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September , 1940 AIRCRAFT ENGINEERING '277 Mathematics for the Engineer — Mechanis m and the Kinematics of Machines Mathematica l Methods in Engineering. The account of Rayleigh's method for the detailed description of particular tooth shapes. By Th. v. Kármán and M. A. Biot. approximate determination of equilibrium con The author passes on to treat gear trains, [McGraw Hill. 26s.] figurations and of the frequencies of oscillation belts, and chains and then has a very useful of vibrating systems is short and rather un chapter on variable speed gears. Synchro-mesh, Professor Kármán combines lucidity with satisfactory. The theorem that the natural constant mesh, and the popular Wilson gear penetration in accounts of his own investiga frequencies of vibration are stationary with box as used in motor cars are all clearly tions, and his surveys of research, which have respect to variation of the modes of vibration, explained. been presented to conferences from time to which is the basis of the method, is not stated A chapter each is devoted to cams, universal time, have shown his capacity for explaining specifically, though it is tru e tha t it can be easily the results of specialized research to general joints, and ratchets. The last chapter in the inferred from statements made in the text. scientific audiences. In collaboration with book describes various miscellaneous mechan Since the theorem can be deduced, as in isms such as the swash-plate and the Z crank. Professor Biot he has now written a book on Rayleigh's original proof, directly from the mathematical methods in engineering with the A notable feature of the book is the compre expressions for the kinetic and potential energies aim of tempting the practical engineer occa hensive set of examples appended to most in terms of the normal co-ordinates, it is a pity sionally to abandon the laboratory for the chapters. In these the author has adopted the t o omit it and merely to state tha t the desired study. To be successful in this difficult task very good plan of including a few major result is obtained by equating the variation of it is necessary that the presentation should be problems of mechanism as exercises, and thus th e Lagrangian function (which is equal to the interesting, and the material closely linked with avoids unduly burdening the text while pro difference between the kinetic and potential practical engineering, and, in addition, it is viding the student with some real tests of his energies) to zero. desirable that an understanding of the argu powers. ments given in any one chapter should not I t is certain that most scientists and There are necessarily some omissions. Inte depend on a detailed knowledge of the earlier engineers will find much of interest in this book grating machines are not touched upon and the chapters. The authors have been successful and perhaps the best way of illustrating this aeronautical engineer will find no mention of in attaining these objects and a copy of this is to give a short list of a few of the matters rotar y pumps and blowers for boosting his book would be a valuable addition to any touched on which the reviewer noted as interest engines or irreversible gears for safe operation engineering library. ing or new to him : the path of a bomb under of his aerodynamical control surfaces. gravity and air resistance, the significance of Small points which the author might consider Apar t from initial chapters on ordinary th e mysterious Coriolis force, theory of the worth modifying in a second edition are the differential equations and on Bessel functions, band-pass filter, spacing of stiffener rings to following. As it is assumed that the student no other complete chapters are devoted to pure reduce stress in a circular pipe subject to in has a working acquaintance with the calculus mathematics, though sections on elliptic ternal pressure, and examples on the condenser it seems unnecessary, not to say irritating, to integrals and on singular points of differential microphone, as an application of Lagrange's have to consider finite quantities and then equations are inserted, and brief discussions of equations to a mixed electrical and clastic laboriously proceed to the limit. Statements other matters such as vectors, operators, problem, and on the pendulum counterweight like the following occur frequently :— matrices, and Fourier's integral theorem are used for the damping of torsional oscillations of introduced at convenient points. With these tan crankshafts. exceptions the subject matter of the book falls H . B. S. (Here by the way looks better than roughly into three parts : (1) general dynamics of particles and rigid bodies ; (2) theory of Mechanis m and the Kinematics of structures, and (3) theor y of vibrations including ■) • Machines . By W. T. Steeds. [Longmans. the use of the operational calculus. The There is no reason why quantities denoted in 18s.] mathematical methods introduced to handle a the figures by etc., should not be marked This is a well balanced book and the author problem in one of these categories are often straightaway, and so long as the student succeeds very well in his avowed intention applied concurrently to corresponding problems understands that he is dealing with small of " steering a middle course between unduly in the other categories; in particular the quantities of the first order nothing is lost and academic treatment on the one hand and mechanical or electrical analogies of an electrical something is gained by avoiding the rigmarole excessively detailed descriptive treatment on or mechanical problem are described in many of proceeding to the limit each time. th e other hand." cases, so tha t the reader is encouraged to make I n discussing the position of a straight line it The first thirty of the three hundred odd use of his familiarity with one branch of might have been better to appeal to the pages discusses the motion of a point. The engineering to increase his knowledge of student's intuitive understanding that having motion of a line as representing plane motion another. In addition, the authors' preference fixed a point through which it passes no is next considered and this is followed by a for the application of Lagrange's equations further freedom is possible other than rotation very useful chapter on what the author calls provides an underlying unification of much of about any two mutually perpendicular axes " geometric design," i.e., design directed to the the material. This may, however, be a through that point, both normal to the given end of limiting the degrees of freedom of a stumbling block for some readers, as generalized line, rather than introduce the mathematical rigid body in the most convenient way and co-ordinates and Lagrange's equations are relation between the three direction cosines. ensuring that no undesired constraints are abstract matters, which need considerable Again something ought to be done about introduced. This brings us to page 63 and a practice before they can be handled with Article 45 on controdes. It gives a highly discussion of the Kinematic chain, higher and confidence. artificial example which is likely to be far from lower pairs, etc., with plenty of typical clear to the student. What is wrong with the examples. A feature of the book is the detailed dis time-honoured but none the less admirable cussion of a few particularly illuminating The thirt y pages tha t follow deal with velocity concrete example of the wheel rolling on a applications of the methods developed. For and acceleration diagrams and include a clear straight line for getting the idea across ? In instance, eight pages are devoted to the ele geometrical exposition of Coriolis's Law. The Fig. 53 SO should surely be shown as a small mentary theory of torsional-aileron wing flutter direct-acting engine mechanism is next treated angle instead of something like 40 deg. If as an example of a non-conservative dynamical and the various standard constructions for drawn properly the fact that the component system, and six pages to the problem of the piston acceleration are described. The import is about an axis perpendicular to the buckling of a rectangular lattice truss under ance of the higher harmonics from a resonance axis of ~ would be self-evident to the student axial load as an example of the use of linear point of view are emphasised and a simple and we should again have avoided " proceeding difference equations. At the end of each method of deriving the appropriate Fourier to the limit." chapter a number of examples is given, with series is given. A short chapter on straight line These, however, are small blemishes in a well- hints for solution where necessary. These are motions and the pantograph comes next after written book that should be of real value to framed to be interesting and useful to engineers which the subject of tooth gearing is well both students and practising engineers. It is and do not, as many textbook problems on covered in a 66 page discussion. The author well illustrated with some 379 figures, it is dynamics do, irritate the reader by asking him is to be congratulated on the clearness with reasonably priced, and the printing reaches the to work out what happens when insects of which this subject is introduced : he is a t pains high standard that Longmans Green & Co. enormous mass crawl with uniform velocity to ensure that the student understands the set themselves. along the spokes of freely rotating wheels. basic principles before proceeding to any D. W.
Aircraft Engineering and Aerospace Technology – Emerald Publishing
Published: Sep 1, 1940
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