Minimum Number of Binary Links in a Constrained Mechanism with Simple Hinges:

If a mechanism contains simple hinges, also the number of joints is given by the following equation:

2 j = 2n₂  + 3n₃  + 4n₄  + ... = in_i                                                               . . . (7.3)

It is because a ternary link joins three links & likewise for other links.

Putting for n from Eq. (7.1) & for j from Eq. (7.3) in the expression for degrees of freedom, the described equation is attained:

F = 3 [(n₂  + n₃  + ... + n_i ) - 1] - [2n₂  + 3n₃  + 4n₄  + ... + in_i ]

As a fully constrained linkage have degrees of freedom equivalent to one. Thus,

1 = n₂  - n₄  + . . . + (3 - i) n_i  - 3                                                   . . . (7.4)

Or,

n₂  = 4 + n₄  + ... + (i - 3) n_i                                                                                              . . . (7.5)

From Eq. (7.5), this is quite evident; the minimum number of binary links is four. Thus, the four bar kinematic chain is the easiest mechanism.