Engineering Kinematics

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Engineering Kinematics

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The increasing importance of the subject of dynamics to engineers demands a rigorous exploration of the division of kinematics. In the pedagogical time-table this division most frequently appears in the second year, and in the role of a course in Mechanism.

The aims and objectives of the mechanism courses concern themselves primarily with preparation for Machine Design and incidentall3 r borrow, as needed, from the formal courses in Applied Mechanics. A series of elements of mechanism is investigated, and their kinematic significance is too frequently subordinated to descriptive material as the individual packages of elements of mechanism are collected.

A more solid base can be built there are ever-present fundamentals of displacement, velocity, and acceleration, which furnish the common back ground of all mechanisms.

These concepts of kinematics are the actual and broader elements of mechanism. Cams, gears, and the other applications are but their applied form.

This text intends to pursue an objective of training in fundamentals and has therefore been constructed upon the bases of displacement, velocity, and acceleration. Mechanisms appear as illustrations, not as divisions of the subject of Engineering Kinematics. They can thus be thoroughly and effectively explored, and their appearance, at first as illustrations of dis- placement, again in applications of velocity, and later as the field of study of accelerations gives coordination to the development of strength ii| ,the study of kinematics. ...

A course in Engineering Kinematics should serve in a liaison capacity between principles expounded in Applied Mechanics, and practices explored in Machine Design. It can enhance further training in both fields.

The courses in Applied Mechanics cannot, in the portion devoted to kinematics, thoroughly explore the applications of principle to specific mechanisms; the courses in Machine Design should not advance to a consideration of the stress distribution, choice of material, methods of lubrication of machine parts before a real foundation of the kinematic significance of those parts has been laid.

The author does not claim any originality in the choice of material from the field usualty covered in the courses in Mechanisms. The departure from tradition has been pedagogical — none of the elements of mechanism are explored before a solid foundation of the general.

TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION 1
II. THE RIGID BODY OF MECHANICS 3
Rigid Body. Rigid Body of Kinematics.
III. VECTORS 6
Vector Quantities. Graphical Representation. The Resultant — Addition of Vectors. Vector Addition by Parallelogram. Subtraction of Vectors. Components of Vectors — Resolution. Rectangular Components. Analytical Method. Orthogonal Components. Theorems of Orthogonal Components.
IV. MOTION 27
Kinematics. Mechanisms and Machines. Cams. Direct-Contact Bodies. Flexible Connectors. Gearing. Screws. Rigid-Connector Mechanisms — Link-Work. Change of Position — Relative Motion.
Degrees of Freedom — Constraint. Translation. Rotation. PlaneMotion. Helical Motion. Spherical Motion. Intermittent Motion.
V. DISPLACEMENT 48
Linear Displacement. Angular Displacement. Relationship between Linear and Angular Displacements. Cams — Geometrical Design for Displacements. Cams — Offset Axis. Positive Motion Cams, Cylindrical Cams. Screw Threads — Differential Screws. Absolute and Relative Displacements.
VI. VELOCITY . . : . 81
Velocity. Linear Velocity. Graphical Calculus — Differentiation.
Graphical Integration. Angular Velocity. Relationship between Linear and Angular Velocity. Graphical Analysis of Velocity Vectors.
Instantaneous Axis of Velocities. Velocity Analysis of Plane Motion Combined Translation and Rotation. Absolute and Relative Velocity.
Sliding Contact. The Instantaneous Axis of Sliding Contact. Rolling Contact. The Instantaneous Axis of Rolling Contact. Friction Wheels — Rolling Bodies. Rolling Cylinders. Rolling Cones. Discand-heel. Non-Circular Rolling Bodies. Series of Rolling Bodies.
Flexible Connectors. Belt Drives. Variable-Speed Belt Drives.
Chain Drives. Flexible Connectors in Hoisting Tackle. Gearing —Definitions and Terminology. Fundamental Law of Tooth Profile.
Sliding Contact in Gear Teeth. Conjugate Curves. The Involute Tooth Profile. Involute Gear Teeth. Relationships in Involute Gearing. Limiting Conditions in Involute Gears. Change in Line of