Page:The Kinematics of Machinery.djvu/349
CONIC QUADMIC CEANK CHAIN. 327
75. The Conic Quadric Crank Chain (-).
If the axes of the four cylinder pairs of the chain (C' be not parallel, but have a common point of intersection at a finite distance, the chain remains movable, and (the former conditions being again fulfilled) also closed. The axoids will no longer be cylinders but cones, as all the instantaneous axes have the point of intersection in common, and the motion of the links will be determined by their conic rolling, the general nature of which we examined in 10. If the lengths of the links measured as arcs of great circles upon a sphere drawn about the point of inter- section (M) of the axes fulfil the conditions laid down for those of (CD in 65, we have a chain of such a form as is shown in Fig. 256. We may call it a conic quadric crank chain, or
four-linked conic crank chain. It stands in a very close relation to the cylindric crank chain, which indeed may be con- sidered as the special case of it when the point of axial intersection, is at an infinite distance. 48 The formula for the chain is a I) c d
C+...2. d c-...2...cz C+...2...C+ C-...2...C-.
It can be contracted into the very simple form ((7J-), in using which we understand not only that the pairs are oblique to each other, but also that their axes have a common point of intersection, as is shown above in Fig. 256.
The various forms of the cylindric chain repeat themselves with