General Function sets theory-based type synthesis of the collaborative 3D printer for planar and non-planar printing

Abstract

3-dimension printing (3DP) or Additive Manufacturing promises rapid prototyping with 3D printers, the precondition for manufacturing complex components and surfaces. Usually, three-axis 3D printers are widely applied with planar slicing, limiting solid freeform fabrication with finite printing direction. Non-planar slicing (or curved layer slicing) has been put forward to break through the layerwise framework with infinite directions, requiring multi-axis 3D printers with more than four DOFs. However, as far as the authors know, the specific design method of 3D printers’ structure has seldom been studied for non-planar printing. Furthermore, there is no specified systematical research on the type synthesis of the 3D printer, which has two collaborative modules functioning together. One module serves as the build platform and the other as the print head attached moving platform. Hence, to obtain topological structures of the collaborative 3D printer for planar and non-planar printing, this paper investigates the type synthesis by introducing a research background at first. Then, the motion characteristics of the collaborative 3D printer are determined based on the planned paths’ geometric characteristics and motion requirements of the 3D printer. After that, General Function sets theory and the distribution principles are introduced, and the case study of 3D printers with 3T, 3T1R, and 3T2R is given. Finally, this research paper proposes a class of rotary 3D printers having 2T1R, 2T2R, and 2T3R innovatively. Furthermore, one prototype of the above case study is designed, and a preliminary experiment for planar and non-planar printing is carried out to verify the feasibility of the type synthesis’s result. In general, aiming at planar and non-planar printing, this paper presents a theory for type synthesis of collaborative 3D printers to offer a much richer set of kinematic structures than the most commonly used three Degree of Freedom printers.

An initial feasibility study into ray-based slicing for revolving thin-wall parts using a rotary 3D printer

“…The motion characteristics of the 3D printer are based on the planned paths' geometric characteristics and motion requirements of the print head. General function sets theory is investigated for the type synthesis of collaborative 3D printers for planar and nonplanar printing in authors' previous work (Zhao and Guo, 2022). Then, mechanical structures are designed after obtaining the rotary 3D printer's topological structures.…”

“…And the cross-section of the extruded filament is regarded as a perfect circle to simplify the modeling. The RSS is represented with a parametric surface P ( u , v ), approximating all the feature points of STL based on the precision requirements (Zhao et al , 2020a). Then, a series of slicing surface P O ( u , v ) could be obtained with equation (1): with the aid of offsetting, the slicing surfaces P O ( u , v ) in Figure 1(b) and FT surfaces P′ O ( u , v ) are obtained: …”

“…Here, it is necessary to satisfy that the product of the angle Δ θ (| θ i − θ i +1 |) between adjacent printing deposition paths corresponding to the outermost curved surface layer r ( x , y , z ) (radial distance r of any point ( x , y , z ) in the path) satisfies path interval . Here, path interval means the distance between adjacent FT points in adjacent FT curves in the same horizontal boundary, which is illustrated in Figures 1(f), 5(c) and 10 in the authors’ previous publication (Zhao et al , 2020a). The polar angle θ takes different values and traverses the printed parts in the entire cylindrical workspace to obtain the printed parts’ radially innermost and outer curved surfaces and the printing path ( r , θ , h ), which is illustrated in Figure 5(c).…”

Process planning of cylindrical printing for a novel 2T2R-type rotary 3D printer and an initial feasibility investigation

“…The details could be observed from the workspace analyses in the authors’ previous research. 9 On the other hand, given the crank-slider input angle θ 1 , the design parameter of print head swing range ψ is larger than the prototype operating parameters.…”

“…Specifically, a class of rotary 3D printers has been proposed, and the authors' previous research has obtained thirty-six topological structures of the rotary 3D printers. 9 Second, the dimensional parameters of a multi-DOF 3D printer determine its workspace during additive manufacturing and rotation capability of the print head to the build platform for CLMEX. Hence, using Performance-Chart Based Design Methodology (PCbDM), the workspace and transmission angle of the multi-bar chains are optimized simultaneously to obtain the shared workspace, where the 4R1P five-bar is optimized based on the classification of Grashof criteria.…”