If a mechanism has mobility M, then the sum of its joints' mobility is also M. The number of joint DOF N must be >= M. When N > M the mobility of some joint DOF must be less than 1 and could be as small as 0. If J represents the Jacobian matrix of constraint equations defining a mechanism, the rows of this matrix represent normals to the mechanism's constraint manifold. Columns of the highest rank orthonormal matrix V, which are orthogonal to the rows of J, represent tangents to the constraint manifold surface. The norm of the ith row of V, 0 <= |V_i| <= 1, represents the physical mobility number, 0 <= M_i <= 1, of the ith joint DOF, where sum over N of M_i = M. If M_j of joint DOF j is greater than M_i of joint DOF i, then qualitatively joint DOF j is more mobile than Joint DOF i. If M_i = 0, this ith joint DOF is locked and cannot be physically changed. If M_j = 1, this jth joint DOF is unconstrained and can be physically changed with minimal effort. If 0 < M_k < 1, this kth joint DOF is partially constrained and can be physically changed with effort inversely proportional (qualitatively) to its mobility number. The distribution of a mechanism's mobility M across its N joint DOF, in the form of individual M_i, changes with its pose and determines its real mobility, its ability to perform the task(s) for which it was designed.
Unfortunately, I didn't record the lecture. But you can have the materials of lecture 5 in the following video ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-MxEb2E2wsjk.html
The same materials are presented in an online e-lecture and can be found following this link ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-_8sR1xLBK18.html
