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have been determined. What is included is a clear, concise presentation of the application of matrix methods to many types of vibration analyses.

Beginning with definitions of matrix terms and basic manipulation, the reader is led through the essentials of determinants, partitioning, inversion and column interchanging. Devoid of all general theorems and proofs, these concepts appear so uncomplicated as to startle the reader who has learned linear algebra in a more rigorous form. A brief treatment is also given to the use of transfer matrices.

Digital computer programming is introduced by specific examples applied to matrix manipulation and vibration problems. This appears to be an effective method for a beginner to develop an appreciation of computer use before confronting the full array of programming dos, don'ts and options. Subjects included range from flow charts to the use of subroutines, polynomial solutions, multi-dimensional arrays and matrix inversion.

Clearly illustrated vibration analyses are presented, covering a wide range of lumped-mass linear systems. Free vibration as well as forced vibration is discussed, including viscous damping, coupled modes, and phase relationships in multi mass and spring combinations. As illustrations of the use of the transfer matrix method, beams with distributed mass and multiple flexible supports are analyzed.

In a chapter on the analysis of lumped mass torsional systems, a broad coverage of undamped resonant frequencies and mode shapes is presented. Stepped shafts, geared systems and branched geared arrangements are solved by the traditional Holzer and Stodola methods, while matrix methods are illustrated only on a simple shaft. This is an unfortunate limitation, since the matrix method is particularly well suited to the analysis of complex branched and geared arrangements.

Though a single page of quality text is undoubtedly worth more than a ream of drivel, this book seems considerably more expensive at $16.75 than its size or content warrants. It is, after all, only 206 small pages; with generous spacing and many space-consuming matrix equations. If one can afford this price for excellence, the book would serve well for independent study in the use of matrix techniques. It could also serve as a text for a second course in vibrations, but would require some supplemental material to fill a complete semester course.

JOSEPH A. DOPKIN Supervising Engineer,

Solid Mechanics Ingersoll-Rand Research Inc. Princeton, NJ 08540, U.S.A.

Seventh all-Union Conference on Basic Problems in the Theory of Machines and Mechanisms, Proceedings--Tbilisi, 16-18 September 1974; Technical Editor, D. S. Tavkhetidze. Published in Moscow and Tbilisi by the Academy of Sciences, U.S.S.R., and the Academy of Sciences of the Georgian Republic, 1974, 131 pp. paperback (in the Russian language.)

THIS SMALL volume contains the proceedings of the most recent in the series of Soviet Union's quadriennial conferences on ToMM, held under the general leadership of Academician Artobolevskii. The previous one, which took place in Leningrad, had become so large that a complete change of style was decreed. At this conference were presented only a dozen invited special lectures by recognized Soviet authorities on all the aspects of the theory of machines and mechanisms: these portray a clear picture of current Soviet thinking on the dynamics and vibration

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problems of machinery, including automatics, those with varying parameters, and with hydraulic or pneumatic control systems, on man-machine systems, manipulators and robotics, on experimental methods, on synthesis of mechanisms, on the theory of spatial mechanisms and on the history of ToMM.

F. R. E. CROSSLEY Professor

University of Massachussetts U.S.A.

Theory and Practice of Robots and Manipulators--Proceedings of the First CISM-IFToMM Symposium, Springer Verlag, Vienna, New York; 1974, 2volumes, 306 + 364 pp., paper backor hard cover.

THESE proceedings cover one of the most successful, limited attendance conferences in which many well-known international scientists with this specialty participated. The symposium was held on 5-8 September 1973 in the CISM Center, Udine, Italy; the proceedings comprise 45 papers, allin the English language.

The first volume contains two opening addresses by Professor Kobrinskii of the U.S.S.R. Academy of Sciences, who was conference chairman, and Professor Thring of the University of London, England, and papers in the areas of Walking Machines, Kinematics and Dynamics, Biomechanics of Motion and Man-Machine Systems. The second volume holds works on Artificial Intelligence, Applications, Control of Motion and a survey paper.

Among the authors included here are:

from Japan from Yugoslavia from West Germany from France from England from Poland from U.S.S.R.

and from U.S.A.

Kato, Sato, Umetani and Yamashito; Tomovic, Vukobratovic and Gavrilovic; Warnecke, Roesler, Paeslack and Muehlenfeld; Vertut--and Italy--Cappuzzo, Luccio; Thring, Parks and Young; Morecki--and Bulgaria--Konstantinov; Artobolevskii, Popov, Kukhtenko, Kobrinskii, Bessonov, Umnov, Gurfinkel, Shishmarev, Ignatiev, Radchenko, Lukishov, Dorokhov, Kuleshov; Roth, Sheridan, Whitney, Nevins, Heer, Deutsch, Flateau, McGhee, Malone, Gill, Paul, Alexander, Weltman, Kugath, Wilt and Moe.

The volumes are profusely illustrated with diagrams and with photographs, some such as the Japanese Waseda Wabot I, being in color. The kinematics of walking, various rate-control schemes for arm-like manipulators, robot vision as a feedback control factor, optical and touch sensors, the meaning of dexterity, details of design of arms and legs, a Russian six-legged vehicle and a Japanese device with serpentine locomotion, are the subjects of many of the papers.