  This paper proposes a novel modelling approach for a heavy-duty manipulator
with parallel$-$serial structures connected in series. Each considered
parallel$-$serial structure contains a revolute segment with rigid links
connected by a passive revolute joint and actuated by a linear hydraulic
actuator, thus forming a closed kinematic loop. In addition, prismatic
segments, consisting of prismatic joints driven by hydraulic linear actuators,
also are considered. Expressions for actuator forces are derived using the
Newton$-$Euler (N$-$E) dynamics formulation. The derivation process does not
assume massless actuators decoupled from manipulator links, which is common in
the Lagrange dynamics formulation. Actuator pressure dynamics are included in
the analysis, leading in total to a third-order system of ordinary differential
equations (ODEs). The proposed model in the N$-$E framework, with fewer
parameters than its predecessors, inspires revision of the virtual
decomposition control (VDC) systematic process to formulate a control law based
on the new model. The virtual stability of each generic manipulator revolute
and prismatic segment is obtained, leading to the Lyapunov stability of the
entire robot.
