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action angle angular velocity appears arrangement attached axes axis band base beginning carried center of motion changes circumference coincide combination communicated cone connected constant construction continuous corresponding curve described diameter direction distance draw driver edge effect employed equal example extremity figure fixed follower fraction frame give given greater half latter length line of centers lower machine manner means mechanism meet method motion move number of teeth obtained opposite pair parallel pass path perpendicular piece pinion pitch circle plane position practice principle produced pully rack radii radius receive represent respect rest revolve rolling rotation round screw shown side sliding space string supposed surface tangent teeth termed tooth train turn upper values varying velocity ratio wheel
Página 114 - Willis deduces the corollary, that if for a set of wheels of the same pitch a constant describing circle be taken and employed to trace those portions of the teeth which project beyond each pitch line by rolling on the exterior circumference, and those which lie within it by rolling on its interior circumference, then any two wheels of the set will work correctly together.
Página 133 - it appeared worth while to investigate some rule by which the necessary cutters could be determined for a set of wheels, so as to incur the least possible chance of error. To this effect I calculated, by a method sufficiently accurate for the purpose, the following series of what may be termed equidistant values of cutters ; that is, a table of cutters so arranged, that the same difference of form exists between any two consecutive numbers.
Página 132 - ... the numbers in the two following series are so arranged that the curves corresponding to them possess this required property. For the outer side of the tooth, 12, 14, 17, 21, 26, 34, 47, 73, 148, Rack. For the inner side, 12, 13, 14, 15, 16, 17, 19, 22, 26, 33, 46, 87, Rack. Now these numbers, although strictly correct, would be very inconvenient and uncouth in practice if employed for a table like that in question, where convenience manifestly requires that the numbers, if not consecutive, should...
Página 131 - ... inch pitch by always taking the nearest number in the manner directed, and a proportionably smaller error in smaller pitches. But to ensure this, the selected numbers should be so taken, that their respective forms shall lie between the extremes at equal distances. Now it appears that the variation of form is much greater among the teeth of small numbers than among the larger ones, and that in fact COUPLING OF HORIZONTAL AXLES.
Página v - At present, questions of this kind can only be solved by that species of intuition which long familiarity with a subject usually confers upon experienced persons, but which they are totally unable to communicate to others. When the mind of a mechanician is occupied with the contrivance of a machine, he must wait until, in the midst of his meditations, some happy combination presents itself to his mind which may answer his purpose.
Página 130 - Fig. 112 represents the Odontograph exactly half the size of the original ; but as it is merely formed out of a sheet of card-paper, this figure will enable any one to make it for use. The side NTM which corresponds to the line QT q in fig.
Página ix - In the new science The movements are to be studied as movements, independent of the power creating them, in the same way as we observe the static bodies around us. especially in such combinations as we call machines.. .This science (Kinematics) ought to include all that can be said with respect to motion in its different kinds, independently of the forces by which it is produced.
Página 289 - A, is employed as a driver, and has firmly secured to it two wheels, a and /z, the first of which gears with the wheel, b, and thus communicates motion to the first wheel, c, of the epicyclic train, and the wheel, h, drives the wheel, g, which thus gives motion to the last wheel, f.
Página 131 - ... corresponding to every wheel, for the error produced by taking those which belong to the nearest as directed, is so small as to be unappreciable in practice. I have calculated the amount and nature of these errors by way of obtaining a principle for the number and arrangement of the wheels selected. It is unnecessary to go at length into these calculations, which result from very simple considerations, but I will briefly state the results. The difference of form between the tooth of one wheel...
Página 234 - E and r, are fixed to it. Below this axis and parallel to it, a stout pin or stud is fixed to the plate, and a tube revolves upon this stud, to one end of which is fixed the minute-hand M, and to the other a wheel e engaged with E. In our present clock E revolves in an hour, consequently the wheels E and e must be equal. A second and shorter tube is fitted upon the tube of the minute-hand so as to revolve freely, and this carries at one end the hour-hand H, and at the other a wheel f, which is driven...