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.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Mesh Network ◽  
Adaptive Antenna ◽  
Optimal Size ◽  
Dimensional Synthesis ◽  
Element Analysis

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2013 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Adaptive Antenna ◽  
Dimensional Synthesis ◽  
Element Analysis ◽  
Initial Element ◽  
Multi Objective Genetic Algorithm ◽  
Improved Design

This paper uses rigid-body mechanism topologies to synthesize distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. A single-actuator compliant mechanism is synthesized from a single degree-of-freedom rigid-body mechanism’s base topology in one of two ways. In one case, the base topology is directly evaluated through dimensional synthesis to determine the compliant mechanism’s optimal dimensions. In the second, the base topology establishes an initial element network for an optimization routine that determines topologies and dimensions simultaneously, and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. A multi-objective genetic algorithm is employed to search the design space, and the deformation is evaluated using geometrically nonlinear finite element analysis. The procedure’s utility is demonstrated with two practical examples — one approximating open-curve profiles of an adaptive antenna and the other closed-curve profiles of a morphing wing.

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.

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.

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

1998 ◽  
Author(s):  
A. Saxena ◽  
Steven N. Kramer
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Beam Equation ◽  
Integration Scheme ◽  
Large Deflections ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism 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 with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

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.

Type Synthesis of Compliant Mechanisms Employing a Simplified Approach to Segment Type

1994 ◽  
Author(s):  
Morgan D. Murphy ◽  
Ashok Midha ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Type Synthesis ◽  
Simplified Approach ◽  
Design Procedures ◽  
Synthesis Techniques ◽  
Design Solutions ◽  
Synthesis Methodology

Abstract The formulation of design procedures for rigid-body mechanisms has benefited from the application of type-synthesis techniques. Therefore, with modifications to allow for inclusions of compliance, type synthesis is seen as a useful tool in the design of compliant mechanisms. Previous efforts have developed methods that result in a large number of possible design solutions to a given problem. This paper deals primarily with the development of a simplified compliant-mechanism type-synthesis methodology that limits the number of design solutions considered. The techniques are derived by modifying existing compliant mechanism type-synthesis techniques to yield a simpler model with greater pragmatic value.

Compliant Pantographs via the Pseudo-Rigid-Body Model

1998 ◽  
Author(s):  
Andrew J. Nielson ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Test Results ◽  
Rigid Link ◽  
Body Model ◽  
Design Flexibility ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Classical Mechanism

Abstract This paper uses a familiar classical mechanism, the pantograph, to demonstrate the utility of the pseudo-rigid-body model in the design of compliant mechanisms to replace rigid-link mechanisms, and to illustrate the advantages and limitations of the resulting compliant mechanisms. To demonstrate the increase in design flexibility, three different compliant mechanism configurations were developed for a single corresponding rigid-link mechanism. The rigid-link pantograph consisted of six links and seven joints, while the corresponding compliant mechanisms had no more than two links and three joints (a reduction of at least four links and four joints). A fourth compliant pantograph, corresponding to a rhomboid pantograph, was also designed and tested. The test results showed that the pseudo-rigid-body model predictions were accurate over a large range, and the mechanisms had displacement characteristics of rigid-link mechanisms in that range. The limitations of the compliant mechanisms included reduced range compared to their rigid-link counterparts. Also, the force-deflection characteristics were predicted by the pseudo-rigid-body model, but they did not resemble those for a rigid-link pantograph because of the energy storage in the flexible segments.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

Application of Rigid-Body-Linkage Static Balancing Techniques to Reduce Actuation Effort in Compliant Mechanisms

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Amrith N. Hansoge ◽  
G. K. Ananthasuresh
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Small Length ◽  
Element Analysis ◽  
Static Balancing ◽  
Free Length ◽  
First Order ◽  
Taylor’S Series

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

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