On derivation of constrained multiple rigid body dynamic equations

Dynamic modeling of constrained multi-link systems are traditionally tackled either in the reduced state space or in the non-reduced state space. In this paper, an alternative approach for deriving dynamic equations for a class of multi-link constrained systems is proposed. The constraints, studied in this paper, are joints where the constraint forces are of interest. The method starts with replacing the joints with virtual links. Next, the augmented state space is formed by the states describing the original physical system and virtual links. The dynamic equations, describing the expanded systems, are then derived in the reduced state space from the viewpoint of the augmented state space. Finally, the dynamic equations for the original multi-link systems are obtained by setting all the physical parameters and states associated with virtual links to zero. This alternative approach has the advantages of both traditional methods in that: (i) the constraint forces can be determined directly, (ii) the violation of constraints is avoided, which is the main problem for dynamic modeling of constrained systems in the non-reduced state space, and (iii) all computer software packages for automatic generation of dynamic equations in the reduced state space can be readily used