Geometry, Perspective Drawing, and Mechanisms

Author: Don Row,Talmage James Reid

Publisher: World Scientific

ISBN: 981434382X

Category: Mathematics

Page: 328

View: 4346

The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter. The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.

Distinguished Figures in Descriptive Geometry and Its Applications for Mechanism Science

From the Middle Ages to the 17th Century

Author: Michela Cigola

Publisher: Springer

ISBN: 3319201972

Category: Technology & Engineering

Page: 248

View: 9675

This book consists of chapters that focus specifically on single figures that worked on Descriptive Geometry and also in Mechanisms Sciences and contain biographical notes, a survey of their work and their achievements, together with a modern interpretation of their legacy. Since Vitruvius in ancient times, and with Brunelleschi in the Renaissance, the two disciplines began to share a common direction which, over the centuries, took shape through less well-known figures until the more recent times in which Gaspard Monge worked. Over the years, a gap has been created between Descriptive Geometry and Mechanism Science, which now appear to belong to different worlds. In reality, however, there is a very close relationship between the two disciplines, with a link based on extremely solid foundations. Without the theoretical foundations of Geometry it would not be possible to draw and design mechanical parts such as gears, while in Kinematics it would be less easy to design and predict the reciprocal movements of parts in a complex mechanical assembly.

Geometry: The Line and the Circle

Author: Maureen T. Carroll,Elyn Rykken

Publisher: American Mathematical Soc.

ISBN: 1470448432

Category: Geometry

Page: 480

View: 3127

Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.

Mechanism, Mentalism and Metamathematics

An Essay on Finitism

Author: J. Webb

Publisher: Springer Science & Business Media

ISBN: 940157653X

Category: Philosophy

Page: 285

View: 8746

This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under mine certain strong arguments against these positions precisely by invok ing G6del's and related work. I also began to realize that the Church Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor ganizing it in the direction of the present book.

Engineering Drawing and Design

Author: David A. Madsen

Publisher: Arden Shakespeare

ISBN: N.A

Category: Engineering design

Page: 960

View: 9198

Offering complete coverage of all the elements of drafting, this second edition remains the most up-to-date compendium on engineering drawing and design available. Based on the latest ANSI/ASME standards, this encyclopedic resource spans the engineering disciplines, including fluid power, structural, civil, electrical, piping, and HVAC/sheet metal. Includes updated CADD applications. 1,400 illus.

Mechanisms and Mechanical Devices Sourcebook, Fourth Edition

Author: Neil Sclater,Nicholas Chironis

Publisher: McGraw-Hill Prof Med/Tech

ISBN: 0071467610

Category: Technology & Engineering

Page: 512

View: 1908

Over 2000 drawings make this sourcebook a gold mine of information for learning and innovating in mechanical design The fourth edition of this unique engineering reference book covers the past, present, and future of mechanisms and mechanical devices. Among the thousands of proven mechanisms illustrated and described are many suitable for recycling into new mechanical, electromechanical, or mechatronic products and systems. Overviews of robotics, rapid prototyping, MEMS, and nanotechnology will get you up-to-speed on these cutting-edge technologies. Easy-to-read tutorial chapters on the basics of mechanisms and motion control will introduce those subjects to you or refresh your knowledge of them. Comprehensive index to speed your search for topics of interest Glossaries of terms for gears, cams, mechanisms, and robotics New industrial robot specifications and applications Mobile robots for exploration, scientific research, and defense INSIDE Mechanisms and Mechanical Devices Sourcebook, 4th Edition Basics of Mechanisms • Motion Control Systems • Industrial Robots • Mobile Robots • Drives and Mechanisms That Include Linkages, Gears, Cams, Genevas, and Ratchets • Clutches and Brakes • Devices That Latch, Fasten, and Clamp • Chains, Belts, Springs, and Screws • Shaft Couplings and Connections • Machines That Perform Specific Motions or Package, Convey, Handle, or Assure Safety • Systems for Torque, Speed, Tension, and Limit Control • Pneumatic, Hydraulic, Electric, and Electronic Instruments and Controls • Computer-Aided Design Concepts • Rapid Prototyping • New Directions in Mechanical Engineering

The Geometry of Biological Time

Author: Arthur T. Winfree

Publisher: Springer Science & Business Media

ISBN: 9780387989921

Category: Mathematics

Page: 779

View: 1693

Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.

Perceiving in Depth, Volume 3: Other Mechanisms of Depth Perception

Author: Ian P. Howard

Publisher: Oxford University Press

ISBN: 019987736X

Category: Psychology

Page: 400

View: 8879

The three-volume work Perceiving in Depth is a sequel to Binocular Vision and Stereopsis and to Seeing in Depth, both by Ian P. Howard and Brian J. Rogers. This work is much broader in scope than the previous books and includes mechanisms of depth perception by all senses, including aural, electrosensory organs, and the somatosensory system. Volume 1 reviews sensory coding, psychophysical and analytic procedures, and basic visual mechanisms. Volume 2 reviews stereoscopic vision. Volume 3 reviews all mechanisms of depth perception other than stereoscopic vision. The three volumes are extensively illustrated and referenced and provide the most detailed review of all aspects of perceiving the three-dimensional world. Volume 3 addresses all depth-perception mechanisms other than stereopsis. The book starts with an account of monocular cues to depth, including accommodation, vergence eye movements, perspective, interposition, shading, and motion parallax. A chapter on constancies in depth perception, such as the ability to perceive the sizes and shapes of objects as they move or rotate in depth, is followed by a chapter on the ways in which depth cues interact. The next chapter reviews sources of information, such as changing disparity, image looming, and vergence eye movements, used in the perception of objects moving in depth. Various pathologies of depth perception, including visual neglect, stereoanomalies, and albanism are reviewed. Visual depth-perception mechanisms through the animal kingdom are described, starting with insects and progressing through crustaceans, fish, amphibians, reptiles, birds, and mammals. The chapter includes a discussion of how stereoscopic vision may have evolved. The next chapter describes how visual depth perception is used to guide reaching movements of the hand, avoiding obstacles, and walking to a distant object. The next three chapters review non-visual mechanisms of depth perception. Auditory mechanisms include auditory localization, echolocation in bats and marine mammals, and the lateral-line system of fish. Some fish emit electric discharges and then use electric sense organs to detect distortions of the electric field produced by nearby objects. Some beetles and snakes use heat-sensitive sense organs to detect sources of heat. The volume ends with a discussion of mechanisms used by animals to navigate to a distant site. Ants find their way back to the nest by using landmarks and by integrating their walking movements. Several animals navigate by the stars or by polarized sunlight. It seems that animals in several phyla navigate by detecting the Earths magnetic field.

Art and Representation

New Principles in the Analysis of Pictures

Author: John Willats

Publisher: Princeton University Press

ISBN: 9780691087375

Category: Art

Page: 394

View: 9671

"All art historians and critics as well as psychologists interested in drawing or painting will need to become familiar with Willats's approach. Art and Representation will create a considerable stir and will change the way both critics and the public think about art." Stuart Sutherland, Sussex UniversityIn Art and Representation, John Willats presents a radically new theory of pictures. To do this, he has developed a precise vocabulary for describing the representational systems in pictures: the ways in which artists, engineers, photographers, mapmakers, and children represent objects. His approach is derived from recent research in visual perception and artificial intelligence, and Willats begins by clarifying the key distinction between the marks in a picture and the features of the scene that these marks represent. The methods he uses are thus closer to those of a modern structural linguist or psychoanalyst than to those of an art historian. Using over 150 illustrations, Willats analyzes the representational systems in pictures by artists from a wide variety of periods and cultures. He then relates these systems to the mental processes of picture production, and, displaying an impressive grasp of more than one scholarly discipline, shows how the Greek vase painters, Chinese painters, Giotto, icon painters, Picasso, Paul Klee, and David Hockney have put these systems to work. But this book is not only about what systems artists use but also about why artists from different periods and cultures have used such different systems, and why drawings by young children look so different from those by adults. Willats argues that the representational systems can serve many different functionsbeyond that of merely providing a convincing illusion. These include the use of anomalous pictorial devices such as inverted perspective, which may be used for expressive reasons or to distance the viewer from the depicted scene by drawing attention to the picture as a painted surface. Willats concludes that art historical changes, and the developmental changes in children's drawings, are not merely arbitrary, nor are they driven by evolutionary forces. Rather, they are determined by the different functions that the representational systems in pictures can serve.Like readers of Ernst Gombrich's famous Art and Illusion (still available from Princeton University Press), on which Art and Representation makes important theoretical advances, or Rudolf Arnheim's Art and Visual Perception, Willats's readers will find that they will never again return to their old ways of looking at pictures.