compliant member that comprises a four bar compliance mechanism. The four bar compliant mechanism provides more robust coupling between the compliant removable battery support and the charger in that the deflection stress is distributed across the compliant mechanism.

Compliant MicroTransmissions for Rectilinear Electrothermal Actuators

Abstract: This paper reports on synthesized designs of compliant microstructures used to modify the force-displacement relationships of electrothermal actuators. The design process uses truss elements and involves topology synthesis and dimensional optimization in a two-stage approach. In order to accommodate buckling constraints, it limits the stress on beam segments. Measurements of devices fabricated from 11.5 µm thick p++ Si and 55 µm electroplated Ni as structural materials match theoretical predictions within 20%. Rectilinear non-resonant displacements up to 100 µm and amplification factors >20x are obtained.

Zum Bewegungsverhalten nachgiebiger Mechanismen

Abstract: Compliant mechanisms bear a resemblance to rigid-body mechanisms but equally have many differences in their behaviour and in their properties. The motion behaviour of compliant mechanisms depends on the structure and geometrical form of the rigid and elastical parts (links and joints) and on the material parameters. Also the modes of input and output of forces and motions have a great influence on the performance of function. The elastic compliance of the mechanism is the basis of its mobility.

Development of Commercially Viable Compliant Mechanisms Using the Pseudo-Rigid-Body Model: Case Studies of Parallel Mechanisms

Abstract: 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.

Study of the degrees of freedom equations in the compliant mechanism design

Abstract: Compliant mechanisms gain some or all their motion from the deflections of flexible members. Preliminary studies demonstrated some advantages over their rigid-body counterparts: versatility, ease of manufacturing, ergonomics, and overload protection, better performance and reliability for their flexible nature. Their kinematic approach provides the synthesis of a conventional rigid mechanism. The degrees of freedom concept is used to help obtain a preliminary design which may then be optimized, and defines a flexure number concept for characterizing flexible-link mechanism. The nomenclature, classification and abstraction for the components involved in compliant mechanism design are shown. The paper describes the evolution of fundamental well-known degrees of freedom equations, and their comparison is discussed. Practical example applications of different formulas are presented, and the advantages and disadvantages are debated according to the conception, capacity and control of new compliant mechanisms.