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Advanced mechanism
244
J. S. B e g g s : A d v a n c e d M e c h a n i s m . Macmillan, New York, Collier Macmillan, L o n d o n , 1966. 111 figs., xiv + 270 pp. Chapter 1. Coordinates and Components (Vector components; transformation matrices; Euler angles; point moving on a spatial curve) Chapter 2. Displacement of a Rigid Body (Chasles's theorem; revolute, translation and screw matrices and their transformations; successive displacements and chains of screws; dual numbers and quaternions) Chapter 3. Instantaneous screws (Spatial dual of the Kennedy-Aronhold theorem; location of instantaneous screws; angular accelerations) Chapter 4. Kinematics (Some useful basic theorems; motion in a plane; approximating path shapes; contacting surfaces) Chapter 5. Graphical Analysis of Mechanism (Vector equations of velocity, acceleration and jerk; locating instantaneous centres; solving vector equations by trial positions; spatial double-slide mechanism) Chapter 6. Matrix Methods of Analysis (Four-bar spatial linkage; linkage with one revolute and three cylindrical pairs; Bennett mechanism; bent-shaft universal joint; swash-plate with toroidal follower) Chapter 7. Design of Mechanisms (Gear profile as an envelope; constant breadth cam; constant velocity coupling with skew shafts, design using complex numbers and graphical techniques; synthesis by vector algebra; design ofa rendez-vous simulator) Chapter 8. Dynamics of Mechanism (Rigid body dynamics; balancing of rotating bodies and mechanisms; dynamics of a spatial mechanism; reaction of mechanisms on a space vehicle; gyroscopic sensing devices) Chapter 9. Transmission o f Forces in a Mechanism (Energy methods; mass-less free-body diagrams; torques on a stable platform) Chapter 10. Inertial Stresses (Their graphical and analytical determination) Chapter 11. Machining of Surfaces (Envelope of successive cutter positions; a milling problem; grinding an acme thread; worm-wheel tooth; undercutting and interference; developable and ruled surfaces) Chapter 12. Kinematics of Geometrical Optics (Mirror-image kinematics; an airborne heliostat) Appendices (on unusual trigonometrical identities, including versines, and on Euler angles) References (fifteen dissertations and theses, reviews and indexes, twenty three papers, and fifty five books covering applied mathematics, dynamics, mechanisms, design; some of these references are important works in German and Russian; one is Beggs's own earlier book, Mechanism (McGrawHill, 1955), useful as preliminary reading for the present text)
THE MAJOR strength o f this b o o k lies in its unfolding o f analytical techniques and demonstrating h o w they can be applied to planar and spatial mechanisms and related devices. It is the first b o o k in English with specific emphasis o n spatial mechanisms, and the author has obviously put an e n o r m o u s a m o u n t o f effort into writing it. Professor Beggs's inspiration has clearly come f r o m the work he has been engaged on in recent years at the University of California, Los Angeles, n o w distilled into his graduate course in advanced kinematics; also f r o m his association with the Douglas Aircraft C o r p o r a t i o n as consultant. A u t h o r and publisher should b o t h be congratulated on p r o d u c i n g a b o o k that is well set out, with excellent illustrations, and is noticeably free f r o m misprints; Advanced Mechanism should long remain an i m p o r t a n t milestone in the literature o f kinematics o f mechanisms.
245
The power of the matrix transformation is amply demonstrated in many contexts in this book. Some of the material is remarkably new, and it is good to have a textbook so well up-to-date. As can be seen from the synopsis of contents, the book is divided according to the kinds of technique that can be used in solving problems of design or analysis. It is hard to see how the book could have been arranged otherwise and still retain the character that the author must have intended, but this ordering of the material does lead to 'mechanism' being presented as illustration of the method rather than the other way round. It is taken for granted that the reader has a good general grounding in mechanism, including spatial mechanisms, so that he can judge for himself why the particular examples are selected from the broad field. The reviewer fears that some hopeful engineers might pick up this book and be discouraged when they discover they are a few laps behind. A good mathematical background is expected of the reader. Though not often stated, it is certainly implied that a digital computer is often a necessary adjunct if the methods presented are to yield practical results. In trying to sum up a book like this, a reviewer can hardly resist the temptation to air some of his personal views at the expense of those of the author. There could, your reviewer feels, have been more to give the reader a real practical feel for mechanical movements--a larger number of pictures of actual hardware, for instance, and even greater emphasis on down-to-earth graphical and elementary vector resolution, especially to assist in the extremely difficult problem of visualizing the way spatial mechanisms function. There could also have been more pages devoted to categorising mechanisms, whether by type, mobility, or application, emphasising more the descriptive and qualitative properties to counterbalance the predominantly analytical flavour. Mobility criteria, such as that attributed to Kutzbach, only get a sidelong glance. And, when concentrating on his analytical techniques, the author does not altogether avoid being enigmatic when, for instance, he introduces topics like curvature theory or dual numbers in so few pages that a reader seeking enlightenment would be hard put to pick out a fully connected argument, let alone a complete one. But this is a book with a personal bias, and why should it not have one, particularly when it is written by a man of remarkable authority in a field that, at least at the present time, is notably free from established traditions in educational methods? The subject badly needs to catch on with the engineering designer and be talked about much more in the wide engineering world. Professor Beggs has done a sterling job in filling a gap, and many educators and practising engineers should welcome this book as a stimulating and scholarly contribution to learning. K. H. HUNT
J. S. B e g g s : A d v a n c e d M e c h a n i s m . Macmillan, New York, Collier Macmillan, L o n d o n , 1966. 111 figs., xiv + 270 pp. Chapter 1. Coordinates and Components (Vector components; transformation matrices; Euler angles; point moving on a spatial curve) Chapter 2. Displacement of a Rigid Body (Chasles's theorem; revolute, translation and screw matrices and their transformations; successive displacements and chains of screws; dual numbers and quaternions) Chapter 3. Instantaneous screws (Spatial dual of the Kennedy-Aronhold theorem; location of instantaneous screws; angular accelerations) Chapter 4. Kinematics (Some useful basic theorems; motion in a plane; approximating path shapes; contacting surfaces) Chapter 5. Graphical Analysis of Mechanism (Vector equations of velocity, acceleration and jerk; locating instantaneous centres; solving vector equations by trial positions; spatial double-slide mechanism) Chapter 6. Matrix Methods of Analysis (Four-bar spatial linkage; linkage with one revolute and three cylindrical pairs; Bennett mechanism; bent-shaft universal joint; swash-plate with toroidal follower) Chapter 7. Design of Mechanisms (Gear profile as an envelope; constant breadth cam; constant velocity coupling with skew shafts, design using complex numbers and graphical techniques; synthesis by vector algebra; design ofa rendez-vous simulator) Chapter 8. Dynamics of Mechanism (Rigid body dynamics; balancing of rotating bodies and mechanisms; dynamics of a spatial mechanism; reaction of mechanisms on a space vehicle; gyroscopic sensing devices) Chapter 9. Transmission o f Forces in a Mechanism (Energy methods; mass-less free-body diagrams; torques on a stable platform) Chapter 10. Inertial Stresses (Their graphical and analytical determination) Chapter 11. Machining of Surfaces (Envelope of successive cutter positions; a milling problem; grinding an acme thread; worm-wheel tooth; undercutting and interference; developable and ruled surfaces) Chapter 12. Kinematics of Geometrical Optics (Mirror-image kinematics; an airborne heliostat) Appendices (on unusual trigonometrical identities, including versines, and on Euler angles) References (fifteen dissertations and theses, reviews and indexes, twenty three papers, and fifty five books covering applied mathematics, dynamics, mechanisms, design; some of these references are important works in German and Russian; one is Beggs's own earlier book, Mechanism (McGrawHill, 1955), useful as preliminary reading for the present text)
THE MAJOR strength o f this b o o k lies in its unfolding o f analytical techniques and demonstrating h o w they can be applied to planar and spatial mechanisms and related devices. It is the first b o o k in English with specific emphasis o n spatial mechanisms, and the author has obviously put an e n o r m o u s a m o u n t o f effort into writing it. Professor Beggs's inspiration has clearly come f r o m the work he has been engaged on in recent years at the University of California, Los Angeles, n o w distilled into his graduate course in advanced kinematics; also f r o m his association with the Douglas Aircraft C o r p o r a t i o n as consultant. A u t h o r and publisher should b o t h be congratulated on p r o d u c i n g a b o o k that is well set out, with excellent illustrations, and is noticeably free f r o m misprints; Advanced Mechanism should long remain an i m p o r t a n t milestone in the literature o f kinematics o f mechanisms.
245
The power of the matrix transformation is amply demonstrated in many contexts in this book. Some of the material is remarkably new, and it is good to have a textbook so well up-to-date. As can be seen from the synopsis of contents, the book is divided according to the kinds of technique that can be used in solving problems of design or analysis. It is hard to see how the book could have been arranged otherwise and still retain the character that the author must have intended, but this ordering of the material does lead to 'mechanism' being presented as illustration of the method rather than the other way round. It is taken for granted that the reader has a good general grounding in mechanism, including spatial mechanisms, so that he can judge for himself why the particular examples are selected from the broad field. The reviewer fears that some hopeful engineers might pick up this book and be discouraged when they discover they are a few laps behind. A good mathematical background is expected of the reader. Though not often stated, it is certainly implied that a digital computer is often a necessary adjunct if the methods presented are to yield practical results. In trying to sum up a book like this, a reviewer can hardly resist the temptation to air some of his personal views at the expense of those of the author. There could, your reviewer feels, have been more to give the reader a real practical feel for mechanical movements--a larger number of pictures of actual hardware, for instance, and even greater emphasis on down-to-earth graphical and elementary vector resolution, especially to assist in the extremely difficult problem of visualizing the way spatial mechanisms function. There could also have been more pages devoted to categorising mechanisms, whether by type, mobility, or application, emphasising more the descriptive and qualitative properties to counterbalance the predominantly analytical flavour. Mobility criteria, such as that attributed to Kutzbach, only get a sidelong glance. And, when concentrating on his analytical techniques, the author does not altogether avoid being enigmatic when, for instance, he introduces topics like curvature theory or dual numbers in so few pages that a reader seeking enlightenment would be hard put to pick out a fully connected argument, let alone a complete one. But this is a book with a personal bias, and why should it not have one, particularly when it is written by a man of remarkable authority in a field that, at least at the present time, is notably free from established traditions in educational methods? The subject badly needs to catch on with the engineering designer and be talked about much more in the wide engineering world. Professor Beggs has done a sterling job in filling a gap, and many educators and practising engineers should welcome this book as a stimulating and scholarly contribution to learning. K. H. HUNT