Extrusion-based additive manufacturing systems usually use three degrees of freedom extrusion tools to perform the deposition operation. This requires the use of support structures to deposit structures with overhang features. The use of support structures can be avoided by adding degrees of freedom to the build platform. The elimination of build structures can offer benefits in terms of reduction of build time and elimination of postprocessing costs. This paper demonstrates that the use of three degrees of freedom build platform enables printing of complex shapes without support structures. We present computational foundations for generating paths and trajectories for synchronizing the motion of three degrees of freedom build platforms and three degrees of freedom extrusion tools. We report results on six different test parts in terms of reduction in build time, accuracy, and surface roughness.