The minimal-form modelling of mechanisms with friction

The paper deals with modelling and analysis of the effect of Coulomb-type friction on the dynamics of mechanisms (one-degree-of-freedom multibody systems), and presents a two-step process of converting the equations of motion for the friction-affected systems from a large set derived in terms of absolute variables to a minimal set in independent variables. The obtained governing equations consist of one dynamic equation, few kinematic equations, and algebraic relations for determination of the joint reactions as functions of the current state variables. The latter enable one to estimate the frictional effects that influence the system dynamics, and consequently to solve the governing equations (which formally are DAEs) as minimal-dimension ODEs. Two simple examples are provided to illustrate the frictional effects, conversion steps, and numerical simulation entanglements.