An on-line trajectory generation algorithm with time-variant kinematic motion constraints is presented in this paper. The algorithm is an extension of a class of trajectory planning method which is applicable with constant kinematic motion constraints only. The extended approach allows the abrupt change in the value of the physical robot constraints(jerk, acceleration, and velocity) at any time instant and keeps these constraints bounded during the trajectory parameter adaptation. Short computation time enables the real-time usage of the proposed algorithm so that it can update the trajectory at any time taking into account the current robot motion limits. It allows sensor integration in low-level robot motion control, that is, making robots have the capability of reacting to unforeseen sensor events in real time. Simulation results are summarized in the paper.