<p>Mechanical systems are extensively utilized in many fields such as the forest, earth-moving, and mining industries. The computer simulation of a mechanical system is often carried out by utilizing a multibody dynamics approach, where various semi-recursive methods can lead to varied computational efficiencies. The objective of this paper is to introduce and systematically compare various semi-recursive multibody methods based on different reference frames in the framework of the index-3 augmented Lagrangian method with projections. The novelty of this paper is the direct formulation and implementation of the method in the center of mass reference frame, whereas the method in the instantaneous reference frame is taken from the literature. Here, simulation models of four-bar, slider-crank, and quick-return mechanical structures are demonstrated as numerical examples. The methods are analyzed depending on the simulation accuracy, violation of constraints, mechanical energy balance, and computational efficiency. The results show that for the presented examples, the center of mass reference frame method is computationally efficient and accurate compared to the method taken from the literature.</p>