TY - GEN
T1 - Nonsmooth Dynamic Modeling of Spatial Multibody Systems with Spherical Clearance Joints on the Special Euclidean Group
AU - Li, Long
AU - Lyu, Shengnan
AU - Ding, Xilun
N1 - Publisher Copyright:
© 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2024
Y1 - 2024
N2 - In this paper, a nonsmooth dynamic modeling and calculation method for spatial multibody systems (SMBS) with spherical clearance joints (SCJs) is proposed within the framework of the three-dimensional Special Euclidean Group SE(3). Based on Newton's collision law, the differential measures of the generalized velocity and impulse are introduced, and the constitutive relationship of a spherical joint with clearance is described as the normal cone inclusion at the velocity-impulse level. The non-smooth generalized-α method is extended to Lie group SE(3). This method can provide a uniform description of a wide range of rigid body motion and joint clearance motion, without introducing any local parameterization of rotational variables, which has the advantages of avoiding singularity and frame-invariant. Finally, a numerical example of a RSSR mechanism with two SCJs is given to illustrate the feasibility and effectiveness of the proposed modeling and calculating methods. The proposed method is compared with a time stepping method which is also formulated in a Lie group setting. From the simulation results, it can be seen that the proposed method has better computational accuracy and numerical stability.
AB - In this paper, a nonsmooth dynamic modeling and calculation method for spatial multibody systems (SMBS) with spherical clearance joints (SCJs) is proposed within the framework of the three-dimensional Special Euclidean Group SE(3). Based on Newton's collision law, the differential measures of the generalized velocity and impulse are introduced, and the constitutive relationship of a spherical joint with clearance is described as the normal cone inclusion at the velocity-impulse level. The non-smooth generalized-α method is extended to Lie group SE(3). This method can provide a uniform description of a wide range of rigid body motion and joint clearance motion, without introducing any local parameterization of rotational variables, which has the advantages of avoiding singularity and frame-invariant. Finally, a numerical example of a RSSR mechanism with two SCJs is given to illustrate the feasibility and effectiveness of the proposed modeling and calculating methods. The proposed method is compared with a time stepping method which is also formulated in a Lie group setting. From the simulation results, it can be seen that the proposed method has better computational accuracy and numerical stability.
KW - Lie group formulation
KW - Nonsmooth Multibody System Dynamics
KW - Spherical Joint with Clearance
UR - https://www.scopus.com/pages/publications/85176915782
U2 - 10.1007/978-3-031-45709-8_63
DO - 10.1007/978-3-031-45709-8_63
M3 - 会议稿件
AN - SCOPUS:85176915782
SN - 9783031457081
T3 - Mechanisms and Machine Science
SP - 648
EP - 657
BT - Advances in Mechanism and Machine Science - Proceedings of the 16th IFToMM World Congress 2023—Volume 3
A2 - Okada, Masafumi
PB - Springer Science and Business Media B.V.
T2 - 16th International Federation of Theory of Machines and Mechanisms World Congress, IFToMM WC 2023
Y2 - 5 November 2023 through 9 November 2023
ER -