Page:The Kinematics of Machinery.djvu/358

 33ti KINEMATICS OF MACHINERY.

thin. When the arrangement of Fig. 269 occurs in practice it is most frequently with well-rounded corners in the recess in &. The manner in which the true form of these round corners can be obtained is not unimportant; it may be looked at as follows.

If we have assumed in the first place some considerable breadth for the slider d, and found the required shape of the envelope in the coupler, we can then draw equidistants to the profile thus obtained ( 35), and may choose such V X V of these as give us for the

JT IG 270. prism a narrower profile than

before. The corresponding

equidistants for the recess in b will then give us the rounded corners required, as is shown in the figure above. The pairing is still, however, incomplete (force-closed) for there is some freedom left between I and d in all positions but those of greatest pressure.

The form in which Leonardo's elliptic chuck is most commonly constructed furnishes us with a remarkable example of a reduced crank chain. This form, to which we have already alluded in 72, is shown in Fig. 271. The reduction here consists in the omission of the coupler b from the turning cross-block, the form of the mechanism is that, therefore, which would be obtained from Fig. 267 if the radius of the slot were made infinite. Its contracted general and special formulsB are (C'^P-^Y ~ b an d (C% PS)* b respectively, for it is driven by the slider d, turning about the pin 1 (compare the mechanism in 72, where b is the driving link). a^ is the end of the headstock, to which the piece & 2 is secured by means of adjusting screws. These two form together the fixed link of the mechanism, the crank a. This carries the bearing for the spindle 1, to which the slide d, carrying the open prism 4, is attached; d is therefore of the form C+...1...P-. The cross-block c, (P+... ...P~) consists here of the full prism paired with d at 4, and of the two pieces 3 3, forming the sides of an open prism, which are shown in the lowest of the accompanying figures. These pieces envelop