Analytical Method for the Kinetostatic Analysis of the Second-Class RRR Assur Group Allowing for Friction in the Kinematic Pairs

The calculation of forces in the kinematic pairs of mechanisms by inverse dynamics is usually performed without friction considerations. In practice, when examination of articulated mechanisms takes into account friction, the solution of the inverse dynamics results in a complex procedure. If a modular approach for the inverse dynamics is used, then exact solutions are available, but not necessarily are practical. For example, the analytical solution for a second-class first-type Assur group is a 16th degree equation. Previous researches proposed an approximated but practical (graphical) method to calculate the forces on the kinematic pairs taking into account the friction forces. In this article, an analytical interpretation of the Artobolevski approximated method is developed for the second-class Assur group with three rotational pairs. The final results for the reactions calculated with the implemented method present a good approximation with respect to the graphical solution. Future work should consider friction forces not only in second-class groups with rotational joints, but also in second-class groups with prismatic joints and high-class Assur groups.