Flexures: Elements of Elastic Mechanisms

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ISBN: 9789056992613 | 9056992619
Cover: Hardcover
Copyright: 8/8/2000

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Introduces the reader to the design process and the necessary background for the static and dynamic analysis of mechanical systems, flexures in particular. Presents basic flexure geometries and the analytical models in which they may be used for specific design applications. For undergraduate and graduate students as well as practicing engineers and scientists.

Preface

xiii

Introduction

(14)

Origins

(1)

Objective

(1)

Advantages of flexures

(1)

Disadvantages of flexures

(1)

Goals of flexure design

(2)

Design considerations

(10)

References

(2)

Essentials

(44)

Overview

(1)

Basic elasticity

(2)

Behavior of materials

(5)

Metals

(3)

Non-metals

(2)

Principal stresses and strains

(4)

Biaxial stress

(1)

Triaxial stresses

(1)

Non-principal stresses

(9)

Plane stress

(5)

Three dimensional stresses

(1)

Shear stresses and shear strain

(3)

Yield criteria

(2)

Ductile materials failure criteria

(1)

Fatigue

(6)

S/N curves

(3)

Effects of notches

(2)

Effects of mean stress

(1)

Damage assessment

(1)

Bending of symmetric beams

(8)

The bending equation

(2)

Deflection of beams

(1)

Sign convention for bending moments

(2)

Moment, shear force and rate of loading relatioships

(1)

Singularity functions

(2)

Torsion

(3)

Torsion of a prismatic beam of circular cross section

(1)

Torsion of a prismatic beam of rectangular cross section

(1)

Mobility

(5)

References

(3)

Rigid body dynamics

(94)

Overview

(1)

Generalized coordinates

(4)

Properties of variational operators

(2)

Commutation

(1)

Minima of a function

(2)

Hamilton's principle

(5)

Example 1: A simple spring mass system

(1)

Example 2: Lateral vibration of a bar

(2)

Lagrange's equation

(4)

Rayleigh's dissipation function

(1)

General use of Lagrange's equation

(1)

Linear systems theory

(7)

The simple, single degree of freedom, linear, spring-mass-damper system

(3)

Some equivalent definitions of a linear system

(1)

Frequency response functions

(3)

Measuring the critical damping ratio

(5)

General linear systems revisited

(5)

Multi-degree of freedom linear systems

(8)

Note on the graphical representation of frequency response functions

(2)

General response function short cuts

100

(6)

Rayleigh's approach to the problem of computing generalized frequency response functions

103

(2)

Example of a two degree of freedom system

105

(1)

Eigen analysis

106

(14)

Conservative systems

108

(4)

Systems with damping

112

(1)

Interpretation of complex eigenvalues and eigenvectors

113

(1)

Summary of primary steps in the derivation of the response function of a linear multi-degree of freedom system

114

(1)

Example: A series, six mass vibration isolator

115

(3)

Results

118

(2)

Vibrations and natural frequencies of continuous systems

120

(26)

Strings

121

(3)

Longitudinal vibrations of a rod

124

(2)

Longitudinal vibrations of a clamped-free rod

126

(1)

Longitudinal vibrations of a free-free or fixed-fixed rod

126

(1)

Longitudinal vibrations of a clamped-free rod with a rigid mass at the free end

127

(2)

Lateral vibration of a bar

129

(1)

Hinged-hinged beam

130

(1)

The free-free or clamped-clamped bar

131

(3)

Lateral vibration of bars with a rigid mass attached

134

(1)

Cantilever beam with a rigid mass attached at the free end

134

(1)

Hinged beam with a central mass, M

135

(1)

Vibration of plates

136

(1)

Vibrations of a circular plate

136

(1)

Free vibration of a circular plate clamped at the perimeter

137

(3)

Rayleigh's method applied to a circular plate with a central mass

140

(5)

Vibrations of a rectangular plate

145

(1)

Free vibrations of a rectangular plate simply supported at the edges

145

(1)

Fundamental frequency's of rectangular plates with other boundary conditions

146

(1)

Case study I: A simple two degree of freedom flexure mechanism

146

(7)

References

151

(2)

Flexure elements

153

(68)

Overview

153

(1)

Leaf type springs

153

(24)

The cantilever as a rotary hinge

154

(4)

The cantilever hinge subject to an axial compressive force

158

(1)

Combined axial and tangential loads

159

(8)

Combined axial and tangential loads plus a moment applied to the free end of a simple cantilever

167

(6)

Leaf type flexures for parallelogram flexure applications

173

(4)

Notch hinge

177

(15)

Theoretical considerations

179

(1)

The leaf type flexure reconsidered

179

(1)

The circular notch hinge

180

(3)

Accuracy of stiffness estimates for a notch type hinge

183

(2)

The notch hinge of elliptic cross section

185

(3)

Compliance's of elliptic hinges in other axes

188

(3)

Results

191

(1)

Finite element results

191

(1)

Other hinge elements

192

(14)

The cross strip pivot

193

(5)

Center shift of the pivot

198

(1)

The cartwheel hinge

199

(2)

Torsional stiffness of the cartwheel hinge

201

(1)

Center shift of the pivot

202

(1)

Stresses in the hinge

203

(1)

The cruciform hinge

204

(2)

Two axis hinges

206

(7)

A simple two axis hinge (y, &thetas;)

206

(2)

The two beam, two degree of freedom flexure (y, &thetas;)

208

(3)

The two axis toroidal hinge (&thetas;x, &thetas;v)

211

(2)

Case study I: Force sensor for contact probe characterization

213

(8)

Toroidal notch type flexure

215

(2)

Two, stacked, notch type flexures

217

(1)

References

218

(3)

Flexure systems

221

(66)

Overview

221

(1)

The four bar link

222

(15)

The simple leaf type rectilinear spring

222

(4)

The simple notch type linear spring

226

(5)

The virtual center

231

(6)

Effect of the drive on the natural frequency

237

(1)

Optimal geometry for the rectilinear motion of components on a simple linear spring

237

(7)

Simple linear spring mechanisms

238

(4)

Effect of axial strains in the flexure supports

242

(1)

Combined effects

243

(1)

Planar mechanisms

244

(7)

Discussion of the simplifying assumptions for reduction of mobility analysis to planar mechanisms

245

(6)

Dynamics of ideal planar flexures (some common mechanisms)

251

(12)

The compound rectilinear spring

252

(4)

The double compound linear spring (including the lever driven spring)

256

(3)

A coupled two-axis flexure

259

(4)

General model for dynamics of planar flexures

263

(17)

Coordinate systems

265

(1)

Notation

266

(2)

Transformations

268

(6)

Case study I: The simple linear spring flexure

274

(4)

Comments on general planar analysis

278

(2)

General dynamics of flexures

280

(3)

Sources of interesting flexure mechanisms

283

(4)

References

284

(3)

Hinges of rotational symmetry

287

(48)

Overview

287

(1)

Introduction

287

(1)

Coil springs

288

(3)

The disc coupling (freedoms &thetas;x, &thetas;z, x)

291

(17)

The inner to outer rim disc coupling

293

(4)

The outer rim disc coupling

297

(7)

Angular stiffness

304

(2)

Axial stiffness

306

(1)

Torsional stiffness

306

(2)

Rotationally symmetric leaf type hinge (axial stiffness of the disc coupling revisited)

308

(9)

Axial stiffness and maximum stress calculations for the rotationally symmetric leaf type flexure system

310

(3)

Simplified equation for maximum stress

313

(1)

Assessment of approximate equations using finite element models

314

(3)

The bellows as a flexure element

317

(9)

Torsional stiffness of the rectangular bellows

320

(2)

Axal stiffness of the rectangular bellows

322

(3)

`S' Shaped distortion of the bellows

325

(1)

The notch and leaf type hinge applied to couplings of rotational symmetry

326

(1)

Case study I: A metrological three-axis translator for constant force profilometry

327

(8)

Principle of operation

328

(3)

References

331

(4)

Levers

335

(38)

Overview

335

(1)

Introduction

335

(1)

Mechanical levers

336

(9)

The rigid lever

337

(6)

Soft spring - stiff spring attenuation

343

(2)

Lost motion

345

(7)

Effects of levers on flexure dynamics

352

(5)

Case study I: A fine adjustment mechanism for motion attenuation

357

(12)

Finite element analysis of the lever flexure

359

(9)

Manufacture of the lever using wire electro-discharge machining

368

(1)

Case study II: Optical levers, galvanometers and the filar suspension

369

(4)

References

372

(1)

Manufacturing and assembly considerations

373

(43)

Overview

373

(1)

Manufacture

374

(14)

Conventional machining

374

(5)

Electro-discharge machining

379

(1)

Plunge electro-discharge machining

379

(1)

Wire electro-discharge machining

380

(1)

Lithographic etching

381

(1)

Flexures produced using microelectronic processing techniques (MEMS)

382

(1)

Lithographic etching of copper sheet

383

(1)

Electroplating (or electro-forming)

384

(1)

Diamond grinding

385

(3)

Assembly

388

(26)

Assembly of flexures

389

(4)

Coupling the actuator to the flexure

393

(3)

Flexure mounts

396

(1)

Adding damping to flexure systems (extracting energy)

396

(1)

Internal friction in solids

396

(7)

Adding damping to a flexure

403

(3)

Effects of manufacturing tolerance on the stiffness of flexure elements

406

(4)

Typical flexure drives

410

(4)

Machining and heat treatment of some common flexure materials

414

(2)

Steels

415

(1)

Beryllium copper

415

(1)

References

416

(3)

Author index

419

(4)

Subject index

423

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Flexures: Elements of Elastic Mechanisms

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

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Flexures: Elements of Elastic Mechanisms

Summary

Table of Contents

Supplemental Materials

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