Analytical Mechanics Of Gears

This volume provides a solid foundation for logical gear design practices and data. Topics include an analysis of conjugate gear-tooth action, nature of the contact, and resulting gear-tooth profiles of several types of gears, plus gear teeth in action. Indispensable guide for engineers concerned with tooth geometry, manufacturing accuracies, and general design. 1949 edition.

This book explores the geometric and kinematic design of the various types of gears most commonly used in practical applications, also considering the problems concerning their cutting processes. The cylindrical spur and helical gears are first considered, determining their main geometric quantities in the light of interference and undercut problems, as well as the related kinematic parameters. Particular attention is paid to the profile shift of these types of gears either generated by rack-type cutter or by pinion-rack cutter. Among other things, profile-shifted toothing allows to obtain teeth shapes capable of greater strength and more balanced specific sliding, as well as to reduce the number of teeth below the minimum one to avoid the operating interference or undercut. These very important aspects of geometric-kinematic design of cylindrical spur and helical gears are then generalized and extended to the other examined types of gears most commonly used in practical applications, such as straight bevel gears; crossed helical gears; worm gears; spiral bevel and hypoid gears. Finally, ordinary gear trains, planetary gear trains and face gear drives are discussed. This is the most advanced reference guide to the state of the art in gear engineering. Topics are addressed from a theoretical standpoint, but in such a way as not to lose sight of the physical phenomena that characterize the various types of gears which are examined. The analytical and numerical solutions are formulated so as to be of interest not only to academics, but also to designers who deal with actual engineering problems concerning the gears

While the basic working principle and the mechanical construction of automatic transmissions has not changed significantly, increased requirements for performance, fuel economy, and drivability, as well as the increasing number of gears has made it more challenging to design the systems that control modern automatic transmissions. New types of transmissions—continuously variable transmissions (CVT), dual clutch transmissions (DCT), and hybrid powertrains—have presented added challenges. Gear shifting in today’s automatic transmissions is a dynamic process that involves synchronized torque transfer from one clutch to another, smooth engine speed change, engine torque management, and minimization of output torque disturbance. Dynamic analysis helps to understand gear shifting mechanics and supports creation of the best design for gear shift control systems in passenger cars, trucks, buses, and commercial vehicles. Based on the authors’ graduate-level teaching material, this well-illustrated book relays how the fundamental principles of hydraulics and control systems are applied to today’s automatic transmissions. It opens with coverage of basic automatic transmission mechanics and then details dynamics and controls associated with modern automatic transmissions. Topics covered include: gear shifting mechanics and controls, dynamic models of planetary automatic transmissions, design of hydraulic control systems, learning algorithms for achieving consistent shift quality, torque converter clutch controls, centrifugal pendulum vibration absorbers, friction launch controls, shift scheduling and integrated powertrain controls, continuously variable transmission ratio controls, dual-clutch transmission controls, and more. The book includes many equations and clearly explained examples. Sample Simulink models of various transmission mechanical, hydraulic and control subsystems are also provided. Chapter Two, which covers planetary gear automatic transmissions, includes homework questions, making it ideal for classroom use. In addition to students, new engineers will find the book helpful because it provides the basics of transmission dynamics and control. More experienced engineers will appreciate the theoretical discussions that will help elevate the reader’s knowledge. Although many automatic transmission-related books have been published, most focus on mechanical construction, operation principles, and control hardware. None tie the dynamic analysis, control system design, and analytic investigation of the mechanical, hydraulic, and electronic controls as does this book.

Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler’s dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves. Bridges theory and practice by providing readers techniques for solving common problems through mechanical, electrical, and electromechanical models alongside the underlying theoretical foundations Describes variable mass, non-inertial systems, dynamic Euler’s equations, gyroscopes, and other related topics Includes a broad offering of practical examples, problems, and exercises across an array of engineering disciplines

The first book of its kind, Theory of Gearing: Kinematics, Geometry, and Synthesis systematically develops a scientific theory of gearing that makes it possible to synthesize novel gears with the desired performance. Written by a leading gearing expert who holds more than 200 patents, it presents a modern methodology for gear design. The proposed theory is based on a key postulate: all the design parameters for an optimal gear pair for a particular application can be derived from (a) a given configuration of the rotation vectors of the driving and driven shafts and (b) the power transmitted by the gear pair. This allows engineers to synthesize the desired gear pairs with only the following input information: The rotation and torque on the driving shaft The configuration of the driven shaft in relation to the driving shaft The desired rotation and torque of the driven shaft Beginning with the fundamentals, the book reconsiders the basic theory of kinematics and geometry of gears to provide a sound basis for the evaluation and development of future designs. It then examines ideal and real gearing for parallel-axis, intersected-axis, and crossed-axis gearing. The book addresses how to minimize vibration and noise in gears, discusses aspects of implementing the theory of gearing, and analyzes principal features of power transmission and the loading of gear teeth. More than 500 figures clearly illustrate the principles. This is an invaluable resource for engineers and researchers who work in gear design, gear production, and the application of gears as well as for students in mechanical and manufacturing engineering. Covering all known gear designs, this book offers an analytical solution to the problem of designing optimal gear pairs for any given application. It also encourages researchers to further develop the theory of gearing.

The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

This updated and enlarged Second Edition provides in-depth, progressive studies of kinematic mechanisms and offers novel, simplified methods of solving typical problems that arise in mechanisms synthesis and analysis - concentrating on the use of algebra and trigonometry and minimizing the need for calculus.;It continues to furnish complete coverag