Bicycles and Tricycles: An Elementary Treatise on Their Design and Construction
Cite this book
Citation
Archibald Sharp. Bicycles and Tricycles: An Elementary Treatise on Their Design and Construction. 1896. cyclearchive.com, https://cyclearchive.com/books/bicycles-and-tricycles-an-elementary-treatise-a-sharp-1896/
Page numbers are pages of the PDF, which can differ from the numbers printed on the page.
Contents
- Sharp explains that cycle design has almost no scientific literature despite an extensive complexity of stresses and strains, and sets out to give a rational, elementary-mathematics account of them, crediting sources including Bourlet's 'Traite des Bicycles et Bicyclettes' and the Cyclist Year Books.
- Defines geometry, kinematics and dynamics (statics and kinetics) as the divisions of mechanics, and fixes the units of space (imperial yard and foot versus the metric metre) and time (sidereal and mean solar day) used throughout the book.
- Distinguishes linear and angular speed (revolutions per minute versus radians) and derives the relation between them, then builds up velocity, acceleration, force and momentum, defining force as the rate of change of momentum. Note: the printed pages carrying this chapter's own opening heading (p.4-5) are missing from this scan -- a duplicated leaf at p.2 (physical pages 27-28) sits where they should be -- so the earliest available anchor is mid-chapter.
- Introduces the graphic (vector) representation of velocity and acceleration on paper, the addition and resolution of velocities by the parallelogram method, relative velocity, and the hodograph construction for uniform circular motion.
- Defines plane motion of a rigid body as translation, rotation, or a combination located by an instantaneous centre, covers point-paths and cycloidal curves traced by link mechanisms, and analyses combined rolling and rubbing contact between two bodies such as a wheel on a road.
- Extends kinematics to three dimensions, finding the resultant of several translations and of rotations about intersecting and non-intersecting axes, building toward the general motion of two bodies in contact -- the groundwork later used for ball motion inside a bearing.
- Covers the graphic representation and composition of forces -- the parallelogram, triangle and polygon of forces, resolution of forces, parallel forces, mass-centre and couples -- and the conditions for stable, unstable and neutral equilibrium.
- States Newton's three laws of motion and develops centrifugal force, work, power, kinetic and potential energy, conservation of energy, and frictional resistance as heat.
- Treats the dynamics of a particle and of a rigid body, circular motion and rotation of a lamina about a fixed axis, impact and collision, the gyroscope, and dynamics of a system of bodies, including a worked example of starting in a cycle race.
- Distinguishes smooth and rough bodies and defines the coefficient of friction, then treats friction of rest, journal friction, collar friction, pivot friction and rolling friction.
- Applies Newton's action-and-reaction law to stress and strain and elasticity, calculates work done in stretching a bar, and analyses framed structures and thin tubes subjected to internal pressure.
- Develops shearing-force and bending-moment diagrams for a loaded beam, the position of the neutral axis and moment of inertia of a section, and the modulus of bending resistance for round, oval, square and rectangular tubes -- the beam theory later applied directly to the frame.
- Covers compression combined with bending, the buckling of long columns via Gordon's formula, shearing and torsion of solid and thick tubes, and compound stress in a shaft subjected to bending and twisting together.
- Sets out the stress-strain diagram and elastic limit, and compares the breaking and working strength of mild steel, wrought iron, tool steel, cast iron, copper alloys, aluminium and wood, plus the weakening effect of repeated stress.
- Traces bicycle evolution from the dandy-horse and early bone-shakers through the Ordinary, Xtraordinary, Facile and Kangaroo, to the geared Ordinary, the diamond-frame rear-driving Safety, pneumatic tyres, gear-cases and tandem bicycles.
- Covers early tricycles such as Lisle's converted 'German' machine, tricycles fitted with differential gear, modern single-driving and tandem tricycles, sociables, convertible tricycles and quadricycles.
- Classifies cycles first by stable versus unstable static equilibrium and then by method of steering, sorting bicycles into front- and rear-drivers and tricycles into front-steering, rear-steering and front- or rear-driving arrangements, plus quadricycles and multicycles.
- Analyses tricycle and quadricycle stability by taking moments about the wheel-contact points, balancing on a bicycle and on the Otto dicycle, wheel load while turning, and the influence of speed and pedal effort on side-slipping and headers.
- Describes the front-frame/rear-frame steering-head joint, weight distribution on the steering wheel, riding without hands, and the specific steering geometries of the Cripper, Royal Crescent, Humber and Olympia tricycles and the Otto dicycle.
- Traces the path of a wheel's centre as it rides up over an obstacle, showing how wheel diameter and saddle position affect the resulting jolt, and quantifies the consequent loss of energy on an uneven road.
- Breaks the total resistance a cyclist must overcome into bearing and gearing friction, rolling resistance, vibration loss and air resistance, and distinguishes the rider's indicated power from the brake power actually delivered to the machine.
- Defines a machine as a train of higher and lower kinematic pairs, discusses mechanical efficiency and variable-speed gearing, and analyses the crank-and-pedal mechanism, including diagrams of crank effort and actual pedal pressure through the stroke.
- Surveys built front- and rear-driving frame designs from makers including Abingdon Works, Humber, Singer and Referee, plus ladies' Safety patterns, describing how each carries the rider's weight as a beam between the two wheel centres via the steering-head hinge.
- Calculates bending-moment diagrams on Ordinary and Safety frames arising from the rider's weight and the saddle-spring loading, working through graphical statics to find the resulting stress on backbone, forks and steering-head.
- Classifies compression-spoke and tension-spoke (tangent) wheel construction, initial compression of the rim, Sharp's own tangent-wheel design, spread of spokes, disc wheels, nipples, rims, hubs and spindles.
- Defines journal, pivot and collar bearings and works through ball-bearing theory in detail -- the rolling and spinning motion of balls in their races, adjustable cycle ball-bearings, thrust bearings, dust-proofing, crushing pressure on the balls and bearing wear.
- Compares power transmission by flexible bands with toothed chains, covers Humber and roller chain design, side-clearance and stretch of the chain, chain-wheel tooth form and common design faults, and friction of the chain gearing and gear-case design.
- Takes friction gearing between smooth rollers as the kinematic basis for toothed wheels, covers trains of wheels and epicyclic trains, involute and cycloidal tooth profiles, and the strength of wheel teeth in front- and rear-driving and variable-speed gears.
- Analyses the four-link kinematic chain underlying lever-and-crank gears such as the Facile and Xtraordinary mechanisms, comparing the pedal and knee-joint speeds each design produces.
- Covers rolling resistance on smooth surfaces, the mechanics of a metal tyre on a soft road, rubber and pneumatic tyre construction (air-tube and outer cover), tubular, interlocking and wire-held tyres, and devices to prevent and minimise punctures.
- Describes pedal-pin and ball-bearing design including Bown's rubber pedal, crank and crank-axle construction, crank-brackets, and the pressure carried by the crank-axle bearings.
- Analyses a spring's behaviour under suddenly applied load, wheel-supporting and saddle springs, cylindrical spiral and flat spring design, and saddle construction including pneumatic saddles.
- Derives brake resistance on the level and downhill from the coefficient of friction between tyre and ground and the load on the braked wheel, then compares tyre-and-rim brakes with band brakes.