Rigid closed chains can admit indeterminate internal reactions even when their motion is fully specified. This paper develops a modular inverse-dynamics workflow that combines path-based motion reconstruction with recovery of uniquely determined actuator and joint-wrench outputs. Analytical second-order differentiation of assembled transformation paths supplies passive velocities and accelerations on a regular closure branch. Spatial Newton--Euler balances are then assembled over the physical body-and-joint graph. Established nullspace and dual criteria identify and recover unique outputs, while balance, ideal-joint admissibility and affine-family diagnostics assess nonunique reference reactions. Evaluation against Simscape Multibody uses prescribed motion of a seven-degree-of-freedom heavy-duty hybrid serial--parallel manipulator under common rigid-body, ideal-joint assumptions. The results show close agreement with the reference for passive positions, actuator efforts and uniquely recoverable constraint-wrench components. Reaction diagnostics support compatibility with the admissible numerical load family.

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