Kinematics: A Treatise on the Modification of Motion, as Affected by the Forms and Modes of Connection of the Moving Parts of Machines. Fully Illustrated by Accurate Diagrams of Mechanical Movements, as Practically Constructed; for the Use of Draughtsmen, Machinists, and Students of Mechanical Engineering
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angle of action angular velocity annular wheel arc of recess assigned base circle bisect circumference common element common normal common tangent conjugate construction curve cutter cycloid cylinder describing circle determined diagram diameter distance draw drive ellipse epicycloidal epitrochoid equal equiangular spiral face fixed axes frusta generatrix helical horizontal projection hyperboloid hypocycloid inside gear instant instantaneous axis intersect involute involute system latter least number length limiting numbers line of action line of centres logarithmic spiral major axis milling cutter motion moving number of teeth obliquity outline pair parallel path of contact perpendicular pinion pitch arc pitch circle pitch surfaces point of contact point of tangency position practical rack radii radius resultant revolution revolving right line rolling contact rotation screw semi-minor axis shown in Fig similar sliding space spiral template tion tooth traced triangles unilobe velocity ratio vertex whence
Page 14 - ... perpendicular BC, and draw AC. Completing the parallelogram CD, it will be perceived that the tangential component is AC, the orthographic projection of AB upon the plane MN, and that AD, the normal component, is equal and parallel to BC, the projecting perpendicular of the point B. may be represented by right lines, which may be in the same or in different planes. Each of these may be resolved into two components, one of which is in the direction of the connecting line, the other perpendicular...
Page 315 - ... readiest and most reliable known method of laying them out. The line which carries the tracing point is called the generatrix or describing line, and the one in contact with which it rolls is called the directrix or base line; either of these may be straight, or both may be curved.
Page 7 - ... determined by the manner of action of the motive power, and those of the third by the nature of the work and the manner in which it is to be done. The motion of the one class has then to be transmitted to the other; and as the given motion of the former may be and usually...
Page 101 - Still, it will be found that if it be made five-eighths instead of onehalf that diameter, the curvature of the flanks will not be so great, with the customary proportions of height to thickness of the teeth, as to make the spaces any wider at the bottom than at the pitch circle ; the teeth can therefore be...
Page 201 - Meantime, since the marking point does not change its position in the circumference of the upper circle, it can trace no curve at all upon its plane. Now let AF be a curve similar to BE, and imagine a pin of no sensible diameter — a rigid material line — to be fixed at A in the upper wheel. Then if the lower one turn to the right, it will drive the pin before it with a constant velocity ratio, the action ending at E, if the driving curve be terminated at f us here shown.
Page 187 - 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.
Page 251 - If one of those bodies is fixed, and the other made to roll upon it, they continue to touch each other in a straight line, which is the instantaneous axis of the rolling body, and the rotation about that instantaneous axis is accompanied by a sliding motion along the same axis so as to give, as the resultant compound motion, a helical motion about the instantaneous axis.
Page 11 - Resultant. — If a material point receives a single impulse in any direction, it will move in that direction with a certain velocity. If it receive? at the same instant two impulses in different directions, it will obey both, and move in an intermediate direction with a velocity differing from that of either impulse alone. The position of the point at the end of the instant is the same as it would have been had the motions, due to the impulses, occurred in successive instants.
Page 200 - ... that the action on ceasing in one plane is continued in the next, these instants become consecutive, the velocity ratio is made constant, and the rotation is transmitted by pure rolling contact. On this last account, as might be expected, the action of these wheels is exceedingly smooth and noiseless, almost as much so, if they be well made, as that of belting; but they are better suited for light work, because the pressure is confined to a single point instead of being distributed along a line....
Page 302 - F oi the minor axis. this case AB, EF, will not be the axes. They are, however, conjugate to each other, for each is parallel to the tangents at the extremities of the other : and since the parallelogram can always be constructed if AB and EF are given, we have thus a simple and ready method of constructing the ellipse upon any pair of conjugate diameters. Fio.