Page:The Kinematics of Machinery.djvu/326

 304 KINEMATICS OF MACHINERY.

of the solution of one and the same kinematic problem by quite different mechanisms.

The motion of the block c (Fig. 228) is also remarkable. Its centroid relatively to a is a great Cardanic circle, described about the centre 3, and the smaller centroid with which this rolls must be

FIG. 229.

imagined to be fixed to a, and to have 2 for its centre. It therefore coincides with the circular centroid of the linkfr. The motion of c can thus be realised by remembering that its centroid rolls about the fixed smaller centroid of a. The point-paths of the block are therefore all peri-trochoids.

71. Expansion of Elements nrthe Slider-crank Chain.

We have not hitherto concerned ourselves at all with the diameter of the cylinder pairs in the crank mechanisms. We know that alterations in the dimensions of the -elements do not affect their motions, so long as the centroids remain unaltered. It will be well, however, to give them some special consideration here, for these external alterations sometimes so conceal the real nature of the mechanism as to cause much indistinctness in its ordinary kinematic treatment. In considering this subject we shall con- fine ourselves in the first place to the changes of the relative