Nonsmooth Dynamic Modeling of Spatial Multibody Systems with Spherical Clearance Joints on the Special Euclidean Group

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.