To find dependent velocities of a four-bar mechanism.

Although a four-bar mechanism has three moving links, the number of independent degrees of freedom is one. Typically, the angular orientation with respect to the positive x-axis of one of the links is chosen as the generalized coordinate. The angular orientations of the remaining two moving links (with respect to the positive x-axis) will then become the dependent variables. This video describes the methodology to determine the dependent velocities using vector equations. 

To find dependent accelerations in a four-bar mechanism

This video describes the methodology to determine the dependent angular accelerations in a four-bar mechanism.