Design Space Analysis of Distributed Compliance in Segmented Beam Templates of Compliant Mechanisms

2009 ◽  
Author(s):  
Stephen L. Canfield ◽  
Alexander Shibakov ◽  
Joseph D. Richardson
Keyword(s):  
Objective Function ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Multiple Objectives ◽  
Elastic Response ◽  
Beam Model ◽  
Closed Form Solutions ◽  
Parametric Studies ◽  
Design Parameterization

A significant amount of research has been conducted in developing optimal synthesis techniques for compliant mechanisms with the expectation that distributed devices would result from the continuum design domain. However, it is commonly noted that much of this work has resulted in mechanisms that show localized rather than distributed compliance. This behavior has been attributed to a variety of sources including numerical discrepancies in the model, objective function formulation, and design parameterizations. In this paper, the nature of compliance distribution over particular objective function formulations and design parameterization are further considered in the absence of numerical or resolution issues. The intent is to better understand the behavior of the objective function over multidimensional subsets of the design space that include a direct measure for distribution of compliance. The approach is based on a simple, representative compliant mechanism formed as a segmented beam model. This mechanism is considered to be representative of compliant mechanism behavior in systems where elastic deformation is dominated by bending. Closed-form solutions for the elastic response of this representative mechanism are presented and parametric studies of the response of traditional objectives over subsets of the design space are conducted. The results show that in the absence of numeric artifacts, mechanism efficiencies are improved as mechanisms tend toward lumped compliance when single objectives are considered on mechanisms dominated by bending. However, when more than one objective is deemed important in the design, there exist preferred regions of the workspace, not necessarily in a lumped region, that depend largely on the interaction of the multiple objectives. Of these preferred regions, one lies in a moderately lumped region (h2/h1 ≈ 0.2) and one in a distributed region (h2/h1 ≈ 0.7). The designs in these regions reveal a higher viability in simultaneously satisfying the multiple objectives. This result is based on a visualization of the design space based on measuring the correlation of a multiple objectives over the design space. The results demonstrate several of the factors which contribute to this behavior, and provide an initial measure of the importance of each. Finally, suggestions are provided based on these results that can be used to improve the optimization process if the desire is to achieve distributed compliance.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

2012 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Flexible Beam ◽  
Beam Model ◽  
Flexible Beams ◽  
Multi Objective Genetic Algorithm ◽  
Optimization Loop

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

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.

Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Isaac L. Delimont ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Closed Form ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Large Deflections ◽  
Center Of Rotation ◽  
Closed Form Solutions ◽  
Potential Development ◽  
Design Guide

Origami-inspired design is an emerging field capable of producing compact and efficient designs. Compliant hinges are proposed as a way to replicate the folding motion of paper when using nonpaper materials. Compliant hinges function as surrogate folds and can be defined as localized reduction of stiffness. The purpose of this paper is to organize and evaluate selected surrogate folds for use in compliant mechanisms. These surrogate folds are characterized based on the desired motion as well as motions typically considered parasitic. Additionally, the surrogate folds' ability to rotate through large deflections and their stability of center of rotation are evaluated. Existing surrogate folds are reviewed and closed-form solutions presented. A diagram intended as a straightforward design guide is presented. Areas for potential development in the surrogate fold design space are noted.

Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms

2014 ◽  
Author(s):  
Isaac L. Delimont ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Closed Form ◽  
Design Space ◽  
Compliant Mechanisms ◽  
Large Deflections ◽  
Center Of Rotation ◽  
Closed Form Solutions ◽  
Potential Development ◽  
Design Guide

Origami-inspired design is an emerging field capable of producing compact and efficient designs. Compliant hinges are proposed as a way to replicate the folding motion of paper when using non-paper materials. Compliant hinges function as surrogate folds and can be defined as localized reduction of stiffness. The purpose of this paper is to organize and evaluate selected surrogate folds for use in compliant mechanisms. These surrogate folds are characterized based on the desired motion as well as motions typically considered parasitic. Additionally the surrogate folds’ ability to rotate through large deflections and their stability of center of rotation are evaluated. Existing surrogate folds are reviewed and closed-form solutions presented. A diagram intended as a straightforward design guide is presented. Areas for potential development in the surrogate fold design space are noted.

scholarly journals Static behavior of weighing cells

2018 ◽  
Vol 7 (2) ◽  
pp. 587-600 ◽  
Author(s):  
Maximilian Darnieder ◽  
Markus Pabst ◽  
Ronny Wenig ◽  
Lena Zentner ◽  
René Theska ◽  
...  
Keyword(s):  
Mechanical Behavior ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Element Model ◽  
Novel Approach ◽  
Stiffness Characteristic ◽  
Highly Sensitive ◽  
Rigid Body Model ◽  
Mechanical Models ◽  
Parametric Studies

Abstract. Compliant mechanisms in precision weighing technology are highly sensitive mechanical systems with continuously rising demands for performance in terms of resolution and measurement uncertainty. The systematic combination of adjustment measures represents a promising option for the enhancement of weighing cells which is not yet fully exhausted. A novel adjustment concept for electromagnetic force compensated weighing cells designed for 1 kg mass standards is introduced. The effect on the mechanical behavior is analyzed in detail using a planar compliant mechanism with semi-circular flexure hinges. Design equations for a first layout of the mechanical system are derived from a linearized rigid body model. Existing adjustment concepts for the stiffness characteristic and the sensitivity to quasi-static ground tilt are included. They are extended by the novel approach to attach trim weights to the levers of the linear guide. Based on this concept, an optimal design for the weighing cell is determined. The comparison with a finite element model reveals further effects given by the more precise description of the mechanical behavior. By parametric studies of the adjustment parameters in the mechanical models, it is shown that the stiffness and tilt sensitivity can be reduced significantly compared to the non-adjusted weighing cell. The principal correlation of the trim weights and their effect on the mechanical properties is experimentally verified using a commercially available weighing cell.

An Optimality Criteria Approach for the Topology Synthesis of Compliant Mechanisms

1998 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Energy Density ◽  
Mathematical Programming ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimality Criteria Method ◽  
New Energy ◽  
Method Of Solution ◽  
Design Parameterization ◽  
The Continuum

Abstract The physical insight used in formulating a multi-criteria optimization problem for the synthesis of compliant mechanisms, is quickly lost if mathematical programming techniques (SLP, SQP etc.) are used to determine the optimal solution. As opposed to the previous works that relied upon mathematical programming search techniques to find the optimum solution, in this paper we present an alternative method of solution called the optimality criteria method. Optimality criteria methods have proven to be effective in structural optimization problems with a large number of variables, and very few constraints as is the case in the topology synthesis of compliant mechanisms. The important new results of this paper include: (i) the derivation of a physically insightful optimal property of compliant mechanisms which states that the ratio of the mutual potential energy density and the strain energy density is uniform throughout the continuum (ii) the development of the optimality criteria method of solution in the form of a simple update formula for the design variables by using the above property (iii) design parameterization using the frame finite-element based ground-structure that appropriately accounts for the requisite bending behavior in the continuum, and (iv) numerical implementation of previously reported density based design parameterization using bilinear plane-stress elements. In addition, a new energy based multi-criteria objective function is presented to maximize the useful output energy (which is equivalent to maximizing the mechanical advantage) while meeting the kinematic requirements. Several examples are included to demonstrate the validity of the optimal property, the optimality-criteria method of solution, and the improvements made possible by the new energy based objective function.

Analysis of the Hex Cell Discretization for Topology Synthesis of Compliant Mechanisms

2007 ◽  
Author(s):  
Nilesh D. Mankame ◽  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Continuous Optimization ◽  
Elastic Response ◽  
Cell Design ◽  
Stable Convergence ◽  
Mechanism Synthesis ◽  
Single Node ◽  
Square Cell ◽  
The Ideal

We use non-linear finite element simulations to study the convergence behavior of the honeycomb or hex cell design discretization for optimization-based synthesis of compliant mechanisms in this paper. Adjacent elements share exactly one common edge in the hex cell discretization, unlike the square cell discretization in which adjacent elements can be connected by a single node. As the single node connections in bilinear quadrilateral plane stress elements allow strain-free relative rotations, compliant mechanism designs obtained from square cell discretizations with these elements often contain elements with single node connections or point flexures. Point flexures are sites of lumped compliance, and as such, are undesirable as they lead to compliant mechanisms designs which deviate from the ideal of distributed compliance. The hex cell design discretization circumvents the problem of point flexures without any additional computational expense (e.g. filtering, extra constraints, etc.) by exploiting the geometry of the discretization. In this work we compare the elastic response of a group of four cells in which two adjacent cells have the least connectivity in both: the square and the hex discretizations. Simulations show that the hex cell discretization leads to a more accurate modeling of the displacement, stress and strain energy fields in the vicinity of the least connectivity regions than the square cell discretization. Therefore, the hex cell discretization does not suffer from stress singularities that plague the square cell discretization. These properties ensure that continuous optimization-based compliant mechanism synthesis procedures that use the hex cell discretization, exhibit a faster and more stable convergence to designs that can be readily manufactured than those that use the square cell discretization.

scholarly journals Accuracy Evaluation of PRBM for Predicting Kinetostatic Behavior of Flexible Segments in Compliant Mechanisms

2011 ◽  
Author(s):  
Guimin Chen ◽  
Aimei Zhang
Keyword(s):  
Quantitative Study ◽  
Strain Energy ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Accuracy Evaluation ◽  
Cantilever Beams ◽  
Characteristic Parameters ◽  
Closed Form Solutions ◽  
Body Model ◽  
Rigid Body Model

The pseudo-rigid-body model (PRBM) method has been widely accepted as one of the most important tools for synthesis and analysis of compliant mechanisms. However, the lack of quantitative study on the accuracy of PRBM for predicting the kinetostatic behavior of flexible members always makes users feel unconfident in the results achieved by PRBM. In this paper, a strain-energy-based approach is proposed for evaluating the accuracy of PRBM for predicting kinetostatic behavior of flexible segments, which compares the results of strain energy calculate using PRBM to those obtained using the derived closed-form solutions. The approach was used to evaluate the accuracy of the PRBM for flexible cantilever beams. It is proved that the PRBM is accurate for modeling segments subject to end-moment loads. A thorough comparison for segments subject to end-force loads is also presented. The results could be useful for PRBM users to assess the accuracy of the models for their compliant mechanism designs, or to choose appropriate values for the characteristic parameters. The results may also be used to improve the PRBM.

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.

scholarly journals Geometric synthesis method of compliant mechanism based on similarity transformation of pole maps

2021 ◽  
Vol 12 (1) ◽  
pp. 375-391
Author(s):  
Song Lin ◽  
Yu Zhang ◽  
Hanchao Wang ◽  
Jingyu Jiang ◽  
Niels Modler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Similarity Transformation ◽  
Compliant Mechanism ◽  
Research Work ◽  
Synthesis Method ◽  
Common Mechanism ◽  
Beam Model ◽  
Motion Generation ◽  
Euler Beam

Abstract. This paper presents a geometric synthesis method for compliant mechanisms based on similarity transformation of pole maps. Motion generation is a typical and common mechanism synthesis task, so this study takes it as the design requirement to expound the proposed method. Most of the current research work relies on numerical solution of the nonlinear Bernoulli–Euler beam model, numerical simulations or physical experiments to study the synthesis method of compliant mechanisms. There is a lack of simpler and more efficient methods to achieve motion generation of compliant mechanisms with various topologies. This study is based on pole map which is a geometric tool to describe the motion of rigid-body mechanisms. In this paper, we first demonstrate the feasibility of applying the similarity transformation of pole map to compliant mechanisms. It is proved that the pole map of compliant mechanisms has the same characteristic as rigid-body mechanisms during similarity transformation. Then we present the procedure of synthesis method in detail and expound the establishment method of function module which can avoid the functional defects of the final designed mechanism. At last, we take the compliant geared linkages and compliant four-bar linkage as examples to illustrate the novel synthesis approach. The result is an applicable and effective synthesis method for motion generation of compliant mechanisms.

Sign in / Sign up

Export Citation Format

Share Document