The objective of this article is to present an efficient extension of Rosen
thal's order-n algorithm to multibody systems containing closed loops. The
equations of motion are created by using relative coordinates and partial v
elocity theory. Closed topological loops are handled by cut joint technique
. The set of constraint equations of cut joints is adjoined to the system's
equation of motion by using Lagrange multipliers. This results in the equa
tion of motion as a differential-algebraic equation (DAE) rather than an or
dinary differential equation. This DAE is then solved by applying the exten
ded Rosenthal's order-n algorithm proposed in this article. While solving D
AE, violation of the kinematic constraint equations of cut joints is correc
ted by coordinate projection method. Some numerical simulations are carried
out to demonstrate efficiency of the proposed method.