## An Essay on the Teeth of Wheels: Comprehending Principles, and Their Application in Practice, to Millwork and Other Machinery. With Numerous Figures |

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angle base bevel geer bevelled wheels Boulton and Watt Breadth of teeth cast iron circumference cloid cone curve cycloid cylinders cylindric staves described diameter distance Ditto Ditto Ditto durability epicy epicycloid C E equal Essay feet per second figure Horse Mill Horse's power inch pitch indefinitely small length line A B line of centres line of table mills millwright mode motion move nion number of horses number of teeth numbers in column observed parallel perpendicular pitch line plane point of contact practice principles proportional circles rack and pinion radii radius B H real radius represented right line ring spur geer Steam Engine straight line strength in horse's Strength of teeth suppose surface table 1st table 2d Table of Pitches teeth of wheels thickness three feet three inches tion tooth touch velocity Water Wheel wheel and pinion wheel and trundle wheels act

### Popular passages

Page 111 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 112 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 99 - ... circle. It has been supposed by some of the best authors that the epicycloidal tooth has also the advantage of completely avoiding friction ; this is however by no means true, and it is even impracticable to invent any form for the teeth of a wheel, which will enable them to act on other teeth without friction. In order to diminish it as much as possible, the teeth must be as small and as numerous as is consistent with strength and durability ; for the effect of friction always increases with...

Page 16 - For when the acting parts of a machine are not truly formed, it may he so loaded as just to be in equilibrio with its work in the most favourable situation of its parts, but when it changes into a less favourable situation, the machine will stop, or at least, stagger, hobble, or work unequally. The best figure, therefore, which can be given to the teeth, is that which shall cause them always to act equally and similarly, in situations equally favourable, and which shall consequently give the machine...

Page 129 - Stress is inversely as the Velocity.^ " For example — if the pitch lines of one pair of wheels be moving at the rate of 6 feet in a second, and another pair of wheels, in every other respect under the same circumstances, be moving at the rate of 3 feet in a second, the stress on the latter is double of that on the former " Of arranging the Numbers of Wheel-Worlt.

Page 99 - ... the actual resistance is not at all increased by increasing the relative velocity; but the effect of that resistance, in retarding the motion of the wheels, may be shown, from the general laws of mechanics, to be proportional to the relative velocity thus ascertained. When it is possible to make one wheel act on teeth fixed in the concave surface of another, the friction may be thus diminished in the proportion of the difference of the diameters to their sum. " If the face of the teeth, where...

Page 79 - A geometrical curve, of which the genesis may be conceived by imagining a nail in the circumference of a wheel : the line which the nail describes in the air, while the wheel revolves in a right line, is the cycloid.

Page 126 - ... wheels. For it is to be remembered, that we are not so much here in search of truths of curious or profound mathematical speculation, as of that kind of evidence, of which the subject admits, and which may be sufficiently satisfactory for any practical purpose.

Page 151 - The thickness of the teeth in each of the lines is varied one-tenth of an inch. The breadth of the teeth is always four times as much as their thickness. The strength of the teeth is ascertained by multiplying the square of their thickness into their breadth, taken in inches and tenths, &c. The pitch is found by multiplying the thickness of the teeth by 2'1. The number that represents the strength of the teeth, will also represent the number of horses' power, at a velocity of about four feet per...

Page 98 - In the first volume of the same work, he makes the following judicious observations on our present subject : «* It has been supposed by some of the best authors that the epicycloidal tooth ,has also the advantage of completely avoiding friction ; this is however by no means true, and it is even impracticable to invent any form for the teeth of a wheel, which will enable them to act on other teeth without friction. " In order to diminish it as much as possible, the teeth must be as small and as numerous...