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# Bicycles & Tricycles: A Classic Treatise on Their Design and Construction

560## Overview

Up until the publication of this book in 1896, no comparable work existed on the science, design, and mechanics of the bicycle — an invention that revolutionized transportation for the average person and had far-reaching social and economic consequences. While other books on the bicycle have been written since, this late-19th-century classic remains unsurpassed in the thorough, accurate, and highly accessible coverage of every aspect of bicycle design and construction. Over 560 illustrations, diagrams, figures, and tables complement an exhaustive examination of such topics as the development of cycles, kinematics, stability, steering, the frame, gears, stresses, mechanical components, and much more. A marvel of scientific exposition for its time, this fascinating treatise will attract a wide audience of readers interested in technology and invention as well as serious and competitive cyclists, bicycle designers, and collectors.

## Related collections and offers

## Product Details

ISBN-13: | 9780486429878 |
---|---|

Publisher: | Dover Publications |

Publication date: | 11/02/2011 |

Series: | Dover Transportation |

Pages: | 560 |

Product dimensions: | 5.50(w) x 8.50(h) x (d) |

## Read an Excerpt

#### Bicycles & Tricycles

#### An Elementary Treatise on Their Design and Construction

**By Archibald Sharp**

**Dover Publications, Inc.**

**Copyright © 1977 The Massachusetts Institute of Technology**

All rights reserved.

ISBN: 978-0-486-14278-4

All rights reserved.

ISBN: 978-0-486-14278-4

CHAPTER 1

*FUNDAMENTAL CONCEPTIONS OF MECHANICS*

**1. Division of the Subject.**—*Geometry* is the science which treats of relations in space. *Kinematics* treats of space and time, and may be called the geometry of motion. *Dynamics* is the science which deals with force, and is usually divided into two parts—statics, dealing with the forces acting on bodies which are at rest; kinetics, dealing with forces acting on bodies in motion. *Mechanics* includes kinematics, statics, kinetics, and the application of these sciences to actual structures and machines.

**2. Space.**—The fundamental ideas of time and space form part of the foundation of the science of mechanics, and their accurate measurement is of great importance. The British unit of length is the *imperial yard*, defined by Act of Parliament to be the length between two marks on a certain metal bar kept in the office of the Exchequer, when the whole bar is at a temperature of 60° Fahrenheit. Several authorised copies of this standard of length are deposited in various places. The original standard is only disturbed at very distant intervals, the authorised copies serving for actual comparison for purposes of trade and commerce. The yard is divided into three *feet*, and the foot again into twelve *inches*. Feet and inches are the working units in most general use by engineers. The inch is further subdivided by engineers, by a process of repeated division by two, so that 1/2", 1/4", 1/8", 1/16", &c., are the fractions generally used by them. A more convenient subdivision is the decimal system into 1/10, 1/100, 1/1000, &C.; this is the subdivision generally used for scientific purposes.

The unit of length generally used in dynamics is the foot*.*

*Metric System.*—The metric system of measurement in general use on the Continent is founded on the *metre*, originally defined as the 1/10,000,000 part of a quadrant of the earth from the pole to the equator. This length was estimated, and a standard constructed and kept in France. The metre is subdivided into ten parts called decimetres, a decimetre into ten centimetres, and a centimetre into ten millimetres. For great lengths a kilometre, equal to a thousand metres, is the unit employed.

1 metre = 39·371 inches = 32809 feet.

1 kilometre = 062138 miles.

1 inch = 253995 millimetres.

1 mile = 160931 kilometres.

3. **Time.**—The measurement of time is more difficult theoretically than that of space. Two different rods may be placed alongside each other, and a comparison made as to their lengths, but two different portions of time cannot be compared in this way. 'Time passed cannot be recalled.'

The measurement of time is effected by taking a series of events which occur at certain intervals. If the time between any two consecutive events leaves the same impression as to duration on the mind as that between any other two consecutive events, we may consider, tentatively at least, that the two times are equal. The standard of time is the *sidereal day*, which is the time the earth takes to make one complete revolution about its own axis, and which is determined by observing the time from the apparent motion of a fixed star across the meridian of any place to the same apparent motion on the following day. The intervals of time so measured are as nearly equal as our means of measurement can determine.

The *solar day* is the interval of time between two consecutive apparent movements of the sun across the meridian of any place. This interval of time varies slightly from day to day, so that for purposes of everyday life an average is taken, called the *mean solar day*. The mean solar day is about four minutes longer than the sidereal day, owing to the nature of the earth's motion round the sun.

The mean solar day is subdivided into twenty-four *hours*, one hour into sixty *minutes*, and one minute into sixty *seconds*. The second is the unit of time generally used in dynamics.

4. **Matter.**—Another of our fundamental ideas is that relating to the existence of matter. The question of the measurement of quantity of matter is inextricably mixed up with the measurement of force. The *mass*, or quantity of matter, in one body is said to be greater or less than that in another body, according as the force required to produce the same effect is greater or less. The mass of a body is practically estimated by its weight, which is, strictly speaking, the force with which the earth attracts it. This force varies slightly from place to place on the earth's surface at sea level, and again as the body is moved above the sea level. Thus, the mass and the weight of a body are two totally different things; and many of the difficulties encountered by the student of mechanics are due to want of proper appreciation of this. The difficulty arises from the fact that the *pound* is the unit of matter, and that the *weight* of this quantity of matter, *i.e.* the force by which the earth attracts it, is used often as a unit of force. A certain quantity of lead will have a certain weight, as shown by a spring-balance, in London at high level water-mark, and quite a different weight if taken twenty thousand feet above sea level, although the mass is the same in both places.

The British unit of mass is the imperial *pound*, defined by Act of Parliament to be the quantity of matter equal to that of a certain piece of platinum kept in the office of the Exchequer.

: The unit of mass in the metrical system of measurement is the *gramme*, originally defined to be equal to the mass of a cubic centimetre of distilled water of maximum density. This is, however, defined practically, like the British unit, as that of a certain piece of platinum kept in Paris.

*SPEED, RATE OF CHANGE OF SPEED, VELOCITY, ACCELERATION, FORCE, MOMENTUM*

5. **Speed.**—A body in relation to its surroundings may either be at rest or in motion. *Linear speed* is the rate at which a body moves along its path.

Speed may be either *uniform* or *variable*. With uniform speed the body passes over equal spaces in equal times; with variable speed the spaces passed over in equal times are unequal. The motion may be either in a straight or curved path, but in both cases we may still speak of the *speed* of a point as the rate at which it moves along its path.

6. **Uniform Speed** is measured by the space passed over in the unit of time. The unit of speed is one foot per second. Let *s* be the space moved over by the body moving with uniform speed in the time *t*, then if *v* be the speed, we have by the above definition.

*v = s/t* · · · · (1)

*Example.*—If a bicycle move through a space of one mile in four minutes we have, reducing to feet and seconds,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

It will be seen that the unit of speed is a compound one, involving two of the fundamental units, space and time.

In the above example, the same speed is obtained whatever be the time over which we make the observations of the space described. For example, in one minute the bicycle will move through a distance of a quarter of a mile, that is 440 yards, or 3 × 440 feet. Using formula (1) we get

*v* = 1320/60 = 22 feet per second,

the same result as before.

Now, consider the space described by the bicycle in a small fraction of a second, say 1/10th, if the speed is uniform, this will be 2·2 ft. Using formula (1) again, we have

*v* = 2 · 2/1/10 = 22 feet per second.

Proceeding to a still smaller fraction of a second, say 1/1000th, if our means of observation were sufficiently refined, the distance passed over in the time would evidently be found to be the 22/1000th part of a foot, *i.e.* = ·022 feet. Again using formula (1) we have

v = 022/1/1000 = 22 feet per second.

*Uniform Motion in a Circle.*—Another familiar example of uniform motion is that of a point moving in a circular path; a point on the rim of a bicycle wheel has, relative to the frame of the bicycle, such a motion, uniform when the speed of the bicycle is uniform. The linear speed, relative to the frame, of a point on the extreme outside of the tyre will be the same as the linear speed of the bicycle along and relative to the road, while that of any point nearer the centre of the wheel will be less.

7. **Angular Speed.**—When a wheel is rotating about its axis, the linear speed of any point on it depends on its distance from the centre, is greatest when the point is on the circumference of the wheel, and is zero for a point on the axis. The number of complete turns the wheel, as a whole, makes in a second gives a convenient means of estimating the rotation. Let *O* (**fig. 1**) be the centre of a wheel, and *A* a point on its circumference; *O A* may thus represent the position of a spoke of the wheel at a certain instant. At the end of one second, suppose the spoke which was initially in the position *O A*1 to occupy the position *O A*2; if the motion of rotation of the wheel is uniform, the linear s peed of the point *A* on the rim is measured by the arc *A*1*A*2, while the angular speed of the wheel is measured by the angle *A*1*O A*2. Generally, the angular speed of a body rotating uniformly is the angle turned through in unit of time.

The angular speed may be expressed in various ways. For example, the number of degrees in the angle *A*1*O A*2 swept out per second may be expressed; this method, however, is little used practically. The method of expressing angular velocity most in use by engineers, is to give the number of revolutions per minute, *n*. One revolution = 360°; revolutions per minute can be converted into degrees per second by multiplying by 360 and dividing by 60, that is, by multiplying by 6.

For scientific purposes another method is used. Mathematicians find that the most convenient unit angle to adopt is not obtained by dividing a right angle into an arbitrary number of parts; they define the unit angle as that which subtends a circular arc of length equal to the radius. Thus, in **figure 1**, if the arc *A*1*A*3 be measured off equal to the radius *O A*1, the angle *A*1*O A*3 will be the *unit angle*. This is called a *radian*.

*(Continues...)*

Excerpted fromBicycles & TricyclesbyArchibald Sharp. Copyright © 1977 The Massachusetts Institute of Technology. Excerpted by permission of Dover Publications, Inc..

All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.

Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

## Table of Contents

PART I PRINCIPLES OF MECHANICSCHAPTER I FUNDAMENTAL CONCEPTIONS OF MECHANICS

Division of the Subject.

Space.

Time.

Matter.

"CHAPTER II SPEED, RATE OF CHANGE OF SPEED, VELOCITY, ACCELERATION, FORCE, MOMENTUM"

Speed.

Uniform Speed.

Angular Speed.

Relation between Linear and Angular Speeds.

Variable Speed.

Velocity.

Rate of Change of Speed.

Rate of Change of Angular Speed.

Acceleration.

Force.

Momentum.

Impulse.

"Moments of Force, of Momentum, &c.."

CHAPTER III KINEMATICS : ADDITION OF VELOCITIES

"Graphic Representation of Velocity, Acceleration, &c.."

Addition of Velocities.

Relative Velocity.

Parallelogram of Velocities.

Velocity of Point on a Rolling Wheel.

Resolution of Velocities.

Addition and Resolution of Accelerations.

Hodograph.

Uniform Circular Motion.

CHAPTER IV KINEMATICS : PLANE MOTION

Definition of Plane Motion.

General Plane Motion of a Rigid Body.

Instantaneous Centre.

"Point-paths, Cycloidal Link Mechanisms."

Speed of Knee-joint when pedalling a Crank

Simple Harmonic Motion.

Resultant Plane Motion.

Simple Cases of Relative Motion of two Bodies in Contact.

Combined Rolling and Rubbing.

CHAPTER V KINEMATICS : MOTION IN THREE DIMENSIONS

Resultant of Translations.

Resultant of two Rotations about Intersecting Axes.

Resultant of two Rotations about Non-intersecting Axes.

Most General Motion of a Rigid Body.

Most General Motion of two Bodies in Contact.

CHAPTER VI STATICS

Graphic Representation of Force.

Parallelogram of Forces.

Triangle of Forces.

Polygon of Forces.

Resultant of any number of Co-planar Forces.

Resolution of Forces.

Parallel Forces.

Mass-centre.

Couples.

"Stabe, Unstable, and Neutral Equilibrium."

Resultant of any System of Forces.

CHAPTER VII DYNAMICS : GENERAL PRINCIPLES

Laws of Motion.

Centrifugal Force.

Work.

Power.

Kinetic Energy.

Potential Energy.

Conservation of Energy.

Frictional Resistance.

Heat.

CHAPTER VIII DYNAMICS (continued)

Dynamics of a Particle.

Circular Motion of a Particle.

Rotation of a Lamina about a fixed axis perpendicular to its Plane.

Pressure on the Fixed Axis.

Dynamics of a Rigid Body.

Starting in a Cycle Race.

Impact and Collision.

Gyroscope.

Dynamics of any system of Bodies.

CHAPTER IX FRICTION

Smooth and Rough Bodies.

Friction of Rest.

Coefficient of Friction.

Journal Friction.

Collar Friction.

Pivot Friction.

Rolling Friction.

CHAPTER X STRAINING ACTIONS : TENSION AND COMPRESSION

Action and Reaction.

Stress and Strain.

Elasticity.

Work done in stretching a Bar.

Framed Structures.

Thin Tubes subjected to Internal Pressure.

CHAPTER XI STRAINING ACTIONS : BENDING

Introductory.

Shearing-force.

Bending-moment.

Simple Example of Beams.

Beam supporting a number of Loads.

Nature of Bending Stresses.

Position of Neutral Axis.

Moment of Inertia of an Area.

Moment of Bending Resistance.

Modulus of Bending Resistance of a Section.

Beams of Uniform Strength.

Modulus of Bending Resistance of Circular Tubes.

Oval Tubes.

D Tubes.

Square and Rectangular Tubes.

"CHAPTER XII SHEARING, TORSION, AND COMPOUND STRAINING ACTION"

Compression.

Compression or Tension combined with Bending.

Columns.

Limiting Load on Long Columns.

Gordon's Formula for Columns.

Shearing

Torsion.

Torsion of a Solid Bar.

Torsion of Thick Tubes.

Lines of Direct Tension and Compression on a Bar subject to Torsion.

Compound Stress.

Bending and Twisting of a Shaft.

CHAPTER XIII STRENGTH OF MATERIALS

Stress : Breaking and Working.

Elastic Limit.

Stress-strain Diagram.

Mild Steel and Wrought Iron.

Tool Steel.

Cast Iron.

Copper.

Alloys of Copper.

Aluminium.

Wood.

Raising of the Elastic Limit.

Complete Stress-strain Diagram.

Work done in breaking a Bar.

Mechanical Treatment of Metals.

Repeated Stress.

PART II CYCLES IN GENERAL

CHAPTER XIV DEVELOPMENT OF CYCLES : THE BICYCLE

Introduction.

The Dandyhorse.

Early Bicycles.

The ' Ordinary.'

The ' Xtraordinary.'

The ' Facile.'

The ' Kangaroo.'

The Rear-driving Safety.

The ' Geared Facile.'

The Diamond-frame Rear-driving Safety.

The Rational Ordinary.'

The ' Geared Ordinary ' and Front-driving Safety.

The ' Giraffe ' and ' Rover Cob.'

Pneumatic Tyres.

Gear-cases.

Tandem Bicycles.

CHAPTER XV DEVELOPMENT OF CYCLES : THE TRICYLE

Early Tricycles.

Tricycles with Differential Gear.

Modern Single-driving Tricycles.

Tandem Tricycles.

Sociables.

Convertible Tricycles.

Quadricycles.

CHAPTER XVI CLASSIFICATION OF CYCLES

Stable and Unstable Equilibrium.

Method of Steering.

Bicycles : Front-drivers.

Bicycles : Rear-drivers.

Tricycles.

Front-steering Front-driving Tricycles.

Front-steering Rear-driving Tricycles.

Rear-steering Front-driving Tricycles.

Quadricycles.

Multicycles.

CHAPTER XVII STABILITY OF CYCLES

Stability of Tricycles.

Stability of Quadricycles.

Balancing on a Bicycle.

Balancing on the ' Otto ' Dicycle.

Wheel Load in Cycles whe

Pedal-clutch Mechanism.

Diagrams of Crank Effort.

Actual Pressure on Pedals.

Pedalling.

Manumotive Cycles.

Auxiliary Hand-Power Mechanisms.

PART III DETAILS

CHAPTER XXII THE FRAME : DESCRIPTIVE

Frames in General.

Frames of Front-drivers.

Frames of Rear-drivers

Frames of Ladies' Safeties.

Tandem Frames.

Tricycle Frames.

Spring frames.

The Front-frame.

CHAPTER XXIII THE FRAME : STRESSES

Frames of Front-drivers.

Rear-driving Safety Frame.

Ideal Braced Safety Frame.

Humber Diamond Frame.

Diamond-frame with no Bending on Frame Tubes.

Open Diamond-frame.

Cross-frame.

Frame of Ladies' Safety.

Curved Tubes.

Influence of Saddle Adjustment.

Influence of Chain Adjustment.

Influence of Pedal Pressure.

Influence of Pull of Chain on Chain-struts.

Tandem Bicycle Frames.

Stresses on Tricycle Frames.

The Front-frame.

General Considerations Relating to Design of Frame.

CHAPTER XXIV WHEELS

Introductory.

Compression-spoke Wheels.

Tension-spoke Wheels.

Initial Compression on Rim.

Direct-spoke Driving-Wheel.

Tangent-spoke Wheel.

Direct-spokes.

Tangent-spokes.

Sharp's Tangent Wheel.

Spread of Spokes.

Disc Wheels.

Nipples.

Rims.

Hubs.

Spindles.

Spring Wheels.

CHAPTER XXV BEARINGS

Definition of Bearings.

"Journals, Pivot and Collar Bearings."

Conical Bearings.

Roller-bearings.

Ball-bearings.

Thrust Bearings with Rollers.

Adjustable Ball-bearing for Cycles.

Motion of Ball in Bearing.

Magnitudes of the Rolling and Spinning of the Balls on their Paths.

Ideal Ball-bearing.

Mutual Rubbing of Balls in the Bearing.

Meneely ' Tubular Bearing.

Ball-bearing for Tricycle Axle.

Ordinary Ball Thrust Bearing.

Dust-proof Bearings.

Oil-retaining Bearings.

Crushing Pressure on Balls.

Wear of Ball-bearings.

Spherical Ball-races.

Universal Ball-bearing.

CHAPTER XXVI CHAINS AND CHAIN GEARING

Transmission of Power by Flexible Bands.

Early Tricycle Chain.

Humber Chain.

Roller Chain.

Pivot Chain.

Roller Chain-wheel.

Humber Chain-wheel.

"Side clearance, and Stretching of Chain."

Rubbing and Wear of Chain and Teeth.

Common Faults in Design of Chain-wheels.

Summary of Conditions determining the Proper Form of Chain-wheels.

Form of Section of Wheel Blanks.

Design of Side-plates of Chain.

Rivets.

"Width of Chain, and Bearing Pressure on Rivets."

Speed-ratio of Two Shafts connected by Chain Gearing.

Size of Chain-wheels.

Spring Chain-wheel.

Elliptical Chain-wheel.

Friction of Chain Gearing.

Gear-case.

Comparison of Different Forms of Chain.

Chain-tightening Gear.

CHAPTER XXVII TOOTHED-WHEEL GEARING

Transmission by Smooth Rollers.

Friction Gearing.

Toothed-wheels.

Train of Wheels.

Epicyclic Train.

Teeth of Wheels.

Relative Motion of Toothed - wheels.

Involute Teeth.

Cycloidal Teeth.

Arcs of Approach and Recess.

Friction of Toothed-wheels.

Circular Wheel-teeth.

Choice of Tooth Form.

Front-driving Gears.

Toothed-wheel Rear-driving Gears.

Compound Driving Gears.

Variable Speed Gears.

CHAPTER XXVIII LEVER-AND-CRANK GEAR

Introductory.

Speed of Knee-joint with ' Facile ' Gear.

Pedal and Knee-joint Speeds with ' Xtraordinary ' Gear.

Pedal and Knee-joint Speeds with ' Geared Facile ' Mechanism.

Pedal and Knee-joint Speeds with ' Geared Claviger ' Mechanism.

Facile ' Bicycle.

Xtra-ordinary.'

Claviger Bicycles.

Early Tricycles.

CHAPTER XXIX TYRES

Definition.

Rolling Resistance on Smooth Surface.

Metal Tyre on Soft Road.

Loss of Energy by Vibration.

Rubber Tyres.

Pneumatic Tyres in General.

Air-tube.

Outer-cover.

Classification of Pneumatic Tyres.

Tubular Tyres.

Interlocking Tyres.

Wire-held Tyres.

"Devices for Preventing, and Minimising the Effect of Punctures."

Non-slipping Covers.

Pumps and Valves.

"CHAPTER XXX PEDALS, CRANKS, AND BOTTOM BRACKETS"

Pedals.

Pedal-pins.

Cranks.

Crank-axles.

Crank-brackets.

Pressure on Crank-axle Bearings.

CHAPTER XXXI SPRINGS AND SADDLES

Spring under the Action of suddenly applied Load.

Spring Supporting Wheel.

Saddle Springs.

Cylindrical Spiral Springs.

Flat Springs.

Saddles.

Pneumatic Saddles.

CHAPTER XXXII BRAKES

Brake Resistance on the Level.

Brake Resistance Down-hill.

Tyre and Rim Brakes.

Band Brakes.

INDEX