Due to hardware limitations, physical constraints, such as joint rate bounds and joint angle limits, always exist. In the present work, these constraints are included in the general formulation of the redundant inverse kinematic problem. To take into account these physical constraints, the computationally efficient compact QP (quadratic programming) method is derived to resolve the kinematic redundancy problem. In addition, the compact-inverse QP method is developed to remedy the unescapable singularity problem. The compact QP (compact and inverse QP) method makes use of the compact formulation to obtain the general solutions and to eliminate the equality constraints. As such, the variables are decomposed into basic and free variables, and the basic variables are expressed by the free variables. Thus, the problem size is reduced and it only requires an optimization algorithm, such as QP, for the free variables subject to pure inequality constraints. This approach will expedite the optimization process and make real-time implementation possible. Two examples are given to demonstrate the generality and superiority of these two methods.