Linkage isomers are analogous to these chemical compounds in that the links (like
atoms) have various nodes (electrons) available to connect to other links' nodes. The
assembled linkage is analogous to the chemical compound. Depending on the particular
connections of available links, the assembly will have different motion properties. The
number of isomers possible from a given collection of links (as in any row of Table 2-2)
is far from obvious. In fact the problem of mathematically predicting the number of isomers
of all link combinations has been a long-unsolved problem. Many researchers have
spent much effort on this problem with some recent success. See references [3] through
[7] for more information. Dhararipragada [6] presents a good historical summary of isomer
research to 1994. Table 2-3 shows the number of valid isomers found for one-DOF
mechanisms with revolute pairs, up to 12 links.