Abstract: Existing methods to avoid the kinematic singularities are complex. A novel approach (named "singularity separation plus damped reciprocal" method) is proposed for PUMA-type manipulators. Firstly, we analyze the singularity conditions and separate the singularity parameters from the Jacobian inverse. Then, the damped reciprocals are used to avoid the singularities by replacing their reciprocals. Since the SVD decomposition and the estimate of the minimum singularity value are not required, the algorithm is more efficient and fit for real-time application. And not all components of the end-effector velocities are sacrificed in accuracy. The method can be used for prescribed or real-time trajectory tracking. Simulation and experiment results verify the method.