scholarly journals Level set-based topology optimisation of a compliant mechanism design using mathematical programming

2011 ◽  
Vol 2 (1) ◽  
pp. 91-98 ◽  
Author(s):  
M. Otomori ◽  
T. Yamada ◽  
K. Izui ◽  
S. Nishiwaki
Keyword(s):  
Mathematical Programming ◽  
Mechanism Design ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Topology Optimisation ◽  
Structural Optimisation ◽  
Level Set Function ◽  
Set Function ◽  
Compliant Mechanism Design

Abstract. We propose a structural optimisation method, based on the level set method and using mathematical programming such as the method of moving asymptotes (MMA), which we apply to the design of compliant mechanisms. A compliant mechanism is a monolithic joint-free mechanism designed to be flexible to obtain a specified motion. In the design of compliant mechanisms, several requirements such as the direction of the deformation and stress concentrations must be considered to obtain the specified mechanical function. Topology optimisation, the most flexible type of structural optimisation, has been successfully used as a design optimisation method for compliant mechanisms, but the utility of topology optimisation results is often spoiled by a plethora of impractical designs such as structures containing grayscale areas. Level set-based topology optimisation methods are immune to the problem of grayscales since the boundaries of the optimal configuration are implicitly represented using the level set function. The proposed method updates the level set function using mathematical programming to facilitate the treatment of constraint functionals. To verify its capability, we apply our method to compliant mechanism design problems that include displacement constraints and stress constraints.

Topology Optimization of Compliant Mechanisms Using Level Set Method without Re-Initialization

2011 ◽  
Vol 130-134 ◽  
pp. 3076-3082 ◽  
Author(s):  
Ben Liang Zhu ◽  
Xian Min Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Signed Distance Function ◽  
Optimal Process ◽  
Level Set Function ◽  
New Formulation ◽  
Set Function

In this paper, a new level set method for topology optimization of compliant mechanisms is presented. A new formulation is developed and built in the traditional level set method to force the level set function to be close to a signed distance function during the optimal process. The validity of the method is illustrated by topology optimization of a widely studied compliant mechanism.

A Well-Behaved Revolute Flexure Joint for Compliant Mechanism Design

1999 ◽  
Vol 121 (3) ◽  
pp. 424-429 ◽  
Author(s):  
M. Goldfarb ◽  
J. E. Speich
Keyword(s):  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Bending Properties ◽  
Thin Beam ◽  
Primary Mechanism ◽  
Joint Characteristics ◽  
Flexure Joints ◽  
Compliant Mechanism Design ◽  
Torsional Properties

This paper describes the design of a unique revolute flexure joint, called a split-tube flexure, that enables (lumped compliance) compliant mechanism design with a considerably larger range-of-motion than a conventional thin beam flexure, and additionally provides significantly better multi-axis revolute joint characteristics. Conventional flexure joints utilize bending as the primary mechanism of deformation. In contrast, the split-tube flexure joint incorporates torsion as the primary mode of deformation, and contrasts the torsional properties of a thin-walled open-section member with the bending properties of that member to obtain desirable joint behavior. The development of this joint enables the development of compliant mechanisms that are quite compliant along kinematic axes, extremely stiff along structural axes, and are capable of kinematically well-behaved large motions.

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Structural Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Equilibrium Equations ◽  
Thermal Actuators ◽  
Level Set Function ◽  
Initialization Scheme ◽  
Set Function

Compliant mechanisms are designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in micro-electromechanical systems by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated or are subjected to an electric potential. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the finite element method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Utilizing a Classification Scheme to Facilitate Rigid-Body Replacement for Compliant Mechanism Design

2010 ◽  
Author(s):  
Brian M. Olsen ◽  
Yanal Issac ◽  
Larry L. Howell ◽  
Spencer P. Magleby
Keyword(s):  
Rigid Body ◽  
Mechanism Design ◽  
Classification Scheme ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
The Other ◽  
Design Approach ◽  
Compliant Mechanism Design

The knowledge related to the synthesis and analysis of compliant mechanisms continues to grow and mature. Building on this growth, a classification scheme has been established to categorize compliant elements and mechanisms in a manner that engineers can incorporate compliance into their designs. This paper demonstrates a design approach engineers can use to convert an existing rigid-body mechanism into a compliant mechanism by using an established classification scheme. This approach proposes two possible techniques that use rigid-body replacement synthesis in conjunction with a compliant mechanism classification scheme. One technique replaces rigid-body elements with a respective compliant element. The other technique replaces a complex rigid-body mechanism by decomposing the mechanism into simpler functions and then replacing a respective rigid-body mechanism with a compliant mechanism that has a similar functionality.

Shape Optimization Framework for the Path of the Primary Compliance Vector in Compliant Mechanisms

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Hylke Kooistra ◽  
Charles J. Kim ◽  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Mechanism Design ◽  
Deformation Mechanism ◽  
General Framework ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Framework ◽  
Kinematic Behavior ◽  
Curve Representation ◽  
Compliant Mechanism Design ◽  
Load Perturbations

Abstract The primary compliance vector (PCV) captures the dominant kinematic behavior of a compliant mechanism. Its trajectory describes large deformation mechanism behavior and can be integrated in an optimization objective in detailed compliant mechanism design. This paper presents a general framework for the optimization of the PCV path, the mechanism trajectory of lowest energy, using a unified stiffness characterization and piecewise curve representation. We present a meaningful objective formulation for the PCV path that evaluates path shape, location, orientation, and length independently and apply the framework to two design examples. The framework is useful for design of planar and shell compliant mechanisms that traverse a specified mechanism trajectory and that are insensitive to load perturbations.

Characteristic Deflection Domain for Various Compliant Segment Types, and its Importance in Compliant Mechanism Synthesis and Analysis

2014 ◽  
Author(s):  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Boundary Conditions ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Solution Process ◽  
Displacement Boundary ◽  
Fundamental Understanding ◽  
Rigid Body Model ◽  
Compliant Mechanism Design ◽  
Insight Into

Compliant mechanism design inherently requires certain specified displacement boundary conditions to be satisfied. Obtaining realistic solutions for such problem types often becomes a challenge as the number of displacement boundary condition specifications increases. Typically, related failures are attributed to the numerical nature of the solution process. Little attention has been given to the fundamental understanding of the deformation behavior of flexible continuum with respect to its limits of mobility or reach. This paper strives to provide an insight into this aspect of compliant mechanism design. To assist a designer with the specification of realistic and achievable requirements, the concept of characteristic deflection domain has been proposed in the past. This paper systematically develops the characteristic deflection domain for a variety of compliant segment types. The pseudo-rigid-body model (PRBM) representation is utilized for determining the lower and upper boundaries of the deflection domain. The paper further investigates the mobility characteristics of compliant mechanisms comprised of multiple segment types. Case studies are presented that help exemplify the use of the characteristic deflection domain plots. The results suggest that the number, type, and orientation of the compliant segments have a significant effect on the mobility of compliant mechanisms. Thus, care must be exercised by the designer when specifying free-choices/boundary conditions in compliant mechanisms synthesis and analysis.

scholarly journals Origami-like creases in sheet materials for compliant mechanism design

2013 ◽  
Vol 4 (2) ◽  
pp. 371-380 ◽  
Author(s):  
K. C. Francis ◽  
J. E. Blanch ◽  
S. P. Magleby ◽  
L. L. Howell
Keyword(s):  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Low Cost ◽  
Homogeneous Material ◽  
Paper Sheet ◽  
Initial State ◽  
Indirect Methods ◽  
Sheet Materials ◽  
Compliant Mechanism Design

Abstract. The purpose of this research is to evaluate the creasing of non-paper sheet materials, such as plastics and metals, to facilitate origami-based compliant mechanism design. Although it is anticipated that most origami-based design will result from surrogate folds (indirect methods of replacing the crease), it is valuable to provide information that may help in more direct approaches for origami-based design in materials other than paper. Planar sheets of homogeneous material are considered as they maintain the principles fundamental to origami (flat initial state, low cost, readily available). The reduced stiffness along the axis of the crease is an enabling characteristic of origami. Hence a metric based on the deformation of the crease compared to the deformation of the panels enables engineering materials to be evaluated based on their ability to achieve the "hinge-like" behavior observed in folded paper. Advantages of both high and low values of this metric are given. Testing results (hinge indexes, residual angles, localized hinge behavior and cyclic creasing to failure) are presented for various metals and polymers. This methodology and subsequent findings are provided to enable origami-based design of compliant mechanisms.

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

2008 ◽  
Author(s):  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Structural Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Equilibrium Equations ◽  
Micro Electro Mechanical Systems ◽  
Thermal Actuators ◽  
Level Set Function ◽  
Set Function

Compliant mechanisms are a new type of mechanism, designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in Micro-Electro Mechanical Systems (MEMS) by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the Finite Element Method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation and the level set method, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

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