Chaos phenomenon and stability analysis of RU-RPR parallel mechanism with clearance and friction

Abstract

The chaos phenomenon often exists in the dynamics system of the mechanism with clearance and friction, which has obvious effect on the stability of the mechanism, then it is worthy of attention for identifying the relationship between the friction coefficient and the stability of the mechanism. Two rotational degrees of freedom decoupled parallel mechanism RU-RPR is taken as the research object. Considering the clearance existing in the revolute pair, Lankarani–Nikravesh contact force model is used to calculate the normal contact force, and the Coulomb friction force model is used to calculate the tangential contact force. The dynamics model is established using Newton–Euler equations, and the Baumgarte stabilization method is used to keep the stability of the numerical analysis. Then, the equations are solved using the fourth adaptive Runge–Kutta method, and the effect of the revolute pair’s clearance on the dynamic behavior is analyzed. Poincare mapping is plotted, and the bifurcation diagrams are analyzed with varying the friction coefficient corresponding to different values of clearance size. The research contents possess a certain theoretical guidance significance and practical application value on the analysis of the chaotic motion and its stability in the dynamics of the parallel mechanism.

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

“…In the course of motion, point P on body i always coincides with point P on body j. Therefore, three constraint equations of spherical joints could be expressed as (24), the spherical joint constraint equation of 4UPS-UPU spatial parallel mechanism can be given as For the 4UPS-UPU mechanism, the distance from Q i ði ¼ 1; 2 . .…”

“…Tian et al 23 developed nonlinear dynamics model of a flexible multi-body system considering clearance and lubricated revolute joint clearance and used a planar absolute nodal coordinate formulation based upon locking free shear deformable beam element to discretize flexible bodies. Hou et al 24 investigated the chaos phenomenon of planar RU-RPR parallel mechanism considering revolute clearance joint. The nonlinear characteristics of the RU-RPR mechanism have been discussed through Poincaré maps and bifurcation diagrams.…”

“…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.…”

“…Respectively, coordinates of spherical joints ðS 2 ; S 3 ; S 4 ; S 5 Þ in local coordinate systems o i À x i y i z i ði ¼ 2; 3; 4; 5Þ are given by S o i i ði ¼ 2; 3; 4; 5Þ. According to equation (24), the spherical joint constraint equation of 4UPS-UPU spatial parallel mechanism can be given as…”

Experimental investigations of the dynamic responses of a multi-link mechanism with revolute clearance joints

“…Bai and Zhao 19 proposed a hybrid contact model with improved stiffness and damping coefficient algorithms for the impact forces calculation between the journal and the bushing in clearance joint. Chen et al 20 and Hou et al 21 numerically analyzed the chaos phenomena in the dynamic responses of a multi-link articulated mechanical system with clearance joint. In high-speed condition, the movement could transition from periodic state to quasi-periodic state, and eventually to chaotic state, which lead to reduced motion accuracy and shortened service life for these mechanism systems.…”