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addendum angle angular velocity ratio arc of action arrangement axes axis belt center of motion circumference clock cogs combination COMMUNICATION OF MOTION cone conical surface connexion contrivance corresponding crank cylinder describing circle detent diameter distance edge ellipse employed epicyclic train epicycloid equal example excentric extremity figure fixed fraction frustum geer given groove hyperboloid hypocycloid involute jointed line of centers link-work logarithmic spiral machine manner mechanism move number of teeth obtained opposite direction oscillation pair parallel pass path perpendicular piece pinion pitch circle pitch line plane plate point of contact position produce pully rack radial radii radius ratchet-wheel reciprocating respectively revolution revolve rods roller rotation round shew shewn side sliding slit solid of revolution space spur-wheel supposed surface synchronal rotations tangent teeth of wheels termed tion toothed wheel values versin wheel-work
Page xiii - instead of considering a machine to be an instrument by means of which we may change the direction and velocity of a given motion, I have treated it as an instrument by means of which we may produce any relations of motion between two pieces.
Page 43 - construction of a toothed wheel has been partly imitated in modern mill-work, for it is found that if in a pair of wheels the teeth of one be of cast-iron, and in the other of wood, that the pair work together with much less vibration and consequent noise, and that the teeth
Page 134 - inch, so that as all the other forms lie between these, it is clear that if we select only four or five examples for the outer side of the tooth and ten or twelve for the inner side, that we can never incur an error of more than the
Page iv - every machine will be found to consist of a train of pieces connected together in various ways, so that if one be made to move they all receive a motion, the relation of which to that of the first is governed by the nature of the
Page 300 - mechanism ; but the reciprocation is produced so simply that it is often worth while to retain the crank, and correct the law of velocity by combining other pieces with it in a train. By trains of link-work very complex laws of motion may be derived from a uniformly revolving driver. This will be best illustrated by the
Page 133 - is also true for an annular wheel of the same radius and number of teeth, n becoming the root and p the point of the teeth. For a rack, the pitch line DE becomes a right line, and DA, EA, perpendiculars to it, at a distance equal to the pitch.
Page 133 - an arc of the given pitch circle, and upon it set off DE, equal to the pitch, and bisected in m. Draw radial lines DA, EA. For the arc within the pitch circle apply the slant edge of the instrument to the radial line AD, placing its extremity D on the pitch circle, as in the figure. In the Table headed,
Page i - MECHANISM, DESIGNED FOR THE USE OF STUDENTS IN THE UNIVERSITIES, AND FOR ENGINEERING STUDENTS GENERALLY.
Page 133 - Numbers for pitches not inserted in the tables may be obtained by direct proportion from the column of some other pitch: thus for 4-inch pitch, by doubling those of 2-inch, and for half-inch pitch by halving those of
Page 252 - be the driver, and let it revolve in the direction from T to t. Then since the radius of contact sP increases by this motion, and the corresponding radius PH decreases, the edge of the driver will press against that of the follower, and so communicate a motion to it