In this paper we consider two situations. In the first, all kinematic chains are elastic, while the second situation is characterized by one rigid kinematic chain, with the rest of them being elastic. In addition, the kinematic joints are considered to be rigid. The calculations are performed using the screw coordinates. For the free vibrations of the rigid solid we determined the rigidity matrix and the eigenpulsations in both cases. It was proved that the results in the second case cannot be considered as limits for the results of the first situation, putting infinite values for the elements of the rigidity matrix of one kinematic chain. We also developed the theory for the forced vibrations of the system. A numerical application is considered and a great variety of cases are developed and discussed. The results obtained for the forced vibrations are presented and discussed. The paper combines elastic and rigid kinematic chains, as well as general configurations of the kinematic chains. The method presented here may be used for any number of kinematic chains, no matter if the structure is symmetrical or asymmetrical.

We present a new approach based on the notion of inertance for the simultaneous collisions without friction of a rigid solid. The calculations are performed using the screw (plückerian) coordinates, while the results are obtained in matrix form, and they may be easily implemented for different practical situations. One calculates the velocities after collision, the energy of lost velocities, and the loss of the kinetic energy. The general algorithm of calculation is described in the paper. The main assumption is that the normal velocities at the contact points vanish simultaneously. The coefficients of restitution at the contact points may be equal or not. Some completely solved applications are also presented, and the numerical results are discussed. The numerical values depend on which coefficient of restitution is used.