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.

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In global climate change, improving carbon productivity holds great importance for China’s sustainable growth. Based on panel data of 30 Chinese provinces and cities from 1997–2017, the drivers, spatial effects, and convergence characteristics of carbon productivity in China are explored by combining a factor decomposition framework and a spatial panel model. The findings show that (1) China’s carbon productivity shows continuous positive growth, and the substitution effect of capital for energy dominates this changing pattern; (2) There is a β-convergence trend and club convergence in China’s carbon productivity, and the spatial technology spillover accelerates the convergence rate; (3) With its accelerated industrial transformation and technological upgrading, China’s current carbon productivity converges faster than its earlier stage, and the role of physical capital investment has gradually shifted to suppression. In contrast, the positive push of human capital investment has been strengthened; (4) From the perspective of the realization mechanism, the convergence of carbon productivity in China mainly comes from the convergence of energy restructuring and capital-energy substitution. These findings can help China narrow the inter-provincial carbon productivity gap in terms of improving factor structure, upgrading technology, etc., and provide references for sustainable growth decision making in China and around the world.