Bicycles & Tricycles: An Elementary Treatise on Their Design and Construction, with Examples and Tables

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Longmans, Green, 1896 - Bicycles - 536 pages

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Page 56 - To every action there is always an equal and contrary reaction ; or the mutual actions of any two bodies are always equal and oppositely directed.
Page 56 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 45 - If three forces, acting at a point, be represented in magnitude and direction by the sides of a triangle taken in order, they will be in equilibrium.
Page 18 - The geometrical process used above is c called -vector addition, 'and is used in compounding any physical quantities that can be represented by, and are subject to the same laws as, vectors. Accelerations, forces acting at a point, rotations about intersecting axes, are treated in this way. In general, the sum of any number of vectors is obtained by placing at the final point of one the initial point of another, and so forming an unclosed irregular polygon ; the vector formed by joining the initial...
Page 71 - But in a non-symmetrical body, eg a pair of bicycle cranks and their axle, the resultant pressure on the bearings cannot be expressed as a single force, but is a couple. Thus, such a rigid body, if perfectly free, will turn about an axis, in general, not parallel to that of the acting couple. From (23), the centrifugal pressure on the fixed axis of any rigid body is the same as if the whole mass were concentrated at the mass-centre G. If the mass-centre lies on the axis of rotation, the centrifugal...
Page 429 - The American gear-wheel makers define the diametral pitch as " The number of teeth in the gear divided by the pitch -diameter of the gear." The latter may be called the pitch-number. It is much more convenient to use the pitch-number than the circular pitch to express the size of wheel-teeth. Figure 469 shows the actual sizes of a few teeth, with pitch-numbers suitable for use in cycle-making. If/ be the circular pitch, s the diametral pitch, and P the pitch-number, P =. - = vsp (3) 305.
Page 26 - If one circle roll on the circumference of another, the curve described by a point on the circumference of the rolling circle is called an epicycloid or a hypocycloid, according as the rolling circle lies outside or inside the fixed circle.
Page 87 - EI where E is a constant, the value of which depends on the nature of the material. The ratio of this elongation to the original length — that is, the extension per unit of length — is called the extension, and denoting it by e we have (3) substituting in (2) we have = E (4) E is called the modulus of elasticity of the material.
Page 67 - That is, the moment of the force is equal to the product of the moment of inertia of the body on which it acts and the angular acceleration it produces.
Page 114 - Zl.) ........ (33) When a tube of circular section is flattened to form an oval tube, its thickness will be nearly uniform throughout, but in the oval tube section, above discussed, the thickness is not constant throughout, but is a little less than / except at the ends of the major and minor axes. The strength of an oval tube of uniform thickness will therefore be under-estimated if the formula (33) be used, so that the error is on the safe side. The area of the ellipse is — ab ; and in the same...

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