The inverse kinematic problem of redundant manipulators is solved by the compact formulation technique. The compact formulation [17,18] is derived by applying Gaussian elimination, then the general solutions are still formulated as one particular solution together with homogeneous solutions. The homogeneous solutions are merely functions of free variables. Inverse kinematic solutions derived by the pseudoinverse formulation can always be converted into a compact form. Also, it is proven that the implementation by the compact formulation is computationally more efficient. The inherent singularity problems of Inverse Kinematics is also considered in this paper. In order to obtain continuous and feasible joint-rate solutions even at or in the neighborhood of singular points and to improve the exactness in the achievable directions, the newly-developed Compact-Inverse method is introduced. The Compact-Inverse method still applies the compact formulation to constrain the manipulator to move into the achievable directions. It is believed that the compact formulation approach can resolve the inverse kinematic redundancy problem more efficiently and exactly than the traditional pseudoinverse formulation.