The progressive clamping technique smoothly enforces a damping towards the joint limit and searches for an optimal task achievement within the remaining joint variation sub-space so that the proposed method helps to avoid the solution to converge to non-optimal final-states in singular contexts as it appears with clamping. The first part presents the interactive control of a kinematic chain with progressive clamping within our Prioritized Inverse Kinematics solver.  The strength of the red color indicates the value of the damping force. The second experiment compares clamping (red color: joint limit reached)  and progressive clamping (strength of red color indicates the damping force). In the last experiment we make a comparison between clamping and progressive clamping for a virtual mannequin where the progressive clamping approach is faster due to kinematic singularity avoidance.