The practice of mechanical drawing for self-instruction by Welch Williams

Author:Welch, Williams. [from old catalog]
Language: eng
Format: epub, pdf
Tags: Mechanical drawing
Publisher: Newberry, S. C. E. H. Aull
Published: 1895-03-25T05:00:00+00:00

Draw lines through the centre, making angles of 15 degrees (Prob. 15). Measure the distance per revolution on one of these lines, and divide the distance into 24 equal parts. With the point as a centre and a radius equal to the distance to the ^rs^ point of division, draw an arc intersecting one of the lines; with a radius equal to the distance to the second point of division, draw an arc intersecting the n<ext line; from the third point of division draw an arc intersecting the third line, and so on. These points of division will be points in the required spiral. It maybe drawn in ink with the compasses by finding centres and radii by trial, which will draw arcs through three of the points at a time.

The INVOLUTE of a circle is drawn by a point in a straight line which rolls on the circle. A pencil fastened to a string, which is kept stretched as it is unwound from a spool, -vrill draw an involute of a circle. This curve is used for drawing the teeth of gear-wheels.

PROB. 47. Draw the involute of a given circle. (Take circle 1 in. in diameter.)

Divide the circle into 24 equal parts. (Prob. 15), and draw lines tangent to the circle at these points of division (with triangles. Fig. 5). With one point of division as a centre, and with a radius equal to the length of the arc between the points of division, draw an arc from the circle to the first tangent line; with the next point of division as a centre, draw an arc from the end of this arc to the next tangent line; with the third point as a centre, continue the curve to the third tangent line, and so on. When 24 divisions are taken the curve will be more accurate, if these ■centres are taken on a circle whose diameter is about 1-94 greater than the diameter of the given circle.

A CYCLOID is drawn by a point in the circumference of a circle which rolls on a line. If the generating circle rolls on the outside of a circle, the curve is an epicycloid; and, if it rolls on the inside, it is a hypocycloid. The circle on which it rolls is the pitch circle. These curves are used for drawing the teeth of gearwheels.

PROB. 43. Draw epi- and hypocj^cloids; the diameters of the circles being given. (Take diameter of pitch circle 4 ins., and diameter of generating circles 1 in., and let both curves start from the same point.)

Draw part of the pitch circle, and draw a generating circle tangent to it on the ■outside, and draw another tangent on the inside. With the centre of the pitch circle as a centre, draw arcs passing through the centres of the generating circles. Make a number of equal divisions on the pitch circle, and draw lines through them from the centre and intersecting the two arcs. With these points of intersection on the arcs as centres, draw parts of the generating circle where the curve is to be drawn.

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