Define kinematic indeterminacy

Kinematic indeterminacy (degree of freedom) is the number of independent joint displacements, translations and rotations, that are unknown and must be determined to describe completely the deformed shape of a structure under load.

It is the number of unknowns in the displacement (stiffness) method. For a plane frame, $D_k = 3j - r + c'$ when axial deformation is allowed, and $D_k = 3j - r - m + c'$ when members are axially rigid. For a plane truss, $D_k = 2j - r$.

Example: A fixed-based portal frame ($j = 4,\ r = 6,\ m = 3$) has $D_k = 12 - 6 - 3 = 3$ for inextensible members: the rotations of the two top joints and one sway. A propped cantilever has $D_k = 1$, the rotation at the roller end.