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.

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.

Multiobjective Topology Extraction of the Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 1941-1948
Author(s):  
Zhao Kun Li ◽  
Hua Mei Bian ◽  
Li Juan Shi ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Threshold Value ◽  
Jump Discontinuity ◽  
Engineering Practice ◽  
Distribution Method ◽  
Black And White ◽  
Design Variables

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.

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.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Stress Constraint ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical, or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary, and every design cell is either solid or void to prevent gray cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Conduct Sensitivity Analysis

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

Topology and Size–Shape Optimization of an Adaptive Compliant Gripper with High Mechanical Advantage for Grasping Irregular Objects

Robotica ◽  
2019 ◽  
Vol 37 (08) ◽  
pp. 1383-1400 ◽  
Author(s):  
Chih-Hsing Liu ◽  
Chen-Hua Chiu ◽  
Mao-Cheng Hsu ◽  
Yang Chen ◽  
Yen-Pin Chiang
Keyword(s):  
Topology Optimization ◽  
Optimal Design ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Experimental Studies ◽  
Design Procedure ◽  
Optimization Methods ◽  
Optimization Method ◽  
Mechanical Advantage

SummaryThis study presents an optimal design procedure including topology optimization and size–shape optimization methods to maximize mechanical advantage (which is defined as the ratio of output force to input force) of the synthesized compliant mechanism. The formulation of the topology optimization method to design compliant mechanisms with multiple output ports is presented. The topology-optimized result is used as the initial design domain for subsequent size–shape optimization process. The proposed optimal design procedure is used to synthesize an adaptive compliant gripper with high mechanical advantage. The proposed gripper is a monolithic two-finger design and is prototyped using silicon rubber. Experimental studies including mechanical advantage test, object grasping test, and payload test are carried out to evaluate the design. The results show that the proposed adaptive complaint gripper assembly can effectively grasp irregular objects up to 2.7 kg.

L-System-Generated Topology Optimization of Compliant Mechanisms Using Graph-Based Interpretation

2018 ◽  
Author(s):  
Brent R. Bielefeldt ◽  
Darren J. Hartl ◽  
Ergun Akleman
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Level Set Methods ◽  
Optimization Techniques ◽  
L System ◽  
Design Variables ◽  
System L ◽  
Reconfigurable Structures

Traditional topology optimization techniques, such as density-based and level set methods, have proven successful in identifying potential design configurations but suffer from rapidly increasing design space dimensionality and convergence to local minima. A heuristic alternative to these approaches couples a genetic algorithm with a Lindenmayer System (L-System), which encodes design variables and governs the development of the structure when coupled with some sort of interpreter. This work discusses the development of a graph-based interpretation scheme referred to as Spatial Interpretation for the Development of Reconfigurable Structures (SPIDRS). This framework allows for the effective exploration of the design space using a limited number of design variables. The theory and implementation of this method are detailed, and a compliant mechanism case study is presented to demonstrate the ability of SPIDRS to generate structures capable of achieving multiple design goals.

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.

scholarly journals Topology Optimization of Multi-Materials Compliant Mechanisms

2021 ◽  
Vol 11 (9) ◽  
pp. 3828
Author(s):  
Wenjie Ge ◽  
Xin Kou
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Optimization Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Method ◽  
Least Square ◽  
Convergent Method ◽  
Material Conditions ◽  
Moving Asymptotes

In this article, a design method of multi-material compliant mechanism is studied. Material distribution with different elastic modulus is used to meet the rigid and flexible requirements of compliant mechanism at the same time. The solid isotropic material with penalization (SIMP) model is used to parameterize the design domain. The expressions for the stiffness matrix and equivalent elastic modulus under multi-material conditions are proposed. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function, and the topology optimization design model of multi-material compliant mechanism is established. The oversaturation problem in the volume constraint is solved by pre-setting the priority of each material, and the globally convergent method of moving asymptotes (GCMMA) is used to solve the problem. Widely studied numerical examples are conducted, which demonstrate the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document