A Treatise on the Teeth of Wheels: Demonstrating the Best Forms which Can be Given to Them for the Purposes of Machinery; Such as Will-work and Clock-work, and the Art of Finding Their Numbers |
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Page 90
... THE NUMBERS OF THE TEETH AND LEAVES OF WHEELS AND PINIONS . I. 572. The numbers of the teeth of wheels or pi- nions must not contain fractions . There cannot , for example , be a wheel of 60 teeth , 90 ON THE TEETH OF WHEELS .
... THE NUMBERS OF THE TEETH AND LEAVES OF WHEELS AND PINIONS . I. 572. The numbers of the teeth of wheels or pi- nions must not contain fractions . There cannot , for example , be a wheel of 60 teeth , 90 ON THE TEETH OF WHEELS .
Page 97
... fraction ( 572 ) , the product W of all the wheels must be a whole number ; and the product p × P , which must be equal to W , will also be a whole number . Hence , when p , which represents the number of the revolutions made by the ...
... fraction ( 572 ) , the product W of all the wheels must be a whole number ; and the product p × P , which must be equal to W , will also be a whole number . Hence , when p , which represents the number of the revolutions made by the ...
Page 98
... fraction , or a multiple of that denominator . Corollary IV . = 578. Considering the equation W px P , it will be readily perceived , That if the number assumed as the value of P , which represents the product of the pinions , is not ...
... fraction , or a multiple of that denominator . Corollary IV . = 578. Considering the equation W px P , it will be readily perceived , That if the number assumed as the value of P , which represents the product of the pinions , is not ...
Page 112
... fractions , the value 730- × Fx 720 GH of their product must be a whole number . 349 Therefore , if the number 730 be multiplied by 720 the product F x G x H of the pinions , the fraction which has 720 for denominator , must become a ...
... fractions , the value 730- × Fx 720 GH of their product must be a whole number . 349 Therefore , if the number 730 be multiplied by 720 the product F x G x H of the pinions , the fraction which has 720 for denominator , must become a ...
Page 113
... fractions for that of the wheels ; and as the fractions must be neglected in the product of the wheels A , B , C ; it is necessary to find for the product of FxGx H of the pinions a whole ... fraction 349 x F x G ON THE TEETH OF WHEELS . 113.
... fractions for that of the wheels ; and as the fractions must be neglected in the product of the wheels A , B , C ; it is necessary to find for the product of FxGx H of the pinions a whole ... fraction 349 x F x G ON THE TEETH OF WHEELS . 113.
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A Treatise on the Teeth of Wheels: Demonstrating the Best Forms Which Can Be ... Charles-Étienne-Louis Camus No preview available - 2013 |
Common terms and phrases
angle axis base bay leaf Camus circle RES circular segment circum convex surface Corollary cumference cuts the line cycloid decomposed describe divided drawn engagement epicy equal equation exterior F x G factors ference finding the numbers force forming the teeth fraction Fx G G x H given Hence High Holborn Imison's Elements impelling inch involute last pinion leaf line of centres machine move the pinion move the rung moved uniformly multiplied number of teeth perpendicular pinion H pinion of seven pitch-line plane plate point of contact portion primitive circle primitive circumference primitive pinion primitive radius primitive wheel proper for moving radii represented revolve rungs infinitely small segment shewn side space spherical epicycloid straight line HEI straight line RT suppose tangent teeth and leaves teeth of wheels templet thirty teeth tion tooth ROS touch traced velocity wheel and pinion wheel or pinion whole number
Popular passages
Page 122 - If I am going to be made a noncommissioned officer next ironth, I am going to be a noncommissioned officer maybe 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 years before I ever get to go to the noncommissioned officer school.
Page 174 - Mr. Saxton of Philadelphia, now in London, who is justly celebrated for his excessively acute feeling of the nature and value of accuracy in mechanism ; and who is reputed not to be excelled by any man in Europe or America for exquisite nicety of workmanship...
Page 175 - ... possible : this plate forms the base of the epicycloid. On the other vertical arbor is a similar plate, but equal in diameter to the radius of the primitive circle of the wheel to be engaged with that about to be rounded : this plate is the generating circle.
Page 172 - ... tooth, at the primitive circle (pitch-circle), and with the other point describe a segment of a circle for the off side of the next tooth. . . . Others set the point of the compasses at different distances from the center of the tooth, nearer or farther off; also within or without the line of centers, each according to some inexplicable notion received from his grandfather or picked up by chance. It is said inexplicable, because no tooth bounded at the sides by segments of circles can work together...
Page 174 - ... man in Europe or America for exquisite nicety of workmanship ; made in Philadelphia, an instrument for cutting the teeth of watch wheels, truly epicycloidal ; or rather for curving them after they were cut down in the ordinary manner, with radial faces. The following, is his verbal description of this instrument. The wheel to be rounded being put on a vertical arbor, another arbor...
Page 119 - To find the numbers of the teeth and leaves of the wheels and pinions of a machine, which being moved by a pinion placed on the spindle of the minute wheel of a clock, shall cause a wheel to make a revolution in 29 days, 12 hours, 44 minutes, 3 seconds, and 12 thirds, which form a mean synodical revolution of the moon.
Page 161 - ... inch from the ends of the teeth at the line of centres ; the ends of the teeth were one inch from the bottoms of the spaces ; the tangent of contact formed an angle of full twenty degrees with the line of centres. In a great number of repetitions of this experiment, a slight receding of sector N0. 2 sometimes appeared. EXPERIMENT VI. The teeth were engaged a quarter of an inch : the ends of the teeth, therefore, were one inch and a quarter from the bottoms of the spaces ; and the points of contact,...
Page 173 - ... true principles. We regret to learn, from the same authority, that there are many wheel-makers who follow no rule of proportion at all in their formation. "In Lancashire, they make the teeth of watch-wheels of what is called the bay-leaf pattern; they are formed altogether by the eye of the workman, and they would stare at you for a simpleton, to hear you talk about the epicycloidal curve.
Page 143 - ... have been so misled by this misconception of the original translator of Camus, that they are daily ''pouring into the market multitudes of cast-iron wheels and pinions, of various magnitudes, for cotton and other machinery, with teeth formed from the epicycloid of the diameter, instead of the radius of the opposite wheel, or pinion,