Today, more and more robots are required to do simple or complex tasks such as painting, servicing, welding, etc. To be able to implement these needs, the orientation modules are used as integrated parts of the robots. The paper deals with a novel type of orientation modules for serial robotic arms actuated by linear actuators. The design of orientation modules for flexion-extension or adduction-abduction motion used an optimized geared linkage with linear actuation and slider crank as base mechanism. Using a proposed optimum synthesis method in order to minimize the deviation between the transmission function and the desired linear transmission function were studied the influence of the imposed parameters on normalized length of the elements and the transmission function. The conclusions were used to set the imposed parameters for the synthesis of the above-mentioned modules. The optimized modules were designed for realizing an oscillation angle of 360 deg without singularities, a minimum number of elements and a favorable transmission angle of the base linkage.