Elementary mechanism

ELEMENTARY MECHANISM
A TEXT-BOOK FOR STUDENTS OF MECHANICAL ENGINEERING.
BY ARTHUR T. WOODS AND ALBERT W. STAHL
NEW YORK: D. VAN NOSTBAND, PUBLISHER, 1886.
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PREFACE
Quite a number of treatises have appeared on the subject of Kinematics, or Pure Mechanism, most of which are now in print, so that a few words of explanation as to the reasons for publishing this book seem necessary.
In searching for a text-book on this subject for the use of our classes of Mechanical Engineering students, we were unable to find a book which met our requirements. Some were so vague and incomplete as to be almost useless, while others were large, exhaustive treatises, more valuable as books of reference than as text-books for the use of students. The following pages were therefore prepared in the form of lectures; the object being, to give s dear description of those mechanical movements which may be of practical use, together with the discussion of the principles upon which they depend. At the same time, all purely theoretical discussions were avoided, except where a direct practical result could be reached by their introduction. These lectures were used in our classes; and, having proved comparatively, satisfactory in that shape, it was thought best to publish them, after making such improvements as our classroom experience dictated.
We make little claim to originality of subject-matter, free use having been made of all available matter bearing on the subject. There is, in fact, very little room for such originality, the ground having been almost completely covered by previous writers. Our claim to consideration is based almost entirely on the manner in which the subject has been presented. Accuracy, clearness, and conciseness are the points that we have tried to keep constantly in view. While much has been omitted that is of merely abstract interest, yet it is believed that nearly all that is of direct practical importance will be found in these pages.
We have, in common with nearly all other writers on this subject, closely followed the general plan of Prafessor Willis "Principles of Mechanism," Other works which have been consulted and to which we are indebted are Rankine's "Machinery and Mill work," Reuleaux "LeConstructeur," and Goodeve's " Elements of Mechanism ; " and in a less degree, Belanger's " Cinematique," Beuleaux' "Kinematics of Machinery," Robinson's "Teeth of Wheels," Grant's " Teeth of Gears," Appleton's " Cycloptedia of Mechanics," and Unwin's " Elements of Machine Design."
In searching for a text-book on this subject for the use of our classes of Mechanical Engineering students, we were unable to find a book which met our requirements. Some were so vague and incomplete as to be almost useless, while others were large, exhaustive treatises, more valuable as books of reference than as text-books for the use of students. The following pages were therefore prepared in the form of lectures; the object being, to give s dear description of those mechanical movements which may be of practical use, together with the discussion of the principles upon which they depend. At the same time, all purely theoretical discussions were avoided, except where a direct practical result could be reached by their introduction. These lectures were used in our classes; and, having proved comparatively, satisfactory in that shape, it was thought best to publish them, after making such improvements as our classroom experience dictated.
We make little claim to originality of subject-matter, free use having been made of all available matter bearing on the subject. There is, in fact, very little room for such originality, the ground having been almost completely covered by previous writers. Our claim to consideration is based almost entirely on the manner in which the subject has been presented. Accuracy, clearness, and conciseness are the points that we have tried to keep constantly in view. While much has been omitted that is of merely abstract interest, yet it is believed that nearly all that is of direct practical importance will be found in these pages.
We have, in common with nearly all other writers on this subject, closely followed the general plan of Prafessor Willis "Principles of Mechanism," Other works which have been consulted and to which we are indebted are Rankine's "Machinery and Mill work," Reuleaux "LeConstructeur," and Goodeve's " Elements of Mechanism ; " and in a less degree, Belanger's " Cinematique," Beuleaux' "Kinematics of Machinery," Robinson's "Teeth of Wheels," Grant's " Teeth of Gears," Appleton's " Cycloptedia of Mechanics," and Unwin's " Elements of Machine Design."
CONTENTS.
- INTRODUCTION
- ELEMENTARY PROPOSITIONS
- COMMUNICATION OF MOTION BY ROLLING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT
- COMMUNICATION OF MOTION BY ROLLING CONTACT. VELOCITY RATIO VARYING. DIRECTIONAL RELATION CONSTANT
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY LINKWORK. VELOCITY RATIO AND DIRECTIONAL RELATION CONSTANT OR VARYING
- COMMUNICATION OF MOTION BY WRAPPING CONNECTORS. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT
- TRAINS OF MECHANISM
- AGGREGATE COMBINATIONS
- ELEMENTARY PROPOSITIONS
- COMMUNICATION OF MOTION BY ROLLING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT
- COMMUNICATION OF MOTION BY ROLLING CONTACT. VELOCITY RATIO VARYING. DIRECTIONAL RELATION CONSTANT
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY SLIDING CONTACT. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT. TEETH OF WHEELS
- COMMUNICATION OF MOTION BY LINKWORK. VELOCITY RATIO AND DIRECTIONAL RELATION CONSTANT OR VARYING
- COMMUNICATION OF MOTION BY WRAPPING CONNECTORS. VELOCITY RATIO CONSTANT. DIRECTIONAL RELATION CONSTANT
- TRAINS OF MECHANISM
- AGGREGATE COMBINATIONS
ELEMENTARY MECHANISM,
1. A Machine is a combination of fixed and movable parts, interposed between the power and the work for the purpose of adapting the one to the other. This definition presupposes the existence of two things; namely, a source of power, and a certain object to be accomplished.
2. Mechanism. In designing a machine, we must take into consideration both the motions to lie produced and the forces to be transmitted. But these two elements may most conveniently be discussed and investigated separately; and such discussions and investigations constitute the two divisions of the general subject of mechanism; namely. Pure Mechanism and Constructive Mechanism.
3. Motion and Rest. These terms are essentially relative. When a body changes its position with regard to some fixed point, it is said to be in motion relatively to that point; when no such change is taking place, it is said to be at rest relatively to that point. Two bodies may evidently be in motion relatively to a third, and still be at rest with regard to each other.
4. Path. When a point moves from one position to another, it describes a line, either straight or curved, connecting the two positions. This line is called its path. But the path atone does not completely define the motion, for the point may move in the path in either of two directions; as, up or down, to the right or to the left, in the direction of the hands of a watch or the reverse.
5. Kinds of Motion. Motion may take place along either a straight or curved path; in the former ease it is termed rectilinear motion, and in the latter case curvilinear motion. In either case, when a moving point travels forward and backward over the same path, it is said to have a reciprocating motion. For example, the piston of a locomotive has reciprocating rectilinear motion. In the particular case where the reciprocating point moves in the are of a circle, as, for example, the weight of a pendulum, it is said to oscillate, or, by some, to vibrate. When the motion of a point is interrupted by certain definite intervals of rest, it is said to have an intermittent motion. The motion of the escape wheel of a clock is of this kind.
6. Revolution and Rotation. These terms are ordinarily used synonymously, to denote the turning of a body about an axis; and no ambiguity is usually likely to arise from so using them. Thus, the fly wheel of an engine is said to rotate or revolve. By more strict definition, rotation should be applied only to the turning of a body about an axis which passes through it, while revolution is a more general term to include the motion of a body along a path which is a closed curve. Thus, the earth rotates about its axis and revolves about the sun.
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2. Mechanism. In designing a machine, we must take into consideration both the motions to lie produced and the forces to be transmitted. But these two elements may most conveniently be discussed and investigated separately; and such discussions and investigations constitute the two divisions of the general subject of mechanism; namely. Pure Mechanism and Constructive Mechanism.
3. Motion and Rest. These terms are essentially relative. When a body changes its position with regard to some fixed point, it is said to be in motion relatively to that point; when no such change is taking place, it is said to be at rest relatively to that point. Two bodies may evidently be in motion relatively to a third, and still be at rest with regard to each other.
4. Path. When a point moves from one position to another, it describes a line, either straight or curved, connecting the two positions. This line is called its path. But the path atone does not completely define the motion, for the point may move in the path in either of two directions; as, up or down, to the right or to the left, in the direction of the hands of a watch or the reverse.
5. Kinds of Motion. Motion may take place along either a straight or curved path; in the former ease it is termed rectilinear motion, and in the latter case curvilinear motion. In either case, when a moving point travels forward and backward over the same path, it is said to have a reciprocating motion. For example, the piston of a locomotive has reciprocating rectilinear motion. In the particular case where the reciprocating point moves in the are of a circle, as, for example, the weight of a pendulum, it is said to oscillate, or, by some, to vibrate. When the motion of a point is interrupted by certain definite intervals of rest, it is said to have an intermittent motion. The motion of the escape wheel of a clock is of this kind.
6. Revolution and Rotation. These terms are ordinarily used synonymously, to denote the turning of a body about an axis; and no ambiguity is usually likely to arise from so using them. Thus, the fly wheel of an engine is said to rotate or revolve. By more strict definition, rotation should be applied only to the turning of a body about an axis which passes through it, while revolution is a more general term to include the motion of a body along a path which is a closed curve. Thus, the earth rotates about its axis and revolves about the sun.
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