# 3D Printing of Objects with Continuous Spatial Paths by a Multi-Axis Robotic FFF Platform
## 1 Introduction  
Additive Manufacturing (AM), also known as 3D printing, has gained a lot of attention in recent years and has been applied in various fields such as rapid prototyping, bioengineering, and architecture [1]. Fused Deposition Modeling (FDM), or Fused Filament Fabrication (FFF), is the most popular process for 3D printing. Standard FDM equipment usually has three degrees of freedom. The nozzle of the equipment travels along the \(X/Y/Z\) axis and deposits the material in the spatial Cartesian coordinate system. Based on this platform feature, most 3D printing toolpath planning methods can be divided into specific steps: (1) obtain a digital model of the printed part, (2) slice the model equidistant using a set of parallel planes, and (3) perform toolpath planning and generate print toolpaths in each layer section. This method is easy to implement but has potential problems, such as introducing manufacturing constraints and staircase effect on the surface. During manufacturing, the FDM printer can deposit material only layer by layer, which results in significant anisotropy. The tensile strength in the build direction (vertical) is about 40% lower than that in layer direction (horizontal) [2]. Simultaneously, the sloping surface of printed parts will suffer from the staircase effect because of layering, which affects the surface quality and leads to stress concentration. These problems weaken the strength of the FDM product and limit its application scenarios, and prompted the researchers to conduct extensive exploratory work.  
At present, the mainstream idea is to increase the DOF of the 3D printing system and add more flexibility to the manufacturing process to make up for the FDM deficiency. The conventional method is to add more DOF, which inevitably increases the complexity and cost of existing systems. With the continuous development of robotics, more and more multi-DOF platforms based on robotic arms are applied to 3D printing, making it an interdisciplinary subject in advanced manufacturing [3]. Compared with traditional printing equipment, robot arms are more flexible, have a broader printing range, and a more mature controlling system.  
However, the toolpath planning method of multi-DOF 3D printing is more complex and less developed [4]. Most of the research on multi-DOF printing aimed to reduce or eliminate the support. There are few work studies on toolpath planning and the fabrication strategy to print parts with complex geometry and corresponding mechanical properties. Because the deposition direction of multi-DOF is different from the traditional 3D printing that deposits in a set of parallel planes, it is necessary to analyze the mechanical properties of the multi-DOF printed parts. In terms of control, there is no set of general control languages for multi-DOF printing. Different platforms usually use different scripting languages to control the hardware, increasing the difficulty of software development.  
This paper presents a global spatial continuous toolpath planning method and the controlling strategy for the multi-DOF robotic 3D printing platform. The rest of this paper is organized as follows. Section 2 reviews the existing multi-DOF 3D Printing systems and corresponding toolpath planning methods. The details of the multi-DOF 3D printing pipeline are presented in Section 3. We report the experimental results in Section 4. Section 5 gives the conclusion and future works.