This paper presents a new method, a fast prediction method based on the Cartesian stiffness model and equivalent spring stiffness (FPM-CSES), to calculate displacement errors of deformation caused by low stiffness for industrial robot. First, the Cartesian stiffness model based on the Jacobian matrix was established for a robot, and then the displacement error model of deformations caused by external force was established based on Cartesian stiffness. Second, the transmission system of the robot’s joint was analyzed, and an equivalent method for joint stiffness was presented based on a series spring system. Meanwhile, the stiffness of the key components including the servo motor, harmonic reducer, and timing belt was deduced in detail. Finally, a compared simulation and a measurement experiment were conducted on a 6-joint series robot. It was found that the FPM-CSES could calculate any configuration among the robot’s workspace. Compared with the finite element analysis (FEA) method, the presented method is feasible and more efficient. The experimental results showed that the prediction accuracy of the FPM-CSES is rather high, with an average rate of more than 83.72%. Hence, the prediction method presented in this study is simple, fast, and reliable, and could be used to predict and analyze the displacement errors caused by the cutting force, and provide the basis for trajectory planning and error compensation, enhancing the robot’s machining performance.

中文翻译：

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工业机器人低刚度位移误差预测新方法

本文提出了一种基于笛卡尔刚度模型和等效弹簧刚度（FPM-CSES）的快速预测方法，用于计算工业机器人低刚度引起的变形位移误差。首先针对机器人建立了基于雅可比矩阵的笛卡尔刚度模型，然后基于笛卡尔刚度建立了外力引起的变形位移误差模型。其次，对机器人关节的传动系统进行了分析，提出了一种基于串联弹簧系统的关节刚度等效方法。同时，对伺服电机、谐波减速器、同步带等关键部件的刚度进行了详细推导。最后，在6关节串联机器人上进行了对比仿真和测量实验。发现 FPM-CSES 可以计算机器人工作空间中的任何配置。与有限元分析（FEA）方法相比，所提出的方法是可行的和更有效的。实验结果表明，FPM-CSES的预测准确率较高，平均达到83.72%以上。因此，本研究提出的预测方法简单、快速、可靠，可用于预测和分析切削力引起的位移误差，为轨迹规划和误差补偿提供依据，提高机器人的加工性能。 . 实验结果表明，FPM-CSES的预测准确率较高，平均达到83.72%以上。因此，本研究提出的预测方法简单、快速、可靠，可用于预测和分析切削力引起的位移误差，为轨迹规划和误差补偿提供依据，提高机器人的加工性能。 . 实验结果表明，FPM-CSES的预测准确率较高，平均达到83.72%以上。因此，本研究提出的预测方法简单、快速、可靠，可用于预测和分析切削力引起的位移误差，为轨迹规划和误差补偿提供依据，提高机器人的加工性能。 .