Research on Judgment Methods for Multi-mode Mechanism Shakiness to Avoid Local Degrees of Freedom Solution

doi:10.3969/j.issn.1004-132X.2026.03.006

Abstract

Abstract:

Mechanism shakiness occured in the transition configuration where the motion branches of different degrees of freedom intersect， which was the key factor causing the poor controllability and motion stability of the mechanisms， and the judgment was crucial. The conditions for determining the kinematic singular shakiness of the mechanisms were presented. When the constraint ideal of the kinematic loop equations of the mechanisms was radical ideal or the real dimension of solution was different from the complex dimension after the decomposition of the constraint ideal， if there were higher-order tangent cones and the intersection of the different dimensional tangent spaces of the higher-order tangent cones existed real solutions， the mechanism was a kinematic singular shakiness mechanism. Combined with the kinematic non-singular shakiness conditions， shakiness types of the mechanisms were summarized. Based on the polynomial ideal and differential tangent cone theory， a unified and general judgment method and algorithm for mechanism shakiness were proposed to avoid local degrees of freedom solution. According to the algorithm， the multi-mode 7R mechanisms were judged to be kinematic singular shakiness mechanisms. The two actuation motors of the mechanisms were enabled and disabled to make the mechanism motion mode switch smoothly and avoid the influences of mechanism shakiness. The 7R mechanism satisfying the scale constraint type was embedded into vehicle latch， and realized electric cinch and auxiliary opening function by mode switching.

Key words: mechanism shakiness, high-order tangent cone, kinematic singular shakiness, multi-mode mechanism, vehicle latch

摘要：

机构抖动发生在不同自由度运动分支相交的过渡构形处，是导致机构可控性和运动稳定性差的关键因素，其判定至关重要。提出机构运动奇异抖动判定条件：当运动学方程组约束理想为根理想，或约束理想素分解的实维数与复维数不同时，如果方程组存在高阶切锥且高阶切锥不同维切空间交点存在实数解，则机构为运动奇异抖动机构。结合运动不奇异抖动条件梳理了机构抖动类型，以多项式理想结合微分切锥理论，提出避免局部自由度求解的机构抖动统一通用判定方法和算法。算法判定了多模式7R机构为运动奇异抖动机构，对机构两驱动电机进行使能及失能操作，使机构运动模式切换平稳，避免机构抖动影响；将满足尺度约束类型的7R机构嵌入汽车门锁，机构模式切换实现了电动吸合、辅助开启功能。

关键词: 机构抖动, 高阶切锥, 运动奇异抖动, 多模式机构, 汽车门锁

CLC Number:

TH112

XIE Yuhang, HANG Lubin, KANG Kaidong, HUANG Xiaobo, CHI Yonglin. Research on Judgment Methods for Multi-mode Mechanism Shakiness to Avoid Local Degrees of Freedom Solution[J]. China Mechanical Engineering, 2026, 37(3): 564-570.

谢宇航, 杭鲁滨, 康开东, 黄晓波, 迟永琳. 避免局部自由度求解的多模式机构抖动判定方法研究[J]. 中国机械工程, 2026, 37(3): 564-570.

Figures/Tables 6

References 21

[1]	KONG Xianwen， PFURNER M. Type Synthesis and Reconfiguration Analysis of a Class of Variable-DOF Single-loop Mechanisms［J］. Mechanism and Machine Theory， 2015， 85：116-128.
[2]	WENGER P， CHABLAT D. A Review of Cuspidal Serial and Parallel Manipulators［J］. Journal of Mechanisms and Robotics， 2023， 15（4）：040801.
[3]	WENGER P. Cuspidal and Noncuspidal Robot Manipulators［J］. Robotica， 2007， 25（6）：677-689.
[4]	SALUNKHE D H， SPARTALIS C， CAPCO J， et al. Necessary and Sufficient Condition for a Generic 3R Serial Manipulator to Be Cuspidal［J］. Mechanism and Machine Theory， 2022， 171：104729.
[5]	ZEIN M， WENGER P， CHABLAT D. Singular Curves and Cusp Points in the Joint Space of 3-RPR Parallel Manipulators［J］. Robotica，2007，25（6）：717-724.
[6]	WOHLHART K. Kinematotropic Linkages［M］//Recent Advances in Robot Kinematics. Dordrecht：Springer Netherlands， 1996：359-368.
[7]	WHITNEY H. Tangents to an Analytic Variety［M］∥Hassler Whitney Collected Papers. Boston， MA： Birkhäuser Boston， 1992：537-590.
[8]	LERBET J. Analytic Geometry and Singularities of Mechanisms［J］. ZAMM—Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik， 1998， 78（10）：687-694.
[9]	MÜLLER A. An Overview of Formulae for the Higher-order Kinematics of Lower-pair Chains with Applications in Robotics and Mechanism Theory［J］. Mechanism and Machine Theory， 2019， 142：103594.
[10]	MÜLLER A. Recursive Higher-order Constraints for Linkages with Lower Kinematic Pairs［J］. Mechanism and Machine Theory， 2016， 100：33-43.
[11]	MÜLLER A. Local Analysis of Singular Configurations of Open and Closed Loop Manipulators［J］. Multibody System Dynamics， 2002， 8（3）：297-326.
[12]	MÜLLER A. Local Kinematic Analysis of Closed-loop Linkages-Mobility， Singularities， and Shakiness［J］. Journal of Mechanisms and Robotics， 2016， 8（4）：041013.
[13]	MÜLLER A， LI Zijia. Identification of Real and Complex Solution Varieties and Their Singularities Defined by Loop Constraints of Linkages Using the Kinematic Tangent Cone［J］. Journal of Mechanisms and Robotics， 2024， 16（11）：111003.
[14]	LI Zijia， MÜLLER A. Mechanism Singularities and Shakiness from an Algebraic Viewpoint［J］. Mechanism and Machine Theory， 2024， 191：105510.
[15]	钟传磊. 汽车侧门锁电动开启与吸合的空间柔顺机构及运动稳定性研究［D］. 上海：上海工程技术大学， 2022.
	ZHONG Chuanlei. Study on Spatial Compliant Mechanism and Motion Stability of Power Release and Electric Cinch in Vehicle Side Door Latch［D］. Shanghai：Shanghai University of Engineering Science， 2022.
[16]	殷传硕，杭鲁滨，钟传磊，等. 面向车门锁电动吸合开启优先功能的凸轮摆杆柔顺连杆组合机构［J］. 机械传动， 2024， 48（4）：138-147.
	YIN Chuanshuo， HANG Lubin， ZHONG Chuanlei， et al. Cam Swing Linkage and Spring Linkage Combined Mechanism for Vehicle Side-door Latches with Electric Cinch and Release Priority Function［J］. Journal of Mechanical Transmission， 2024， 48（4）：138-147.
[17]	钟传磊，杭鲁滨，王明远，等. 用于汽车门锁的多运动模式空间柔顺开启机构及稳定性分析［J］. 机械科学与技术， 2023， 42（11）：1801-1810.
	ZHONG Chuanlei， HANG Lubin， WANG Mingyuan， et al. Stability Analysis and Spatial Compliant Power Release Mechanism of Vehicle Door Latch with Multi-mode Motion［J］. Mechanical Science and Technology for Aerospace Engineering， 2023， 42（11）：1801-1810.
[18]	HUSTY M L， PFURNER M， SCHRÖCKER H P， et al. Algebraic Methods in Mechanism Analysis and Synthesis［J］. Robotica， 2007， 25（6）：661-675.
[19]	HUSTY M L， SCHRÖCKER H P. Algebraic Geometry and Kinematics［M］∥Nonlinear Computational Geometry. New York：Springer New York， 2009：85-107.
[20]	王东明. 多项式代数［M］. 北京：高等教育出版社， 2011：137-142.
	WANG Dongming. Polynomial Algebra［M］. Beijing： Higher Education Press， 2011：137-142.
[21]	LÓPEZ-CUSTODIO P C， MÜLLER A， KANG X， et al. Tangential Intersection of Branches of Motion［J］. Mechanism and Machine Theory， 2020， 147：103730.