Abstract: Firstly, the structural parameters of the printer were introduced to represent the positions of two rotational axes and the workpiece in frame coordinate system. The general forward kinematics model of table-tilting five-axis 3D printer was established by exponential product theory. Secondly, the specific expressions of double solution of the rotational axis angles were obtained by combining the periodicity of the trigonometric function, the rotational axis travel and the five-axis structure features. The selection principle was proposed to obtain the optimal combination of the rotational axis angles based on the shortest path of the rotational angle. The displacements of each translational axis were obtained by the selected rotational axis angles. All the motions obtained were absolute motions based on zero position of each axis, and then the NC printing codes used directly for machining were generated, which might be processed without the help of rotational tool center point functions. Then, the general post-processing method was studied in combination with three different types of five-axis 3D printers: table-tilting, spindle/table-tilting, and spindle-tilting. Finally, the proposed method was applied for five-axis 3D printing, five-axis CNC machining experiments and five-axis machining simulations of various structure types were carried out to verify the correctness and generality of the method.

Key words: five-axis 3D printing, kinematics, exponential product theory, post-processing technology, multiple solution selection

摘要： 引入打印机的结构参数以表示两旋转轴与工件在机架坐标系中的位置，并采用指数积理论建立了双转台五轴3D打印机通用正向运动学模型。结合三角函数周期性、旋转轴行程、五轴结构特点等获得旋转轴角度双解的具体表达式，并提出基于旋转角度最短路径的选择原则以获得旋转轴角度的最佳组合。利用选择的旋转轴角度求出各平动轴位移量，获得的所有运动量都是基于各轴零位的绝对运动所得，进而生成能直接用于加工的数控打印代码，可在没有旋转刀具中心点跟随功能的帮助下完成加工。结合双转台、摆头转台、双摆头3种不同类型的五轴3D打印机研究了通用后置处理方法。将该方法用于五轴3D打印、五轴数控加工试验和多种结构类型的五轴加工仿真，验证了其正确性与通用性。

关键词: 五轴3D打印, 运动学, 指数积理论, 后置处理技术, 多解选择