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angular velocity annular wheel arc of recess assigned base circle bisect circumference coincidence common element common normal common tangent components construction curve cutter cycloid cylinder describing circle determined diagram diameter distance draw drive ellipse epicycloidal epitrochoid equal equiangular spiral face fixed axes flanks generatrix given helical horizontal projection hyperboloid hypocycloid instant instantaneous axis intersect involute involute system latter least number limiting numbers line of action line of centres linear velocity Lobed Wheels logarithmic spiral major axis milling cutter motion number of teeth obliquity outline pair parallel perpendicular pinion pitch arc pitch circle pitch surfaces point of contact point of tangency position practical rack radial radii radius resultant revolution revolving right line rigid body rolling contact rotation screw semi-minor axis shown in Fig similar sliding space spiral template tion tooth traced triangles trilobe unilobe velocity ratio vertex whence
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 - This curve is traced by a point in the circumference of a circle which rolls upon its tangent. In Fig.
Page 307 - THE HYPERBOLA. The hyperbola is a plane curve generated by a point moving so that the difference of its distances from two fixed points, called the "focuses,
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 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 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 43 - The angular velocities arc to each other inversely as the perpendiculars from the centres of motion upon the Line of Action; or, inversely as the segments into which the line of action divides the line of centres. II. The rotations have the same direction if the centres of motion lie on the same side of the line of action ; and contrary directions if they lie on opposite sides. III. The rate of sliding, in contact...