Accurate musculoskeletal simulation requires robust computation of muscle paths that wrap around anatomical structures. We previously introduced a geodesic model, which treats muscles as taut strings constrained by underlying surfaces, providing a rigorous framework for this task. However, the previous model used a fixed global coordinate frame to parameterise the muscle path during numerical simulation, leading to discontinuities during complex motions (particularly when combining translations and rotations) [1]. To increase robustness for complex spatial joint motions, we propose to adaptively change the frame of reference used to describe muscle paths. Introducing a new local parameterisation, we automatically update the reference frame at each simulation step. Specifically, each discrete node of the muscle path is represented in the local coordinate frame of its currently closest anatomical body. The efficacy of this approach is demonstrated using a comprehensive upper-limb model with substantial anatomical complexity, adapted from[2]. The model incorporates five rigid bodies from the scapula to the forearm and eleven muscles—including nine muscles in the rotator cuff group and the elbow flexors/extensors (biceps and triceps)—actuating a spherical shoulder and a revolute elbow joint. Simulations were performed for combined motions involving shoulder flexion and abduction as well as elbow flexion. With the original global parameterisation, several muscles, notably one of the rotator cuff muscles, exhibited path discontinuities and non-physiological jumps during concurrent shoulder–elbow movements. The total muscle length showed sudden increases, indicating discontinuous muscle motion. In contrast, the proposed local parameterisation consistently yielded smooth, continuous muscle length profiles across the entire motion range. This work demonstrates that a locally adaptive reference frame is highly beneficial for the numerical robustness of geodesic muscle-wrapping algorithms. Acknowledgement: This work was partly funded by the Deutsche Forschungsgemeinschaft – SFB 1483 –Project-ID 442419336, EmpkinS. REFERENCES [1] J. Penner et al. A discrete mechanics approach for musculoskeletal simulations with muscle wrapping, Multibody Syst. Dyn.2022. [2] M. Lavaill et al. Muscle path predictions using a discrete geodesic Euler–Lagrange model in constrained optimisation: comparison with OpenSim and experimental data, Multibody Syst. Dyn.2025