Page:The Kinematics of Machinery.djvu/182

 160 There is nothing to prevent our choosing larger radii for these equidistants,—in Fig. 114, for instance, they are l 1/6 times as long as the chord P Q. The profile form obtained only differs from the

115.

former one in having the vertex angles at P, Q and R rounded by arcs having those points as centres. From a practical point of view the resulting profile is a great improvement on the former one, on account of the removal of its sharp edges at P, Q and R. We have before used a similar construction to this in Plates XII. and XIII. If the radii of the equidistants be chosen less than PQ we get unusable forms, such as the one shown in dotted lines.

A third illustration of the use of equidistant profiles is furnished to us by the higher pair of elements shown in Fig. 115, which has already been described. Here the nature of the motion is known from two given point-paths,—the straight lines in which the points b and c move. Equidistants to these lines give us the profiles of the prismatic slots in the piece a a d d, while the equidistants to the two points are the circular profiles of the pins b and c. Here we do not even require to know the centroids in order to construct the pair of profiles. They have, however, as follows from § 22, the form of Cardanic circles, or their arcs.

§36. Sixth Method. Approximations to Curved Profiles by Circular Arcs. Willis' Method.

If the profiles of elements be curves of varying radius their construction is somewhat troublesome, and it may be very convenient