Industrial drawing: by Mahan D

Author:Mahan, D[ennis] H[art], 1802-1871. [from old catalog] & Thompson, Dwinel F. [from old catalog]
Language: eng
Format: epub
Tags: Mechanical drawing. [from old catalog], Drawing instruments. [from old catalog]
Publisher: New-York, J. Wiley & sons
Published: 1877-03-25T05:00:00+00:00

F prolonged, and with a radius equal to 8 — h, that of the base of the horizontal cylinder. This circle may be regarded as the projection of the horizontal cylinder on a vertical plane, taken perpendicular to the axis of the cylinder. In this position of the plane and cylinder, the elements of the cylinder will be projected into the circumference e'u'%'\ &c., of the circle; and its axis into the point /, the centre of the circle. The two elements cut from the cylinder, by the plane of which t — u is the trace, for example, will be projected in the points u\ and -d'; each at the equal distances v' — u'^ and v' — u" from the horizontal diameter e' — h'\ of this circle. Drawing the lines i! — u\ and t" — u'\ at the same distance from ^ — K as the points u' and t^" are above and below the horizontal diameter e' — h'\ they will be the projections on the primitive vertical plane of the same elements, of which v! and u" are the projections on the vertical plane perpendicular to the axis. The four points a?', x\ and x'\ x'\ in which the lines t^ — u\ and t^^ — u'^ cut the lines m'—»', and n' — z' will be the projections of four points of the curves in which the cylinders intersect. In like manner, the vertical projections of as many points of the curves, in which the cylinders intersect above and below the axis of the horizontal cylinder, may be found, as will be requisite to enable us to draw the outlines of their projections.

The portions of the curves, drawn in full lines, lie in front of the two cylinders; the portions in dotted lines, lie on the other side of the cylinders.

The highest points rf, and c of the lower curve will lie on the elements of the vertical cylinder, projected in the points d^ and c. The lowest points y, y of the same will lie on the lowest element of the horizontal cylinder, projected in r —«. The corresponding points of the upper curve will hold a reverse position to those of the lower.

Prob. 107. (PI. XIII. Fig. 129.) To construct the projections of the cv/rves of intersection of two right cylinders, one of which is vertical, and the other inclined to the horir Bontal plane, the oases of both being parallel to the vertical plcme.

Let the trapezoid a'Vldo' be the vertical projection of the

vertical, and the rectangle ^fg'h* that of the inclincid cylinder. The horizontal projection of the first will be the circle adhc; that of the second ^gare/liknm / the two ends of the Becond being projected into the two eqnt^l ellipses J^lem, and gihn.

Intersecting these cylinders, as in Proi. 106, by planes parallel to the vertical plane; any such plane, as the one of which t — Uy for example, is the trace, will cut, from the inclined cylinder,

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