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Robot arms with redundant degrees of freedom (DOF) are crucial in service robots where smooth trajectories and obstacle avoidance in the working area are needed. This paper presents a closed form analysis on the joint limits, and elbow movement minimization using the redundancy of a seven DOF manipulator based on a closed form inverse kinematics. Using the redundancy circle of the redundant arm, the NULL space, the motion planning has been performed. The solution provided has the advantage of being exact with low computational cost. Consequently, this method eliminates the need for trial-and-error which takes times and may not result in a desirable solution. Experimental results have been provided showing the advantages of closed form inverse kinematics over the iterative methods.