A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

Abstract

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket, which compose a spherical joint, are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian-based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudopenetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four-bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

“…However, the friction force was not included in their dynamics model. Marques et al [281] studied the influence of the Coulomb's law based friction force models on the dynamic responses of a spatial four-bar mechanism with a spherical clearance joint between its rocker and coupler. It was observed that the presence of friction helped to stabilize the system's response and made it less chaotic, while the friction force models utilized did not significantly affect the dynamic response of the mechanism.…”

Dynamic modeling of spatial parallel mechanism with multi-spherical joint clearances

“…Chen et al 25 analyzed the influence of the clearance size, input driving velocity, flexible links on dynamics behavior for crank slider mechanism through experiment, and ADAMS. Marques et al 26 proposed an investigation on dynamic modeling and analysis of a spatial four-bar mechanism containing spherical clearance joints including friction. Liu et al 27 studied the dynamics and control of a rigid-flexible multi-body system containing multiple cylindrical clearance joints via the absolute coordinate-based method.…”

“…It takes into account the influence of damping force and includes the elastic deformation in the process of collision. 19,24,26,27 But this model is only suitable for the analysis of materials whose recovery coefficient is approximately 1. However, the application of Flores contact force model is not limited by the restitution coefficient.…”

“…According to equation (26), the constraint equation of the prismatic joint of 4UPS-UPU spatial parallel mechanism is obtained as follows…”

Dynamic Modeling, Response, and Chaos Analysis of 2-DOF Hybrid Mechanism with Revolute Clearances

“…Ma and Qian [18] modeled and simulated the planar multibody system with multirevolute clearance joints. Marques et al [19] considered the joint with spherical clearance and studied its dynamic characteristics. Wang et al [20] used a new nonlinear contact force model to study the dynamic characteristics of plane mechanical systems with clearances.…”