Robotic welding is widely used in industrial manufacturing, where the welding torch is often connected to the generator through an external umbilical. With the increasing deployment of lightweight and collaborative robots, the dynamic influence of this umbilical can significantly affect the robot motion and the actuation forces. This paper proposes a constrained multibody dynamic model of a welding umbilical, represented as a serial chain of rigid bodies interconnected by passive joints with elastic and dissipative effects. Prescribed motions at the distal anchor point are introduced through holonomic kinematic constraints. The equations of motion are reduced by projecting the dynamics onto the subspace of admissible velocities, yielding an efficient formulation free of Lagrange multipliers. The reaction wrench exerted by the umbilical on the robot is explicitly recovered. A planar case study illustrates the approach.

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