Much additive manufacturing research focuses on systems suitable for industrial applications, especially research on metal processing. Our research aims to design a desktop-scale prototyping machine to process metal wire. Possible applications for this research include various wire structures, such as wire sculptures. The wire joining technology is the most important subsystem of the envisioned layer-based process. In this research, three concepts are proposed and analyzed according to the power required to fully melt the wire. The selected approach uses a wire bender to create the desired geometry of the product, and a pulse TIG welder to join the metal wire to retain the shape. Experiments were conducted to evaluate the joining strength of pulse TIG welds to verify the joining efficiency of the method. The experimental results indicate that filler metal is required to produce acceptable welding strength. A conceptual CAD model of the complete system is presented.