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This paper proposes an analytical methodology of inverse kinematic computation for 7 DOF redundant manipulators with joint limits. Specifically, the paper focuses on how to obtain all feasible inverse kinematic solutions in the global configuration space where joint movable ranges are limited. First, a closed-form inverse kinematic solution is derived based on a parameterization method. Second, how the joint limits affect the feasibility of the inverse solution is investigated to develop an analytical method for computing feasible solutions under the joint limits. Third, how to apply the method to the redundancy resolution problem is discussed and analytical methods to avoid joint limits are developed in the position domain. Lastly, the validity of the methods is verified by kinematic simulations.