Multi-Body Systems

If a body is composed of several sub-bodies, then the degree of freedom of the multibody system is calculated using the following formula:
$3·\mathrm{n}-(\mathrm{r}+\mathrm{v})$
n = number of sub-bodies
r = number of reaction forces
v = number of internal joint forces

A pin joint results in two connection reactions, as is the case with a roller support. Each additional bar connected to a (free-floating) pin joint increases the number of connection reactions by another two.

f < 0: statically indeterminate (overconstrained)
f = 0: statically determinate
f > 0: tatically underdetermined (position undefined)