Book contents
- Frontmatter
- Miscellaneous Frontmatter
- Contents
- PREFACE
- PART I FOURIER SERIES
- PART II SOME DIFFERENTIAL EQUATIONS
- PART III ORTHOGONAL SERIES
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm–Liouville equation I
- 38 Liouville
- 39 The Sturm–Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 42 Linkages
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- PART IV FOURIER TRANSFORMS
- Part V FURTHER DEVELOPMENTS
- PART VI OTHER DIRECTIONS
- Appendix A The circle T
- Appendix B Continuous function on closed bounded sets
- Appendix C Weakening hypotheses
- Appendix D Ode to a galvanometer
- Appendix E The principle of the argument
- Appendix F chase the constant
- Appendix G Are share prices in Brownian motion?
- Index
42 - Linkages
Published online by Cambridge University Press: 05 June 2014
Book contents
- Frontmatter
- Miscellaneous Frontmatter
- Contents
- PREFACE
- PART I FOURIER SERIES
- PART II SOME DIFFERENTIAL EQUATIONS
- PART III ORTHOGONAL SERIES
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm–Liouville equation I
- 38 Liouville
- 39 The Sturm–Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 42 Linkages
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- PART IV FOURIER TRANSFORMS
- Part V FURTHER DEVELOPMENTS
- PART VI OTHER DIRECTIONS
- Appendix A The circle T
- Appendix B Continuous function on closed bounded sets
- Appendix C Weakening hypotheses
- Appendix D Ode to a galvanometer
- Appendix E The principle of the argument
- Appendix F chase the constant
- Appendix G Are share prices in Brownian motion?
- Index
Summary
During the last third of the eighteenth century Watt embarked on a total redesign of the Newcomen steam engine turning it from a special purpose machine to an economical general purpose power source. This involved the solution not just of one but many technical problems each one requiring either a new idea (like the separate condenser) or the astute adaptation of an old one (like the centrifugal governor which we shall briefly return to in Chapter 72).
One of the problems that had to be overcome was that of turning the rectilinear motion of a piston into the circular motion of a wheel and vice versa. Spurred on by his partner Boulton, Watt patented five different solutions. The one we shall discuss is called Watt's parallelogram. Watt is reported to have been prouder of this invention than of any other.
In its simplest form it consists of three bars AB, BC and CD linked as shown in Figure 42.1 with A and D fixed but D and C free to move. The ‘tracer point’ Q is on BC. A little experiment will show the reader that as C rotates round D, Q performs quite a complicated motion. However, for many purposes it is sufficient that the path of Q is approximately linear for rotations of CD through a small angle θ(∣θ∣ < 20° say).
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- Fourier Analysis , pp. 197 - 200Publisher: Cambridge University PressPrint publication year: 1988
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