The constraints on thephysical limit should be considered in a kinematic redundancy resolutionproblem of a robot. This paper proposes a new optimization scheme toresolve kinematic redundancy of the robot while considering physicalconstraints. In the proposed scheme, quadratic inequality constraintsare used in place of linear inequality constraints, thus a quadraticallyconstrained optimization technique is applied to resolve the redundancy.It is shown that the use of quadratic inequality constraintsconsiderably reduces the number of constraints. Therefore, the proposedmethod reduces the problem size considerably and makes the problemsimple resulting in computational efficiency. A numerical example of a4-link planar redundant robot is included to demonstrate the efficiencyof the proposed optimization technique. In this example, simulationresults using the proposed method and another well-known method arecompared and discussed.