An analytical formulation for computing kinematic sensitivity of the spatial four-bar mechanism is presented. The experimental code developed is used to compute an assembled configuration for the mechanism due to a design variation. The mechanism is modeled into a graph where a body is defined as a node and a kinematic joint is defined as an edge. The spherical joint is cut to convert the model into a spanning tree structure. Cutting an edge introduces the spherical constraint. The variation of this constraint is computed while maintaining the joint-attachment vectors and orientation matrices as variables. The variation of these variables determine the new kinematic design of the system. A recursive formulation is introduced to obtain the state variation of a body in terms of the state variation of a junction body and of the relative coordinates along the chain. The Jacobian matrix is then transformed from Cartesian coordinate space to joint coordinate space using velocity transformation matrices. Kinematic sensitivity analyses due to changing a joint-attachment vector and an orientation are presented.