## A new general theory of the teeth of wheels |

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2d Point 6th Point analytic curve angular motion angular velocities assumed augment axes axis circumference co-ordinates compute condition of contact continue contour curvature curve of sines cutter cycloidal D Q E divisor draw ellipse epicycloid equal equation friction gear geometrical give Hence hour-glass curve indeterminate equation integral intersection involute limits line of centres linear velocity loss of force metacentric distance Nine Contacts normal number of contacts number of teeth obliquity obtain orbit osculates outline parallel pass permutability perpendicular pinion pitch line pitch point Plate plerotic contact point of contact point Q porism position pragmatic action pragmatic contacts pressure radii radius ratio result seven contacts shew shewn in figure side simultaneously straight line straight rack suppose surfaces tangent teeth of wheels tion tooth tracing point truncation turn wheel-work whence wherefore zero

### Popular passages

Page 33 - ... it slightly graze the edge of the prepared blank, and make in the ordinary way, a series of cuts all round. By turning the notch ring a little forward, bring the cutter deeper on the blank, make another series of cuts; again advance the notch ring, and continue this process until the cutter passes entirely clear of the metal, then shall we have a wheel whose teeth are truly formed to work with our assumed rack; and all wheels formed in this way will gear truly into each other. "All wheels of...

Page 35 - ... system, we might have assumed any one wheel. Thus, to give the subject a practical aspect, having obtained a pinion wire, we may require to cut out the teeth of a wheel which may be led by it. Let the assumed form of the wheel be extended into a cylindroid as in the pinion wire; let it be notched so as to form a series of cutting edges as on the bar cutter; and let it be freed in such a manner as to slide parallelly to the axis of the index wheel, while it may be turned upon its own axis by means...

Page 36 - ... blank so as to make a cut, repeat this in the usual way all around. Turn now the pinion wire on its own axis by a fraction of a tooth, and at the same time, turn the stop ring by a similar fraction of a revolution; repeat the cut all around in the usual way, and continue this until the stop ring has made a complete revolution, then is the blank toothed in such a way as to gear truly with the pinion.

Page 97 - ... it is at all times expedient to try for a simple train, and to have recourse to the travelling arm only when the other fails us.

Page 9 - A skew arch has a direct and an oblique span ; the former, or span on the square, is the perpendicular distance between the abutments, the latter, or span on the skew, is the distance between the abutments parallel to the face of the arch. The former is less than the latter in the ratio of the cosine of the angle of obliquity to unity. It is the span on the skew which is equal to that of the corresponding rectangular arch.