## Kinematics: A Treatise on the Modification of Motion, as Affected by the Forms and Modes of Connection of the Moving Parts of Machines |

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### Common terms and phrases

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 follower 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 cone 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

### Popular passages

Page 5 - Galileo the theory that the earth rotates on its axis and revolves around the sun was contrary to common sense; yet this theory prevailed.

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 14 - 5 ' 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 to it. And the simultaneous motions are subject to this condition, that the components along...

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 187 - 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 89 - ... of a pair of skew-bevel wheels, although the relative positions of the axes may be the same in each case. There are, in consequence, six varieties or classes of toothed gearing to be met with in practice, viz : 1. Spur Gearing. 4. Twisted Gearing. 2. Bevel Gearing. 5. Screw Gearing. 3. Skew Gearing. 6. Face Gearing. come, in general, mere lines, or elements of surfaces in contact. The relative motions of these surfaces will be the same as those of the wheels from which they are thus derived,...

Page 23 - AE are of the same lengths in both diagrams, in which therefore the motions of C at the given instant are identical, and the rotations about the moving line are alike. 57. III. Let the primary motion be one of revolution about an axis which intersects the line. The resultant will then be a rotation about an instantaneous axis lying in the plane of the other two, and passing through their point of intersection. In Fig. 21, let CO be the line, OA the axis, both in the vertical plane. Draw CA at pleasure,...

Page 3 - Mechanism. 7. Purposing now to confine our attention to this latter branch of the science, it is necessary, before entering upon its study, to define and explain the sense in which certain terms and phrases of frequent occurrence shall be used. And first of all, we perceive that we have not, as yet, assigned to the word machine a meaning which is precise and in accordance with the above limitation. We must therefore modify the definition once more ; and considering it with reference to its motion...

Page 307 - The Hyperbola is a plane curve generated by the motion of a point subject to the condition that the difference of its distances from two fixed points called the foci shall always be equal to a given line, whose length must be less than the distance between the foci.

Page 3 - If two bodies, both moving in space, remain in the same relative position in regard to each other, they are said to be at rest, one relatively to the other; if they do not, either may be said to be in motion relatively to the other. Motion may thus be either relative, or it may be absolute, provided we assume some point as fixed.