Page:The Kinematics of Machinery.djvu/172

 radius = the central distance c a, and from b with radius = 5 A a arcs of circles, the intersection of these gives us the required profile- point, a v In this way the profile a: b. . . can be exactly deter- mined point by point. If great accuracy be not required the following approximate method (by Poncelet), can be used. Erect normals in a sufficient number of points a, c, e ... of the assumed profile, and con- tinue these to their intersections FlG - 104 - b, d,f. . . with the correspond-

ing centroid. Find the corre- sponding points b v dp/! . . on the centroid B, and describe from them circular arcs with radii equal to the central distances a I, c d t

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e f, etc.; a curve enveloping these arcs gives a near approximation to the required profile.

The foregoing method in its application to spur-wheels is known in Germany as the "general method" of drawing teeth,