  This paper presents a new geometric and recursive algorithm for analytically
computing the forward dynamics of heavy-duty parallel-serial mechanisms. Our
solution relies on expressing the dynamics of a class of linearly-actuated
parallel mechanism to a lower dimensional dual Lie algebra to find an
analytical solution for the inverse dynamics problem. Thus, by applying the
articulated-body inertias method, we successfully provide analytic expressions
for the total wrench in the linear-actuator reference frame, the linear
acceleration of the actuator, and the total wrench exerted in the base
reference frame of the closed loop. This new formulation allows to backwardly
project and assemble inertia matrices and wrench bias of multiple closed-loops
mechanisms. The final algorithm holds an O(n) algorithmic complexity, where $n$
is the number of degrees of freedom (DoF). We provide accuracy results to
demonstrate its efficiency with 1-DoF closed-loop mechanism and 4-DoF
manipulator composed by serial and parallel mechanisms. Additionally, we
release a URDF multi-DoF code for this recursive algorithm.
