532 KINEMATICS OF MACHINERY.
synthesis) forms and arranges all the possible pairs of elements, and then (as general synthesis) finds all the combinations of these pairs into chains. From this systematised arrangement of pairs and chains the special combinations best suited to each particular case can then be chosen by an inductive process. When the required chains have thus been found the remaining processes of forming them into mechanisms and machines present no difficulties.
We must now examine the results to which this indirect synthetical method leads us.
�Synthesis of the Lower Pairs of Elements.
In 55 we chose twelve class symbols for the kinematic elements, of which ten were for rigid elements :
$ Screw, H Hyperboloid,
E Bevolute, G- Sphere,
P Prism, A Sector (portion of a revolute),
C Cylinder, Z Tooth,
K Cone, V Vessel,
and two for the flectional elements,
T Tension-organ. Q Pressure-organ.
We shall first look at the combination of the rigid elements into pairs. We may therefore omit the element V, which is always paired with the pressure-organ Q. G, also, stands only for a particular revolute, and A for a portion of the same element, so that these symbols may both be included under JR. Seven elements therefore,
S,R,P,H,K,C,Z
remain for synthetic treatment. Three of the pairs which can be formed from these elements are already well-known to us; the three common lower pairs :
�~ or (S) the screw- or twisting-pair,
E^E~ or (R) the revolute- or turning-pair,
PtP~ or (P) the prism- or sliding-pair.
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