Space robotics increasingly relies on compliant manipulation for safe, low-impact docking under pose uncertainty. PACOMA is a 6-RUS (Revolute–Universal–Spherical) parallel continuum manipulator designed for low-impact docking. This thesis develops a control-oriented flexible multibody framework at the leg level, modeling a planar surrogate as a four-bar mechanism with two rigid links and one flexible Timoshenko beam. The beam is discretized via the finite element method and coupled to the rigid links through holonomic constraints, yielding differential-algebraic equations implemented in MATLAB and integrated with a generalized-α scheme. Two self-contained verification blocks support the framework: a compact rigid four-bar baseline and an isolated beam module.