This research addresses singularity issues in robotics. It analyses new types of manipulation systems with the goal of eliminating all singularities. The class of actuator considered is the symmetrically actuated double pointing system (SADPS). A configuration using SADPS joints both for shoulder and wrist motion is analyzed. The resulting manipulation system is expected to be singularity free. The research comprises four steps, including (1) derivation of kinematic equations of motion for this manipulation system, (2) determination of the Jacobian matrix of the system, (3) determination of singularity configurations, and (4) development of preliminary mechanical designs. The expected improvement in dexterity would imply greater manufacturing flexibility in industrial robotic systems.