Overconstrained mechanism

In mechanical engineering, an overconstrained mechanism is a linkage that has more degrees of freedom than is predicted by the mobility formula. The mobility formula evaluates the degree of freedom of a system of rigid bodies that results when constraints are imposed in the form of joints between the links.

If the links of the system move in three-dimensional space, then the mobility formula is

${\displaystyle M=6(N-1-j)+\sum _{i=1}^{j}f_{i},}$

where N is the number of links in the system, j is the number of joints, and f_i is the degree of freedom of the ith joint.

If the links in the system move planes parallel to a fixed plane, or in concentric spheres about a fixed point, then the mobility formula is

${\displaystyle M=3(N-1-j)+\sum _{i=1}^{j}f_{i}.}$

If a system of links and joints has mobility M = 0 or less, yet still moves, then it is called an overconstrained mechanism.