Stiffness–footprint Trade-offs in Circular External Fixation: Identifying the Optimal Offset and Angulation for Constant Excursion Half-pin Constructs

Background: Circular external fixation constructs are increasingly designed to be more compact while maintaining mechanical stability. In hexapod systems, limited ring space and strut clearance constrain fixation placement, making fixation cube-hole position (offset) and half-pin divergence key design variables. However, limited guidance exists on how these factors should be balanced when a constant bone-capture (excursion) distance must be maintained. This study evaluated the stiffness–footprint trade-off across five fixation cube-hole configurations under a constant excursion constraint. Methods: A benchtop circular external fixation construct was assembled using a 150-mm reference ring and a 38-mm Delrin cylinder as a bone surrogate. A 5.0-mm half-pin was mounted via a five-hole fixation cube. Five configurations were tested while maintaining a constant excursion of 65.52 mm. As cube-hole position moved proximally, ring–block offset decreased (65.52–17.52 mm) and required divergence increased (0°–30°). Axial compression testing was performed, and stiffness was calculated from the slope of the load–displacement response within the 2–10 lb linear region (peak load 12–15 lb). Three repeat trials of a single construct assembly were performed per configuration. Configuration-depentdent mechanical behaviors were compared using one-way Analysis of Variance ANOVA with Tukey post-hoc testing. Results: Axial stiffness varied markedly across configurations. One-way ANOVA demonstrated large between-configuration differences ( F [4,10] =5540.4, P < 0.001; η 2 = 0.999). Post hoc comparisons showed clear separation between all configurations (Tukey HSD, all P < 0.001), with minimal overlap in measured stiffness values. The orthogonal configuration (0°) was least stiff (293.6 ± 0.8 lb/in). Stiffness increased with divergence, peaking at 20° (486.7 ± 0.1 lb/in; +65.7% vs. baseline). Further divergence to 30° reduced stiffness but remained above baseline (+43.5%). All pairwise comparisons were significant ( P < 0.001). Footprint decreased progressively from 2025.0 mm 2 to 788.6 mm 2 (−61%). Conclusions: While the tested comparisons represent technical repeats rather than independent construct replicates, these results indicate consistency in the measurements within each configuration and the separation between configurations. Moderate half-pin divergence (≈20°) maximized axial stiffness, while greater divergence (30°) minimized footprint with preserved rigidity. These findings support configuration optimization in circular and hexapod fixation.