Multijoint industrial robots can be used for 3D printing to manufacture the complex freeform surfaces. The postprocessing is the basis of the precise printing. Due to the nonlinear motion of the rotational joint, nonlinear error is inevitable in multijoint industrial robots. In this article, the postprocessing and the path optimization based on the nonlinear errors are proposed to improve the accuracy of the multijoint industrial robots-based 3D printing. Firstly, the kinematics of the multijoint industrial robot for 3D printing is analyzed briefly based on product of exponential (POE) theory by considering the structure parameters. All possible groups of joint angles for one tool pose in the joint range are obtained in the inverse kinematics. Secondly, the nonlinear error evaluation based on the interpolation is derived according to the kinematics. The nonlinear error of one numerical control (NC) code or one tool pose is obtained. The principle of minimum nonlinear error of joint angle is proposed to select the appropriate solution of joint angle for the postprocessing. Thirdly, a path smoothing method by inserting new tool poses adaptively is proposed to reduce the nonlinear error of the whole printing path. The smooth level in the smoothing is proposed to avoid the endless insertion near the singular area. Finally, simulation and experiments are carried out to testify the effectiveness of the proposed postprocessing and path optimization method.

中文翻译：

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基于非线性误差的多关节工业机器人3D打印后处理与路径优化

多关节工业机器人可用于 3D 打印以制造复杂的自由曲面。后处理是精密印刷的基础。由于旋转关节的非线性运动，多关节工业机器人不可避免地会产生非线性误差。本文提出了基于非线性误差的后处理和路径优化，以提高基于多关节工业机器人的3D打印精度。首先，基于指数乘积（POE）理论，考虑结构参数，简要分析了用于3D打印的多关节工业机器人的运动学。在反向运动学中获得关节范围内一个工具姿势的所有可能的关节角度组。第二，根据运动学推导出基于插值的非线性误差评估。获得一种数控 (NC) 代码或一种刀具姿态的非线性误差。提出关节角非线性误差最小的原则，为后处理选择合适的关节角解。第三，提出了一种自适应插入新工具姿态的路径平滑方法，以减少整个打印路径的非线性误差。平滑中的平滑级别是为了避免奇异区域附近的无限插入。最后，通过仿真和实验验证了所提出的后处理和路径优化方法的有效性。提出关节角非线性误差最小的原则，为后处理选择合适的关节角解。第三，提出了一种自适应插入新工具姿态的路径平滑方法，以减少整个打印路径的非线性误差。平滑中的平滑级别是为了避免奇异区域附近的无限插入。最后，通过仿真和实验验证了所提出的后处理和路径优化方法的有效性。提出关节角非线性误差最小的原则，为后处理选择合适的关节角解。第三，提出了一种自适应插入新工具姿态的路径平滑方法，以减少整个打印路径的非线性误差。平滑中的平滑级别是为了避免奇异区域附近的无限插入。最后，通过仿真和实验验证了所提出的后处理和路径优化方法的有效性。