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angular velocity annular wheel arc of recess assigned base circle bisect circumference coincide common element common normal common tangent components construction curve cutter cycloid cylinder describing circle determined diameter distance draw drive ellipse epicycloidal epitrochoid equal equiangular spiral face fixed axes flanks generatrix given gorge 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 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 tion tooth trace triangles trilobe unilobe velocity ratio vertical projection whence
Page 5 - Revolution, just as we say that the earth rotates on its axis, and revolves around the sun.
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 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 202 - ... 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 / as shown. If the pins be made of a sensible diameter, the outlines of the teeth upon the other wheel are curves parallel to the original epicycloids, as shown in Fig.
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 11 - If two forces acting at a point be represented in magnitude and direction by the adjacent sides of a parallelogram, the resultant...
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 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 302 - APPENDIX. 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.