An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.