This study proposes an analytic inverse kinematic solution considering joint limit and self-collision avoidance for a redundant 7DOF manipulator with spherical shoulder and wrist joints. An analytic approach is used to satisfy the sub-task. The arm angle is used to restrain the manipulator redundancy. The analytic inverse kinematic solution set satisfying the sub-task is proposed by determining the range of the feasible arm angle. The effectiveness of the proposed method was verified through a simulation. We confirmed that the solution of the proposed method always satisfies the joint limit constraints and self-collision avoidance.