Design of Planar Large-Deflection Compliant Mechanisms With Decoupled Multi-Input-Output Using Topology Optimization

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Benliang Zhu ◽  
Qi Chen ◽  
Hai Li ◽  
Hongchuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Geometrical Nonlinearity ◽  
Method Comparison ◽  
Output Coupling ◽  
Large Displacements ◽  
Interpolation Scheme ◽  
Input Output ◽  
Output Behavior

This paper presents a method for topology optimization of large-deflection compliant mechanisms with multiple inputs and outputs by considering the coupling issue. First, the objectives of the design problem are posed by modeling the output loads using several springs to enable control of the input–output behavior. Second, a scheme is proposed to obtain a completely decoupled mechanism. Both input coupling and output coupling are considered. Third, with the implementation of an energy interpolation scheme to stabilize the numerical simulations, the geometrical nonlinearity is considered to appropriately capture the large displacements of compliant mechanisms. Finally, several numerical examples are presented to demonstrate the validity of the proposed method. Comparison studies with the obtained results without considering the coupling issues are also presented.

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

Multiobjective Topology Optimization of Multi-Input and Multi-Output Compliant Mechanisms with Geometrically Nonlinearity

2013 ◽  
Vol 706-708 ◽  
pp. 864-877
Author(s):  
Zhao Kun Li ◽  
Xian Min Zhang ◽  
Hua Mei Bian ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Decision Function ◽  
Output Coupling ◽  
Element Formulation ◽  
Conflicting Objectives ◽  
Incremental Scheme ◽  
Coupling Terms ◽  
Suppression Strategy ◽  
Moving Asymptotes

Multiple degree-of-freedom compliant mechanisms are widely used in the fields of micro-positioning and micro-manipulation. This paper deals with multiobjective topology optimization of multi-input and multi-output compliant mechanisms undergoing large deformation. The objective function is defined by the minimum compliance and maximum geometric advantage to meet both stiffness and flexibility requirements. The suppression strategy of input and output coupling terms is studied and the expression of the output coupling terms is further developed. The weighted sum of the conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. Geometrically nonlinear mechanism response is calculated using the Total-Lagrange finite element formulation and the equilibrium is found using an incremental scheme combined with Newton-Raphson iterations. The solid isotropic material with penalization approach is used in design of compliant mechanisms. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Numerical examples of multiple inputs and outputs are presented to show the validity of the new method. Simulation results show that the compliant mechanisms can be deformed in the desirable manner and the coupling output displacements are suppressed significantly by using the presented method.

Dynamic Model of Mechanisms With Highly Compliant Members

2005 ◽  
Author(s):  
Chao-Chieh Lan ◽  
Kok-Meng Lee
Keyword(s):  
Dynamic Model ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Wide Spectrum ◽  
Geometrical Nonlinearity ◽  
Geometric Constraints ◽  
Axial Deformation ◽  
Small Deflection ◽  
Deflection Theory

The dynamic model for links in most mechanisms has often based on small deflection theory without considering geometrical nonlinearity. For applications like light-weight links or high-precision elements, it is necessary to capture the large deflection caused by bending forces. A complete dynamic model is presented here to characterize the motion of a compliant mechanism capable of large deflection with shear and axial deformation. We derive the governing equations from Hamilton’s principle along with the essential geometric constraints that relate deformation and coordinate variables, and solve them using a semi-discrete method based on the Newmark scheme and shooting method. The dynamic model has been validated experimentally. We also extend the model for analyzing compliant mechanisms. It is expected that the dynamic model will serve as a basis for analyzing a wide spectrum of compliant multi-link mechanisms.

Reliability-Based Topology Optimization of Compliant Mechanisms with Geometrically Nonlinearity

2014 ◽  
Vol 556-562 ◽  
pp. 4422-4434 ◽  
Author(s):  
Zhao Kun Li ◽  
Hua Mei Bian ◽  
Li Juan Shi ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Geometric Nonlinearity ◽  
Compliant Mechanisms ◽  
Optimization Problems ◽  
Geometrical Nonlinearity ◽  
Optimization Method ◽  
Response Analysis ◽  
Element Formulation ◽  
Reliability Method ◽  
Geometrical Nonlinear

A new reliability-based topology optimization method for compliant mechanisms with geometrical nonlinearity is presented. The aim of this paper is to integrate reliability and geometrical nonlinear analysis into the topology optimization problems. Firstly, geometrical nonlinear response analysis method of the compliant mechanisms is developed based on the Total-Lagrange finite element formulation, the incremental scheme and the Newton-Raphson iteration method. Secondly, a multi-objective topology optimal model of compliant mechanisms considering the uncertainties of the applied loads and the geometry descriptions is established. The objective function is defined by minimum the compliance and maximum the geometric advantage to meet both the stiffness and the flexibility requirements, and the reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Thirdly, the computation of the sensitivities is developed with the adjoint method and the optimization problem is solved by using the Method of Moving Asymptotes. Finally, through numerical calculations, reliability-based topology designs with geometric nonlinearity of a typical compliant micro-gripper and a multi-input and multi-output compliant sage are obtained. The importance of considering uncertainties and geometric nonlinearity is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs, which shows that the reliability-based topology optimization yields mechanisms that are more reliable than those produced by deterministic topology optimization.

scholarly journals Comparing global input-output behavior of frozen-equivalent LPV state-space models

2017 ◽  
Vol 50 (1) ◽  
pp. 9766-9771 ◽  
Author(s):  
Ziad Alkhoury ◽  
Mihály Petreczky ◽  
Guillaume Mercère
Keyword(s):  
State Space ◽  
State Space Models ◽  
Input Output ◽  
Output Behavior

Piezoelectric Actuator Performance Metrics and Relation to Compliant Mechanism Design

2001 ◽  
Author(s):  
Hima Maddisetty ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Performance Metrics ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanical Efficiency ◽  
High Energy ◽  
High Energy Density ◽  
High Bandwidth ◽  
Compliant Mechanism Design ◽  
Actuator Performance

Abstract Piezoceramic actuators have gained widespread use due to their desirable qualities of high force, high bandwidth, and high energy density. Compliant mechanisms can be designed for maximum stroke amplification of piezoceramic actuators using topology optimization. In this paper, the mechanical efficiency and other performance metrics of such compliant mechanism/actuator systems are studied. Various definitions of efficiency and other performance metrics of actuators with amplification mechanisms from the literature are reviewed. These metrics are then applied to two compliant mechanism example problems and the effect of the stiffness of the external load is investigated.

A Methodology for Compliant Mechanisms Design: Part I — Introduction and Large-Deflection Analysis

1992 ◽  
Author(s):  
A. Midha ◽  
I. Her ◽  
B. A. Salamon
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Companion Paper ◽  
Computational Techniques ◽  
Shooting Methods ◽  
Mechanism Synthesis ◽  
Calculation Algorithm ◽  
Deflection Analysis ◽  
Kinematic Properties

Abstract A broader research proposal seeks to systematically combine large-deflection mechanics of flexible elements with important kinematic considerations, in yielding compliant mechanisms which perform useful tasks. Specifically, the proposed design methodology will address the following needs: development of the necessary nomenclature, classification and definitions, and identification of the kinematic properties; categorization of mechanism synthesis types, both structurally as well as by function; development of efficient computational techniques for design; consideration of materials; and application and validation. Contained herein, in particular, is an introduction to the state-of-the-art in compliant mechanisms, and the development of an accurate chain calculation algorithm for use in the analysis of a large-deflection, cantilevered elastica. Shooting methods, which permit specification of additional boundary conditions on the elastica, as well as compliant mechanism examples are presented in a companion paper.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

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