Designing Distributed Compliant Mechanisms With Characteristic Stiffness

2007 ◽  
Author(s):  
Shikui Chen ◽  
Michael Yu Wang
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Model ◽  
Mechanism Optimization ◽  
Edge Problem ◽  
Geometric Boundary ◽  
Novel Method ◽  
New Formulation ◽  
Sharp Interfaces ◽  
Large Output

A novel method is proposed in this paper to address the cutting-edge problem of topology optimization of distributed compliant mechanisms, which requires the design to possess both large output displacements and evenly distributed compliance simultaneously. The design is represented by a level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. Existing techniques for eliminating de facto hinges in the design are reviewed. Further, the intrinsic deficiencies in the widely used “spring model” are discussed and a new formulation considering the “characteristic stiffness” of the mechanism is proposed. The proposed method is demonstrated with benchmark examples of compliant mechanism optimization. The result is a design with evenly distributed compliance and a more desirable characteristic, which uniquely distinguishes our method.

A Kinetoelastic Approach to Continuum Compliant Mechanism Optimization

2008 ◽  
Author(s):  
Michael Yu Wang
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Technique ◽  
State Equation ◽  
Rigid Bodies ◽  
Leaf Spring ◽  
Initial Development ◽  
Structure Topology ◽  
New Perspective ◽  
New Formulation

This paper presents a new approach to designing continuum compliant mechanisms—the kinetoelastic approach. We present a new formulation of the design problem, incorporating not only the kinematic function requirements of the mechanism but, more importantly, the compliance characteristics of the mechanism’s structure. In our kinetoelastic model, the kinematics of the compliant mechanism is defined on rigid-bodies of input/output ports and is related to a set of kinetoelastic factors of mechanism’s structure in a state equation of the mechanism defined by the elasticity theory. Central to defining the compliance characteristics of the mechanism is the mechanism eigensystem with principal eigen-stiffness or eigen-compliance. In this new perspective, we further apply the kinetoelastic model to the problem of designing compliant translational joints with a structure topology optimization technique. This application demonstrates the capability of the kinetoelastic approach in producing compliant designs with desirable compliance properties, such as in the leaf-spring type sliding joint as opposed to the notch-type joint. The paper represents an initial development towards a complete methodology for continuum compliant mechanism design.

Design of Crashworthy Structures With Controlled Energy Absorption in the Hybrid Cellular Automaton Framework

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Punit Bandi ◽  
James P. Schmiedeler ◽  
Andrés Tovar
Keyword(s):  
Energy Absorption ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Synthesis ◽  
Load Paths ◽  
Fully Stressed Design ◽  
Novel Method ◽  
The Given ◽  
Synthesis Approach

This work presents a novel method for designing crashworthy structures with controlled energy absorption based on the use of compliant mechanisms. This method helps in introducing flexibility at desired locations within the structure, which in turn reduces the peak force at the expense of a reasonable increase in intrusion. For this purpose, the given design domain is divided into two subdomains: flexible (FSD) and stiff (SSD) subdomains. The design in the flexible subdomain is governed by the compliant mechanism synthesis approach for which output ports are defined at the interface between the two subdomains. These output ports aid in defining potential load paths and help the user make better use of a given design space. The design in the stiff subdomain is governed by the principle of a fully stressed design for which material is distributed to achieve uniform energy distribution within the design space. Together, FSD and SSD provide for a combination of flexibility and stiffness in the structure, which is desirable for most crash applications.

Design of Multimaterial Compliant Mechanisms Using Level-Set Methods

2005 ◽  
Vol 127 (5) ◽  
pp. 941-956 ◽  
Author(s):  
Michael Yu Wang ◽  
Shikui Chen ◽  
Xiaoming Wang ◽  
Yulin Mei
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Level Set Methods ◽  
Single Output ◽  
Geometric Boundary ◽  
Single Input ◽  
Applied Forces ◽  
Multiple Materials

A monolithic compliant mechanism transmits applied forces from specified input ports to output ports by elastic deformation of its comprising materials, fulfilling required functions analogous to a rigid-body mechanism. In this paper, we propose a level-set method for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum heterogeneous structures. Central to the method is a multiphase level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure. Combined with the classical shape derivatives, the level-set method yields an Eulerian computational system of geometric partial differential equations, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. The proposed method is demonstrated for single-input and single-output mechanisms and illustrated with several two-dimensional examples of synthesis of multimaterial mechanisms of force inverters and gripping and clamping devices. An analysis on the formation of de facto hinges is presented based on the shape gradient information. A scheme to ensure a well-connected topology of the mechanism during the process of optimization is also presented.

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.

Design of Crashworthy Structures With Controlled Energy Absorption in the HCA Framework

2012 ◽  
Author(s):  
Punit Bandi ◽  
James P. Schmiedeler ◽  
Andrés Tovar
Keyword(s):  
Energy Absorption ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Synthesis ◽  
Load Paths ◽  
Fully Stressed Design ◽  
Novel Method ◽  
The Given ◽  
Synthesis Approach

This work presents a novel method for designing crashworthy structures with controlled energy absorption based on the use of compliant mechanisms. This method helps in introducing flexibility at desired locations within the structure, which in turn reduces the peak force at the expense of a reasonable increase in intrusion. For this purpose, the given design domain is divided into two subdomains: flexible (FSD) and stiff (SSD) subdomains. The design in the flexible subdomain is governed by the compliant mechanism synthesis approach for which output ports are defined at the interface between the two subdomains. These output ports aid in defining potential load paths and help the user make better use of a given design space. The design in the stiff subdomain is governed by the principle of a fully-stressed design for which material is distributed to achieve uniform energy distribution within the design space. Together, FSD and SSD provide for a combination of flexibility and stiffness in the structure, which is desirable for most crash applications.

A Kinetoelastic Formulation of Compliant Mechanism Optimization

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Michael Yu Wang
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
State Equation ◽  
Rigid Bodies ◽  
Leaf Spring ◽  
Compliance Matrix ◽  
Initial Development ◽  
Mechanism Optimization ◽  
Current Design ◽  
Translational Joint

The current design algorithms for compliant mechanisms often generate solutions that imitate rigid-body linkages by means of point flexures or flexure pivots, by using the popular spring model formulation. This paper presents a kinetoelastic formulation for compliant mechanism optimization. With a state equation of the mechanism defined by the elasticity theory, the model incorporates not only the kinematic function requirements of the mechanism but, more importantly, the necessary conditions on the compliance characteristics of the mechanism’s structure. The kinematics of the compliant mechanism is defined on rigid bodies of input/output ports and is related to a set of kinetoelastic factors of the mechanism’s compliance matrix. The kinetoelastic formulation is applied to the problem of optimizing a compliant translational joint, producing compliant designs with compliance properties such as the leaf spring type sliding joint as opposed to the notch-type joint. This paper represents an initial development toward a more general methodology for compliant mechanism optimization.

Bistable Compliant Four-Bar Mechanisms With a Single Torsional Spring

2006 ◽  
Author(s):  
Adarsh Mavanthoor ◽  
Ashok Midha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanism Design ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Stored Energy ◽  
Element Analysis ◽  
Bistable Behavior ◽  
Torsional Spring ◽  
Bistable Mechanism

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.

Design of a Generic Zero Stiffness Compliant Joint

2010 ◽  
Author(s):  
Femke M. Morsch ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Great Promise ◽  
Optimized Design ◽  
Analytic Model ◽  
Total Potential ◽  
Fea Model ◽  
Compliant Joint ◽  
Joint Element ◽  
Cross Axis

The objective of this paper is to design a generic zero stiffness compliant joint. This compliant joint could be used as a generic construction element in a compliant mechanism. To avoid the spring-back behavior of conventional compliant joints, the principle of static balancing is applied, implying that for each position of the joint the total potential energy should be constant. To this end, a conventional balanced mechanism, consisting of two pivoted bodies which are balanced with two zero-free-length springs, is taken as an initial concept. The joint is replaced by a compliant cross-axis flexural pivot and each spring is replaced by a pair of compliant leaf springs. For both parts an analytic model was implemented and a configuration with the lowest energy fluctuation was found through optimization. A FEA model was used to verify the analytic model of the optimized design. A prototype was manufactured and tested. Both the FEA model and the experiment confirm the reduction of the needed moment to rotate the compliant joint. The experiment shows the balanced compliant joint is not completely balanced but the moment required to rotate the joint is reduced by 70%. Thus, a statically balanced compliant generic joint element was designed which bears great promise in designing statically balanced compliant mechanisms and making this accessible to any designer.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

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