A multi-body planar system with friction-affected sliders and hinges is considered. The equations for the computation of the accelerations are established with Newton-Euler's equation and Lagrange's formalism. In general, because of the non-linear friction laws, the solutions can be determined only by numerical and iterative methods. The convergence properties and efficiency of several numerical schemes and the influence of the governing equations are investigated. By an example the advantages of Lagrange's equation without multipliers and the direct iteration scheme are pointed out.