Distributed Shape Optimization of Compliant Mechanisms Using Intrinsic Functions

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Chao-Chieh Lan ◽  
Yung-Jen Cheng
Keyword(s):  
Stress Concentration ◽  
Shooting Method ◽  
Abrupt Change ◽  
Compliant Mechanisms ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Design Method ◽  
Geometry Optimization ◽  
Systematic Design ◽  
Body Type

A compliant mechanism transmits motion and force by deformation of its flexible members. It has no relative moving parts and thus involves no wear, lubrication, noise, or backlash. Compliant mechanisms aim to maximize flexibility while maintaining sufficient stiffness so that satisfactory output motion may be achieved. When designing compliant mechanisms, the resulting shapes sometimes lead to rigid-body type linkages where compliance and rotation is lumped at a few flexural pivots. These flexural pivots are prone to stress concentration and thus limit compliant mechanisms to applications that only require small-deflected motion. To overcome this problem, a systematic design method is presented to synthesize the shape of a compliant mechanism so that compliance is distributed more uniformly over the mechanism. With a selected topology and load conditions, this method characterizes the free geometric shape of a compliant segment by its rotation and thickness functions. These two are referred as intrinsic functions and they describe the shape continuously within the segment so there is no abrupt change in geometry. Optimization problems can be conveniently formulated with cusps and intersecting loops naturally circumvented. To facilitate the optimization process, a numerical algorithm based on the generalized shooting method will be presented to solve for the deflected shape. Illustrative examples will demonstrate that through the proposed design method, compliant mechanisms with distributed compliance will lessen stress concentration so they are more robust and have a larger deflected range. It is expected that the method can be applied to design compliant mechanisms for a wide variety of applications.

Distributed Shape Optimization of Compliant Mechanisms Using Intrinsic Functions

2007 ◽  
Author(s):  
Chao-Chieh Lan ◽  
Yung-Jen Cheng
Keyword(s):  
Stress Concentration ◽  
Shooting Method ◽  
Abrupt Change ◽  
Compliant Mechanisms ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Design Method ◽  
Geometry Optimization ◽  
Systematic Design ◽  
Body Type

A compliant mechanism transmits motion and force by deformation of its flexible members. It has no relative moving parts and thus involves no wear, lubrication, noise, and backlash. Compliant mechanisms aims to maximize flexibility while maintaining sufficient stiffness so that satisfactory output motion can be achieved. When designing compliant mechanisms, the resulting shapes sometimes lead to rigid-body type linkages where compliance and rotation is lumped at a few flexural pivots. These flexural pivots are prone to stress concentration and thus limit compliant mechanisms to applications that only require small-deflected motion. To overcome this problem, a systematic design method is presented to synthesize the shape of a compliant mechanism so that compliance is distributed more uniformly over the mechanism. With a selected topology and load conditions, this method characterizes the free geometric shape of a compliant segment by its rotation and thickness functions. These two are referred as intrinsic functions and they describe the shape continuously within the segment so there is no abrupt change in geometry. Optimization problems can be conveniently formulated with cusps and intersecting loops naturally circumvented. To facilitate the optimization process, a numerical algorithm based on the generalized shooting method will be presented to solve for the deflected shape. Illustrative examples will demonstrate that through the proposed design method, compliant mechanisms with distributed compliance will lessen stress concentration so they can be more robust and have larger deflected range. It is expected that the method can be applied to design compliant mechanisms that have a wide variety of applications from precision instruments to biomedical devices.

Optimum Design of a Compliant Uniaxial Accelerometer

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Simon Desrochers ◽  
Damiano Pasini ◽  
Jorge Angeles
Keyword(s):  
Stress Concentration ◽  
Optimum Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Pareto Frontier ◽  
Cad Model ◽  
Multi Objective Optimization ◽  
Design Objective ◽  
Multi Objective ◽  
Pareto Plot

This work focuses on the multi-objective optimization of a compliant-mechanism accelerometer. The design objective is to maximize the sensitivity of the accelerometer in its sensing direction, while minimizing its sensitivity in all other directions. In addition, this work proposes a novel compliant hinge intended to reduce the stress concentration in compliant mechanisms. The paper starts with a brief description of the new compliant hinge, the Lamé-shaped hinge, followed by the formulation of the aposteriori multi-objective optimization of the compliant accelerometer. By using the normalized constrained method, an even distribution of the Pareto frontier is found. The paper also provides several optimum solutions on a Pareto plot, as well as the CAD model of the selected solution.

An Ants-Search Based Method for Optimum Synthesis of Compliant Mechanisms

2016 ◽  
Author(s):  
Nadim Diab ◽  
Ahmad Smaili
Keyword(s):  
Swarm Intelligence ◽  
Smart Materials ◽  
Compliant Mechanisms ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Topology Design ◽  
Micro Electro Mechanical Systems ◽  
Amplification Ratio ◽  
The Past ◽  
Optimum Synthesis

Compliant mechanisms are widely used in the industry and have gained more popularity in the past few decades with the advancements in smart materials and micro-electro mechanical systems (MEMS). Compliant mechanisms offer huge advantages over the classical rigid linkages due to their flexible behavior. Such flexible mechanisms reduce production time and cost especially that they eliminate the need of joints that can get pretty hectic especially at micro level manufacturing and assembly. By avoiding multi-joints in the design and their consequent clearances, a compliant mechanism can offer higher precision over its rigid counterpart. However, these advantages come with a price; compliant mechanisms are more challenging in terms of design and analysis. Many compliant mechanisms are designed to undergo relatively large deflections which in turn impose geometric nonlinearities. In the past, many compliant designs were based on intuition, experience, and trial and error. Later on, many theories developed to assist in designing and analyzing compliant mechanisms before proceeding with the manufacturing phase. This paper covers topology optimization of compliant structures using beam elements. The swarm intelligence technique known as Ant Search (AS) is used to find the optimum design that satisfies the required mechanism performance. A case study that involves the topology design of a miniature compliant displacement amplifier is presented and results are compared with the finite element solver ANSYS. The optimized topology mechanism produced a much larger amplification ratio as compared to that presented in literature. Results produced show the high potential of swarm intelligence and AS in particular at solving multi-disciplinary optimization problems that should not be limited to designs that involve physical paths.

A Two-Stage Design Method for Compliant Mechanisms Having Specified Non-Linear Output Paths

2006 ◽  
Author(s):  
Masakazu Kobayashi ◽  
Hiroshi Yamakawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Two Stage ◽  
Traditional Methods ◽  
Stage Design ◽  
Second Stage ◽  
Additional Constraints

Compliant mechanisms generated by traditional topology optimization methods have linear output response, and it is difficult for traditional methods to implement mechanisms having non-linear output responses, such as nonlinear deformation or path. To design a compliant mechanism having a specified nonlinear output path, a two-stage design method based on topology and shape optimization is constructed here. In the first stage, topology optimization generates an initial and conceptual compliant mechanism based on ordinary design conditions, with “additional” constraints that are used to control the output path at the second stage. In the second stage, an initial model for the shape optimization is created, based on the result of the topology optimization, and the additional constraints are replaced by spring elements. The shape optimization is then executed, to generate a detailed shape of the compliant mechanism having the desired output path. In this stage, parameters that represent the outer shape of the compliant mechanism and the properties of spring elements are used as design variables in the shape optimization. In addition to configuration of the specified output path, executing the shape optimization after the topology optimization also makes it possible to consider the stress concentration and large displacement effects. This is an advantage offered by the proposed method, since it is difficult for traditional methods to consider these aspects, due to inherent limitations of topology optimization.

An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms

2005 ◽  
Vol 128 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Charles J. Kim ◽  
Sridhar Kota ◽  
Yong-Mo Moon
Keyword(s):  
Conceptual Design ◽  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometry Optimization ◽  
Building Blocks ◽  
Cross Sectional ◽  
Rigid Body Model ◽  
Cross Sectional Size

As with conventional mechanisms, the conceptual design of compliant mechanisms is a blend of art and science. It is generally performed using one of two methods: topology optimization or the pseudo-rigid-body model. In this paper, we present a new conceptual design methodology which utilizes a building block approach for compliant mechanisms performing displacement amplification/attenuation. This approach provides an interactive, intuitive, and systematic methodology for generating initial compliant mechanism designs. The instant center is used as a tool to construct the building blocks. The compliant four-bar building block and the compliant dyad building block are presented as base mechanisms for the conceptual design. It is found that it is always possible to obtain a solution for the geometric advantage problem with an appropriate combination of these building blocks. In a building block synthesis, a problem is first evaluated to determine if any known building blocks can satisfy the design specifications. If there are none, the problem is decomposed to a number of sub-problems which may be solved with the building blocks. In this paper, the problem is decomposed by selecting a point in the design space where the output of the first building block coincides with the second building block. Two quantities are presented as tools to aid in the determination of the mechanism's geometry – (i) an index relating the geometric advantage of individual building blocks to the target geometric advantage and (ii) the error in the geometric advantage predicted by instant centers compared to the calculated value from FEA. These quantities guide the user in the selection of the location of nodes of the mechanism. Determination of specific cross-sectional size is reserved for subsequent optimization. An example problem is provided to demonstrate the methodology's capacity to obtain good initial designs in a straightforward manner. A size and geometry optimization is performed to demonstrate the viability of the design.

Synthesis of Planar Compliant Mechanisms

2007 ◽  
Author(s):  
Tewodros E. Mengesha ◽  
Kerr-Jia Lu
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Computing Time ◽  
Structural Connectivity ◽  
Solution Space ◽  
Repair Process ◽  
Discrete Topology ◽  
Topology Optimization Problem ◽  
Path Representation

This paper introduces a compliant mechanism design method that guarantees structural connectivity and planarity of the resulting design. The structural connectivity is ensured by a path-representation, while a coin-optimization process is introduced to verify the planarity of the design. A non-planar design can be “planarized” by a coin-repair process, thus all non-planar designs can be effectively excluded from the solution space. The discrete topology optimization problem is incorporated in a genetic algorithm. The resulting topology is further processed through size and shape optimization for improved stress distribution. The results from two benchmarking design examples showed that the proposed method is capable of producing planar mechanisms in a reasonable amount of computing time. The presented design method will be incorporated into an on-going research in the design of biomimetic wings for Micro-Aerial Vehicles (MAVs).

scholarly journals Integrated Multi-Step Design Method for Practical and Sophisticated Compliant Mechanisms Combining Topology and Shape Optimizations

2007 ◽  
Vol 19 (2) ◽  
pp. 141-147
Author(s):  
Masakazu Kobayashi ◽  
◽  
Shinji Nishiwaki ◽  
Hiroshi Yamakawa ◽  
◽  
...  
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Traditional Methods ◽  
Second Stage ◽  
Spring Element ◽  
Design Variables ◽  
Additional Constraints

Compliant mechanisms designed by traditional topology optimization have a linear output response, and it is difficult for traditional methods to implement mechanisms having nonlinear output responses, such as nonlinear deformation or path. To design a compliant mechanism having a specified nonlinear output path, we propose a two-stage design method based on topology and shape optimizations. In the first stage, topology optimization generates an initial conceptual compliant mechanism based on ordinary design conditions, with “additional” constraints used to control the output path in the second stage. In the second stage, an initial model for the shape optimization is created, based on the result of the topology optimization, and additional constraints are replaced by spring elements. The shape optimization is then executed, to generate the detailed shape of the compliant mechanism having the desired output path. At this stage, parameters that represent the outer shape of the compliant mechanism and of spring element properties are used as design variables in the shape optimization. In addition to configuring the specified output path, executing the shape optimization after the topology optimization also makes it possible to consider the stress concentration and large displacement effects. This is an advantage offered by the proposed method, because it is difficult for traditional methods to consider these aspects, due to inherent limitations of topology optimization.

Multi-Stage Design Method for Practical Compliant Mechanisms by Topology and Shape Optimizations and Shape Conversion Method Utilizing Level Set Method

2008 ◽  
Author(s):  
Masakazu Kobayashi ◽  
Shinji Nishiwaki ◽  
Masatake Higashi
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Stage Design ◽  
Conversion Method ◽  
Multi Stage

This paper proposes a multi-stage design method for a design of practical compliant mechanisms. The proposed method consists of topology and shape optimizations and a shape conversion method that incorporates two optimizations. In the 1st stage, an initial and conceptual compliant mechanism is created by topology optimization. In the 2nd stage, an initial model of shape optimization is created from the result of topology optimization by the shape conversion method based on the level set method. In the 3rd stage, the shape optimization yields a detailed shape of the compliant mechanism by considering non-linear deformation and stress concentration. Execution of the shape optimization after the topology optimization enables evaluation of stress concentration and large deformation effect that are normally difficult for the traditional topology optimization. On the other side, the precise conversion from the model by topology optimization to the one for the shape optimization becomes possible by the shape conversion method that is utilizing the level set method. Using the proposed multi-stage method, a practical compliant mechanism can be designed with the designer’s minimum efforts that are indications of design conditions of the topology and shape optimizations and several parameters and threshold values of the shape conversion method.

A Material Selection and Design Method for Multi-Constraint Compliant Mechanisms

2016 ◽  
Author(s):  
John Sessions ◽  
Nathan Pehrson ◽  
Kyler Tolman ◽  
Jonathan Erickson ◽  
David Fullwood ◽  
...  
Keyword(s):  
Performance Metrics ◽  
Compliant Mechanisms ◽  
Material Selection ◽  
Compliant Mechanism ◽  
Design Method ◽  
Solar Array ◽  
Multiple Constraints ◽  
Systematic Method ◽  
Electrically Conductive ◽  
Compliant Mechanism Design

One of the challenges often encountered in compliant mechanism design is managing material selection given the need to meet multiple constraints. Many methods have been offered previously to systematically facilitate that decision process. However, these methods struggle to incorporate a systematic method for material selection in multi-functional compliant mechanisms. This work seeks to address this gap by generically implementing a new Ashby-based material selection and design method for compliant mechanisms with multi constraint design criteria. To help demonstrate the method, the design of an electrically conductive lamina emergent torsion (LET) joint used for a back-packable solar array is explored. The methodology described here can be used to create other compliant mechanism performance metrics to address the design of specific compliant mechanisms.

Design of a Beam-Based Variable Stiffness Actuator via Shape Optimization in a CAD/CAE Environment

2018 ◽  
Author(s):  
Pietro Bilancia ◽  
Giovanni Berselli ◽  
Umberto Scarcia ◽  
Gianluca Palli
Keyword(s):  
Shape Optimization ◽  
Position Control ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Variable Stiffness ◽  
Industrial Robots ◽  
Physical Interaction ◽  
Precise Position ◽  
Trivial Shape

Industrial robots are commonly designed to be very fast and stiff in order to achieve extremely precise position control capabilities. Nonetheless, high speeds and power do not allow for a safe physical interaction between robots and humans. With the exception of the latest generation lightweight arms, purposely design for human-robot collaborative tasks, safety devices shall be employed when workers enter the robots workspace, in order to reduce the chances of injuries. In this context, Variable Stiffness Actuators (VSA) potentially represent an effective solution for increasing robot safety. In light of this consideration, the present paper describes the design optimization of a VSA architecture previously proposed by the authors. In this novel embodiment, the VSA can achieve stiffness modulation via the use of a pair of compliant mechanisms with distributed compliance, which act as nonlinear springs with proper torque-deflection characteristic. Such elastic elements are composed of slender beams whose neutral axis is described by a spline curve with non-trivial shape. The beam geometry is determined by leveraging on a CAD/CAE framework allowing for the shape optimization of complex flexures. The design method makes use of the modeling and simulation capabilities of a parametric CAD software seamlessly connected to a FEM tool (i.e. Ansys Workbench). For validation purposes, proof-concept 3D printed prototypes of both non-linear elastic element and overall VSA are finally produced and tested. Experimental results fully confirm that the compliant mechanism behaves as expected.

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