Guide-Based Kinematic Reconstruction of Reference-Cylinder Trajectories in Step-Precision Winding

Step-precision winding requires coordinated selection of winding ratios, stage connections, and guide-reversal motion under prescribed stroke and period constraints. This study develops a process-oriented kinematic framework linking winding-angle requirements to staged ratio inputs and guide-based trajectories on a reference cylinder. Spindle angle and accumulated traverse phase provide a common state description, while an adopted LSPB law relates reversal width to interior speed and peak acceleration. Analytical and numerical comparisons establish position and velocity continuity conditions and quantify the trade-off between a constant-angle interior and reversal motion demand. With recorded spindle angle as input, calibration on 20 double traverses followed by continuous prediction over 40 gives a guide-position root-mean-square error (RMSE) of 0.827 mm and a maximum absolute error of 2.128 mm over a 200-mm stroke. A second record contains 11 ratio stages and ten actual changes. Using stage inputs identified from stable feedback intervals outside the evaluated transition windows, continuous-phase reconstruction achieves an RMSE of 0.541 mm over 7935 samples, compared with 0.731 mm for the triangular profile under the same identified phase and stroke scale. These complementary prediction and retrospective reconstruction results support a common representation for evaluating winding-ratio schedules and guide-reversal choices. The spatial trajectories are kinematic reference paths derived from guide motion.