# Grubler’s Formula

Consider a mechanism consisting of $N$ links, where ground is also regarded as a link. Let $J$ be the number of joints, $m$ be the number of degrees of freedom of a rigid body ($m=3$ for planar mechanisms and $m=6$ for spatial mechanisms), $f_{i}$ be the number of freedoms provided by joint $i$, and $c_{i}$ be the number of constraints provided by joint $i$, where $f_{i}+c_{i}=m$ for all $i$.
$dof=m(N−1−J)+∑_{i=1}f_{i}$
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*This formula holds only if all joint constraints are independent. If they are not independent then the formula provides a lower bound on the number of degrees of freedom.*