Fourier-Encoded Plücker Line Fields for Globally Bounded Inverse Velocity Mapping of Axisymmetric Parallel Mechanisms

To address inverse-velocity amplification and numerical instability of axisymmetric parallel mechanisms near dead-point regions, this paper proposes a low-dimensional feature representation and stable inverse-solving framework based on Fourier-encoded Plücker line fields. The limb axes are first represented by normalized Plücker line vectors, and the discrete rod-axis set is lifted to a circumferential continuous line field. A compact feature vector composed of first-order Fourier coefficients is then constructed, from which the continuous feature coefficients and the corresponding feature Jacobian are derived in closed form. Under constant-length constraints, feasible sensitivity and worst-case gain are introduced to characterize local inverse amplification, and a weighted damped KKT inverse solver is formulated to obtain globally bounded inverse solutions for feature velocities. Numerical results show that, in the ideal axisymmetric model, higher-order harmonics remain at numerical-residual levels and the first-order truncation stays dominant, while the most unfavorable amplification location is governed by the trough of feasible sensitivity. For fully reachable targets, the proposed solver reduces the peak generalized velocity by about 4.32%. For targets containing unreachable components, the damped KKT inverse introduces only a small additional residual while keeping the velocity bounded. Additional tests under mild geometric perturbations show that non-ideal errors mainly affect low-order fitting accuracy and higher-order spectral leakage, whereas the peak worst-case gain and the peak-shaving ratio remain largely stable. These results demonstrate that the proposed framework provides a unified description for inverse velocity mapping of axisymmetric parallel mechanisms with analytical interpretability, global boundedness, and robustness under mild geometric imperfections.