Degrees of Freedom

Grubler’s Formula

Consider a mechanism consisting of links, where ground is also regarded as a link. Let be the number of joints, be the number of degrees of freedom of a rigid body ( for planar mechanisms and for spatial mechanisms), be the number of freedoms provided by joint , and be the number of constraints provided by joint , where for all . #to-review 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.