The need for \( C^2 \) -continuous cable tensions profiles arises in torque-based control of Cable-Driven Parallel Robots (CDPRs), when considering cable elasticity, as discontinuous profiles can hinder smooth motor torques and overall system performance. To tackle this, we propose a novel Tension Distribution Algorithm (TDA) formulated as an optimization problem. The method incorporates a 9th-degree polynomial trajectory generation to ensure \( C^2 \) -class continuity in desired motions while generating tension profiles that respect system constraints and avoid abrupt changes. Using an inverse quadratic penalty-based cost function, the approach guarantees regularity and smoothness, as demonstrated through rigorous mathematical proofs. Simulation results validate the method on a 6-DoF CDPR with eight actuating cables. This contribution lays the groundwork for achieving enhanced trajectory tracking and precise control in future applications.