In order that a kinematic chain may be made the basis of a mechanism, every point in any link of it must be completely constrained with regard to every other link.
The Reuleaux system, therefore, consists essentially of the analysis of every mechanism into a kinematic chain, and since each link of the chain may be the fixed frame of a mechanism quite diverse mechanisms are found to be merely inversions of the same kinematic chain.
There is a corresponding kinematic peculiarity, in that the connection is now not strictly rigid, an infinitely small relative displacement being possible.
Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.
Compound chains are formed by the super-position of two or more simple chains, and in these more complex chains links will be found carrying three, or even more, halves of kinematic pairs.
The Joy valve gear mechanism is a good example of a compound kinematic chain.
A kinematic link of the simplest form is made by joining up the halves of two kinematic pairs by means of a rigid link.
In the Reiileaux system of analysis of mechanisms the principle of comparative motion is generalized, and mechanisms apparently very diverse in character are shown to be founded on the same sequence of elementary combinations forming a kinematic chain.
These principles may be applied to examine any possible combination of links forming a kinematic chain in order to test its suitability for use as a mechanism.
From the purely kinematic point of view, the t of our formulae may be any continuous independent variable, suggested (it may be) by some physical process.