面向包装生产线调姿作业的3-SPS+PS并联机构运动学建模与几何误差敏感度分析

申博; 郭文孝

doi:10.19554/j.cnki.1001-3563.2026.15.024

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包装工程（技术栏目） ›› 2026, Vol. 47 ›› Issue (15) : 232-239. DOI: 10.19554/j.cnki.1001-3563.2026.15.024

自动化与智能化技术

面向包装生产线调姿作业的3-SPS+PS并联机构运动学建模与几何误差敏感度分析

申博^1,*, 郭文孝^2,3

作者信息 +

Kinematics Modeling and Geometric Error Sensitivity Analysis of the 3-SPS+PS Parallel Mechanism for Packaging Pose Adjustment Operations

SHEN Bo^1,*, GUO Wenxiao^2,3

Author information +

文章历史 +

摘要

目的为满足包装生产线高精度调姿作业需求,本文提出一种具有三转一移（3R1T）自由度的3-SPS+PS并联机构,并开展运动学与误差分析。方法运用螺旋理论和修正的G-K公式分析机构自由度特性;采用闭环矢量法建立运动学模型并推导位置正逆解;采用一阶摄动法建立几何误差映射模型,揭示几何参数误差对末端位姿的影响规律;通过数值仿真验证了理论模型的正确性。结果该机构具有3R1T自由度,逆解可解析表达;杆长误差对平台垂直方向位置精度的敏感度为0.36 mm/mm,静平台与动平台铰点垂直方向位置误差的影响系数分别为-0.33、+0.33 mm/mm;绕俯仰方向的姿态误差对静平台铰点垂直方向误差的敏感度为0.25 °/mm。结论该机构运动学模型正确,误差分析结果为精度设计与误差补偿提供了理论依据,研究表明该机构适用于包装工程中的高精度调姿作业。

Abstract

To address precision pose-adjustment tasks in packaging automation, the work aims to propose a 3-SPS+PS parallel mechanism with three rotational and one translational (3R1T) degrees of freedom and conduct kinematic and error analyses. The screw theory combined with the modified Grübler-Kutzbach criterion was adopted to verify the mechanism's mobility, while the closed-loop vector equations were used to establish the kinematic model and derive the forward and inverse position solutions. The first-order perturbation method was employed to construct the geometric error mapping model and reveal the effect law of geometric parameter errors on the end-effector pose. Numerical simulations were performed to verify the correctness of the theoretical models. This mechanism possessed 3R1T degrees of freedom, and its inverse solutions could be expressed analytically. The sensitivity of the platform's vertical positional accuracy to rod-length errors was 0.36 mm/mm. The effect coefficients for the vertical-direction position errors of the hinge points on the fixed platform and moving platform were -0.33 mm/mm and +0.33 mm/mm, respectively. The sensitivity of the pitch-oriented attitude error to the vertical error of hinge points on the fixed platform was 0.25°/mm. The kinematic model of the mechanism is valid. The error analysis results provide a theoretical basis for precision design and error compensation. The research indicates that this mechanism is suitable for high-precision pose-adjustment operations in packaging engineering.

导出引用

申博, 郭文孝. 面向包装生产线调姿作业的3-SPS+PS并联机构运动学建模与几何误差敏感度分析[J]. 包装工程. 2026, 47(15): 232-239 https://doi.org/10.19554/j.cnki.1001-3563.2026.15.024

SHEN Bo, GUO Wenxiao. Kinematics Modeling and Geometric Error Sensitivity Analysis of the 3-SPS+PS Parallel Mechanism for Packaging Pose Adjustment Operations[J]. Packaging Engineering. 2026, 47(15): 232-239 https://doi.org/10.19554/j.cnki.1001-3563.2026.15.024

中图分类号： TB486 TH112

参考文献

[1] 崔冰艳, 桂小庚, 曾鸿泰, 等. 三自由度并联分拣机器人的动力学建模与仿真[J]. 包装工程, 2024, 45(3): 218-225.
CUI B Y, GUI X G, ZENG H T, et al.Dynamic modeling and simulation of 3-DOF parallel sorting robot[J]. Packaging Engineering, 2024, 45(3): 218-225.
[2] 于润泽, 冯砚博, 岳继昌, 等. 一种用于狭窄空间的检测并联机器人[J]. 包装工程, 2023, 44(9): 217-223.
YU R Z, FENG Y B, YUE J C, et al.A parallel robot for detection in narrow space[J]. Packaging Engineering, 2023, 44(9): 217-223.
[3] 李仕华, 田志立, 王子义, 等. 具有连续转轴的对称2R1T三自由度并联机构型综合[J]. 机械工程学报, 2017, 53(23): 74-82.
LI S H, TIAN Z L, WANG Z Y, et al.Type synthesis of 2R1T symmetrical parallel mechanism with continuous rotation axes[J]. Journal of Mechanical Engineering, 2017, 53(23): 74-82.
[4] CHENG G, YU J L, GU W.Kinematic analysis of 3-SPS+PS bionic parallel test platform for hip joint simulator based on unit quaternion[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(2): 257-264.
[5] MERLET J P.Parallel robots[M]. 2nd ed. Dordrecht: Springer, 2006.
[6] 汪满新, 黄田. 1T2R三自由度并联机构拓扑结构综合[J]. 机械工程学报, 2015, 51(17): 1-7.
WANG M X, HUANG T.Type synthesis of 3-DOF 1T2R parallel mechanisms[J]. Journal of Mechanical Engineering, 2015, 51(17): 1-7.
[7] 夏纯, 张海峰, 李秦川, 等. 基于等效运动链的并联机器人运动学标定方法[J]. 机械工程学报, 2022, 58(14): 71-84.
XIA C, ZHANG H F, LI Q C, et al.Kinematic calibration method of parallel robot based on equivalent kinematic chain[J]. Journal of Mechanical Engineering, 2022, 58(14): 71-84.
[8] 刘晓飞, 刘洋, 何阳, 等. 2RPU+2UPR+RPR多冗余驱动并联机构运动学分析与优化[J]. 农业机械学报, 2023, 54(3): 440-450.
LIU X F, LIU Y, HE Y, et al.Kinematic analysis and optimization of 2RPU+2UPR+RPR multi-redundantly actuated parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery, 2023, 54(3): 440-450.
[9] 周亚杰, 李仕华, 徐奇, 等. 3-PUS-PU柔顺并联机构运动学分析与优化设计[J]. 农业机械学报, 2022, 53(9): 417-424.
ZHOU Y J, LI S H, XU Q, et al.Kinematic analysis and optimal design of 3-PUS-PU compliant parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(9): 417-424.
[10] ZHANG D, GAO Z.Forward kinematics, performance analysis, and multi-objective optimization of a bio-inspired parallel manipulator[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(4): 484-492.
[11] TSAI M S, SHIAU T N, TSAI Y J, et al.Direct kinematic analysis of a 3-PRS parallel mechanism[J]. Mechanism and Machine Theory, 2003, 38(1): 71-83.
[12] 汪满新, 刘海涛, 黄田. 3-SPR并联机构运动学性能评价[J]. 机械工程学报, 2017, 53(5): 108-115.
WANG M X, LIU H T, HUANG T.Kinematic performance evaluation of 3-SPR parallel mechanism[J]. Journal of Mechanical Engineering, 2017, 53(5): 108-115.
[13] RUSSO M, CECCARELLI M, TAKEDA Y.Force transmission and constraint analysis of a 3-SPR parallel manipulator[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232(23): 4399-4409.
[14] 张德权, 李星奥, 张宁, 等. 工业机器人全域误差场精细化建模方法及其误差补偿策略[J]. 机械工程学报, 2024, 60(13): 316-329.
ZHANG D Q, LI X A, ZHANG N, et al.Global refined error field modeling method for industrial robots and error compensation strategy[J]. Journal of Mechanical Engineering, 2024, 60(13): 316-329.
[15] 孟庆梅, 李佳宇, 李菊, 等. 半对称三平移Delta-CU并联机构运动误差分析与标定[J]. 农业机械学报, 2021, 52(1): 393-400.
MENG Q M, LI J Y, LI J, et al.Error modeling analysis and calibration of semi-symmetrical three-translation Delta-CU parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery, 2021, 52(1): 393-400.
[16] 高文斌, 黄琪, 余晓流, 等. 模块化机器人几何误差分析及参数辨识研究[J]. 中国机械工程, 2022, 33(7): 811-817.
GAO W B, HUANG Q, YU X L, et al.Geometric error analysis and parameter identification of modular robot[J]. China Mechanical Engineering, 2022, 33(7): 811-817.
[17] CHABLAT D, BARON L, JHA R. Kinematics and workspace analysis of a 3PPPS parallel robot with U-shaped base[C]//Proceedings of the ASME2017 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Cleveland, USA: ASME, 2017: DETC2017-67087.
[18] DU X, WANG B, ZHENG J.Geometric error analysis of a 2UPR-RPU over-constrained parallel manipulator[J]. Machines, 2022, 10(11): 1093.
[19] TANNOUS M, CARO S, GOLDSZTEJN A.Sensitivity analysis of parallel manipulators using an interval linearization method[J]. Mechanism and Machine Theory, 2014, 71: 93-112.
[20] CARO S, BINAUD N, WENGER P.Sensitivity analysis of 3-RPR planar parallel manipulators to geometric errors and joint clearances[C]//Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. San Diego, USA: ASME, 2009: 1117-1126.
[21] 李菊, 朱忠颀, 沈惠平, 等. 三平移并联机构拓扑设计与运动学分析[J]. 农业机械学报, 2022, 53(9): 425-433.
LI J, ZHU Z Q, SHEN H P, et al.Topological design and kinematic analysis of three-translation parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(9): 425-433.
[22] ZHAO Y, CHENG G.Dimensional synthesis of a 3UPS-PRU parallel robot[J]. Robotica, 2017, 35(12): 2319-2329.
[23] 张立杰, 郭菲, 李永泉, 等. 基于运动学分配性能的并联机构优化设计[J]. 农业机械学报, 2015, 46(4): 365-371.
ZHANG L J, GUO F, LI Y Q, et al.Optimum design of parallel mechanisms based on kinematic distribution performance[J]. Transactions of the Chinese Society for Agricultural Machinery, 2015, 46(4): 365-371.