Abstract The heterogeneous multiscale methods (HMM) extend the classical methods of averaging to a purely numerical approach for the solution of problems involving multiple scales. Especially for highly oscillatory ordinary differential equations HMM were recently seen to be competitive with usual time integration schemes. We study this hypothesis in the special case of penalty formulations for index-three differential-algebraic equations arising in multibody dynamics which have the particular property of solution-dependent oscillations with variable frequencies. First we motivate some additional assumptions on the structure of the proposed problems and give error estimates extending the results of Engquist et al. Limitations of the considered approach will be illustrated by means of the seven body mechanism benchmark.