Abstract: In the vicinity of bifurcation singularities of non-redundant robot manipulators, null-space based quasiarc length method will face difficulties due to the existence of more then one solution branches of the inverse kinematics while tracking the desired path in the workspace. By calculating the local model of the solution curve near the bifurcation,an approach is presented to follow the solution curve starting from the singular point to both sides of it. Simulation results demonstrate that the approach effectively helps to solve the path-tracking problem in the vicinity of bifurcation.