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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 Lobed Wheels 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
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 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.
Page 7 - ... from a description of their big trading expeditions. All these activities are dependent upon the social power of the chief and the influence of the respective magicians. In all of them the quantity of the produce, the nature of the work and the manner in which it is carried out — all of which are essentially economic features — are highly modified by the social organisation of the tribe and by their magical belief. Customary and legal norms, magical and mythological ideas, introduce system...
Page 10 - ... an arrow-head is used to indicate the direction in which the point is moving. If the path of the moving point be a curve of any kind, the direction of the curve at any point is that of its tangent at that point, which indicates the direction of motion as well. 19. 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?
Page 14 - 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 to it. And the...
Page 315 - It is the curve which is traced by a point in the circumference of a circle which rolls along a straight line.
Page 3 - Path. — A point moving in space describes a line called its path, which may be rectilinear or curvilinear. The motion of a body is determined by the paths of three of its points selected at pleasure.
Page 304 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
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 302 - F of 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.