WITHDRAWN: Comparison of bristles' friction models in dynamics analysis of spatial linkages

Abstract

Abstract In the paper forward dynamics mathematical model of a one-dof spatial linkage with friction phenomenon in the joints is presented. It is assumed that linkage has serial structure with closed-loop. Joint coordinates and homogenous transformations were applied in order to describe to motion of the links. Dynamics equations of motion were formulated using the Lagrange equations of the second kind. Cut-joint technique was used in order to transform closed loop kinematic chain into two separate open-loop kinematic chains. In order to model friction phenomenon in revolute and prismatic joints three friction models, the Dahl, LuGre and elasto-plastic, were considered. All friction models, formulated as additional first order differential equations solved in each time step, allow us to model both friction regimes, pre-sliding and sliding, without using any switching functions. Additionally the LuGre and elasto-plastic models are capable to capture the Stribeck effects associated directly with stick–slip friction. Numerical simulations were performed for the spatial RUSP linkage. Results obtained for the Dahl, LuGre and elasto-plastic friction models are presented and discussed in the paper.