scholarly journals A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Flexible Joints ◽  
Precision Engineering ◽  
Design Constraint ◽  
Analysis And Synthesis ◽  
Prismatic Joints

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis 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.

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.

Analysis of Parasitic Motion in Compliant Mechanisms Using Eigenwrenches and Eigentwists

2018 ◽  
Author(s):  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Degree Of Freedom ◽  
Compliance Matrix ◽  
Parasitic Motion ◽  
Actual Degree ◽  
Motion Metrics ◽  
Mechanism Kinematic ◽  
Kinematic Information

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.

scholarly journals DAS-2D: a concept design tool for compliant mechanisms

2016 ◽  
Vol 7 (2) ◽  
pp. 135-148 ◽  
Author(s):  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Tool ◽  
Concept Design ◽  
Simulation Tools ◽  
Element Simulation ◽  
Mechanism Research ◽  
Analysis And Synthesis ◽  
Engineering Practices

Abstract. Compliant mechanisms utilize the deformation of the elastic members to achieve the desired motion. Currently, design and analysis of compliant mechanisms rely on several commercial dynamics and finite element simulation tools. However, these tools do not implement the most recently developed theories in compliant mechanism research. In this article, we present DAS-2D (Design, Analysis and Synthesis), a conceptual design tool which integrates the recently developed pseudo-rigid-body models and kinetostatic analysis/synthesis theories for compliant mechanisms. Coded in Matlab, the software features a kinematic solver for general rigid-body mechanisms, a kinetostatic solver for compliant mechanisms and a fully interactive graphical user interface. The implementation details of all modules of the program are presented and demonstrated with four different case studies. This tool can be beneficial to classroom teaching as well as engineering practices in design of compliant mechanisms.

Origami Kaleidocycle-Inspired Symmetric Multistable Compliant Mechanisms

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Hongchuan Zhang ◽  
Benliang Zhu ◽  
Xianmin Zhang
Keyword(s):  
Arbitrary Number ◽  
Compliant Mechanisms ◽  
Rotation Angle ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Mobility Analysis ◽  
Stable States ◽  
Deployable Structures ◽  
Basic Dimension ◽  
Metamorphic Robots

Compliant kaleidocycles can be widely used in a variety of applications, including deployable structures, origami structures, and metamorphic robots, due to their unique features of continuous rotatability and multistability. Inspired by origami kaleidocycles, a type of symmetric multistable compliant mechanism with an arbitrary number of units is presented and analyzed in this paper. First, the basic dimension constraints are developed based on mobility analysis using screw theory. Second, the kinematic relationships of the actual rotation angle are obtained. Third, a method to determine the number of stabilities and the position of stable states, including the solution for the parameterized boundaries of stable regions, is developed. Finally, experimental platforms are established, and the validity of the proposed multistable mechanisms is verified.

Multiple-Segment-Pseudo-Rigid-Body Model Concept in Compliant Mechanism Design and Analysis

2000 ◽  
Author(s):  
Gregory A. Mettlach ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Synthesis Methods ◽  
Model Concept ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Beam Type

Abstract The concept of a pseudo-rigid-body model for a flexible member proven very instrumental in the design and analysis of compliant mechanisms. It provides a means by which a compliant mechanism may be modeled as an equivalent pseudo-rigid-body mechanism. This makes it possible for compliant mechanisms to be analyzed and designed using a wealth of existing methods for rigid-body mechanisms. Oftentimes, however, it is not possible to model a compliant member with a typical pseudo-rigid-body model. This may be due to a force or displacement boundary condition applied to a compliant member at a point other than the beam end. For situations such as these, a planar, multiple-segment pseudo-rigid-body model concept is introduced which allows arbitrary beam type compliant members, regardless of geometry, loading, or boundary conditions, to be modeled as an assemblage of rigid members with torsional springs at characteristic pivots. This methodology enables existing analysis and synthesis methods to be applied in the design of complex compliant mechanisms.

A Generalized Loop-Closure Theory for the Analysis and Synthesis of Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Energy Storage ◽  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanism Analysis ◽  
Model Concept ◽  
Loop Closure ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant mechanisms gain at least some of their motion from flexible members. The combination of large-deflection beam analysis, kinematic motion analysis, and energy storage makes the analysis of compliant mechanisms difficult. The design of mechanisms often requires iteration between synthesis and analysis procedures. In general, the difficulty in analysis has limited the use of compliant mechanisms to applications where only simple functions and motions are required. The pseudo-rigid-body model concept promises to be the key to unifying the compliant and rigid-body mechanism theories. It simplifies compliant mechanism analysis by determining an equivalent rigid-body mechanism that accurately models the kinematic characteristics of a compliant mechanism. Once this model is obtained, many well known concepts from rigid-body mechanism theory become amenable for use to analyze and design compliant mechanisms. The pseudo-rigid-body-model concept is used to develop a generalized loop-closure method for the analysis and synthesis of compliant mechanisms. Synthesis is divided into two major categories: (i) rigid-body replacement synthesis, wherein only kinematic constraints are considered, and (ii) synthesis for compliance, wherein considerations of the energy storage and input/output force/torque characteristics of compliant mechanisms are utilized. The method allows compliant mechanisms to be designed for tasks that would have earlier been assumed to be unlikely, if not impossible, applications of compliant mechanisms. Examples of function, motion, and path generation of compliant mechanisms are presented for the first time.

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