A standardized ex vivo bone model was used in a paired controlled design with repeated measures. The primary outcome was post-penetration overdrill depth (mm), defined as the linear distance by which the K-wire tip advanced beyond the outer surface of the far cortex after breakthrough. Within the robotic drill-through stopping system, we evaluated the effects of feed rate and spindle speed on overdrilling and assessed the system's consistency and robustness under repeated measurements. In addition, paired comparisons were performed at adjacent, non-interfering sites on the same bone to compare overdrill depth between the robotic system and manual drilling performed by a senior pediatric orthopedic surgeon, who stopped wire advancement based on tactile feedback. Hole allocation and drilling order were randomized using a computer-generated sequence. Overdrill measurements were performed by assessors blinded to group assignment and parameter level. Outcome assessment and blinding. Overdrill-depth measurements were performed by investigators not involved in drilling execution. After drilling, each hole was assigned a randomized identifier for outcome recording. Overdrill-depth results were not disclosed to the surgeon after individual manual holes; values were unmasked only after completion of all paired blocks and final data entry to minimize potential learning or performance drift. Operator blinding was not feasible because the robotic and handheld procedures are inherently different.

Because of ethical and availability constraints, pediatric distal humeral specimens could not be obtained. Following previous experimental work, distal porcine humeri were therefore used as a surrogate model (11). Porcine bone has been shown to resemble human bone at both anatomical and histological levels, particularly with respect to the microstructure of trabecular and cortical bone and patterns of mineralization and remodeling (12). Distal humeri were harvested from freshly slaughtered pigs (age 6–8 months, body weight 90–100 kg) at a local abattoir. All soft tissues and periosteum were removed, and specimens were kept moist throughout preparation and testing with saline-soaked gauze at room temperature (24 °C).

Each bone was rigidly fixed in a custom drilling platform using mechanical clamps. To minimize mechanical interaction between adjacent drill holes, a regular grid was drawn on the bone surface with a fine-line marker and verified using a digital caliper. The center-to-center distance between holes was maintained at ≥10 mm, and the distance from each hole center to the specimen edge was also ≥10 mm. All experiments were performed using K-wires from the same manufacturing lot. To reduce tool-related variability, a new 2.0-mm K-wire was used for every hole. Specimen number and hole capacity. In total, 11 distal porcine humeri were used. With a center-to-center spacing of ≥10 mm and a ≥ 10 mm distance from hole center to the specimen edge, the lateral condyle region could typically accommodate approximately six non-interfering holes per specimen.

Definition of a hole block. A “hole block” was defined as a set of three non-overlapping holes on the same specimen, corresponding to the three parameter levels (one hole per level), with the execution order randomized within the block.

For all experiments, the bone block was fixed on the platform with the drilling axis oriented 60° to the longitudinal axis of the humerus and 0° to the coronal plane. In each trial, a 2.0-mm K-wire was introduced from the lateral supracondylar region toward the medial–proximal cortex, passing through cancellous bone until breakthrough of the far cortex.

In the robotic group, drilling was performed with a UR10-based robotic system equipped with an integrated electric drill (model WS6090-48, HQuDJ, China; rated power 500 W; speed range 0–3,000 r min⁻¹). The force-sensing controller detected the characteristic drop in axial force and then automatically issued a stop command. In the manual group, drilling was performed using a conventional orthopedic power drill (model BJ1107B, Bojin, China; speed range 0–1,200 r min⁻¹). The surgeon relied on tactile and auditory cues to recognize cortical breakthrough and attempted to promptly reduce force and stop advancement to minimize inertial overdrilling.

K-wire diameter and batch were identical between groups. All experiments used 2.0 mm × 150 mm Kirschner wires (Yutong, China) from the same manufacturing lot. To minimize tool-related variability, a new K-wire was used for each hole. Before data collection, a standardized familiarization session was conducted. Any obvious deviation from the intended trajectory, overload shutdown, or other anomalies were documented and managed according to a predefined protocol. Throughout the experiments, the allocation of hole positions and the sequence of drilling were randomized, and a unified positioning procedure was applied to ensure reproducibility.

The custom force-controlled bone drilling system (Figure 1) consisted of a six-degree-of-freedom UR10 robotic arm, a six-axis force/torque sensor, an electric spindle with controller, and dedicated fixation jigs. The system supported initialization of the robot and spindle, configuration of motion parameters, real-time sensor acquisition, and data logging. Force/torque data were sampled at 125 Hz and time-synchronized with position data.

Drilling was executed within a predefined safe thrust range. Robot feed was executed in a position/velocity-controlled mode with a constant commanded feed rate. Brief transient deviations in instantaneous measured velocity may occur around cortical breakthrough due to local compliance changes; however, the command profile was not intentionally altered. Drill-through stopping was triggered by a transient drop in axial force (Fx). The primary penetration criterion was defined as:ΔFx=Fx(t1)−Fx(t1−t2),where Fx(t1) is the instantaneous axial force at time t1, and Fx(t1−t2) is the axial force at an earlier time t1−t2. Penetration was flagged when all of the following conditions were simultaneously satisfied:

∣Fx(t1)∣≥Farm and ∣Fx(t1−t2)∣≥Farm (both samples above a preset arm force threshold);

Raw force/torque signals were denoised using low-pass and median filtering before being passed to the penetration detection module for analysis.

To mitigate potential failure modes (e.g., sensor artifacts, missed detection, and actuator non-response), the system incorporated multi-layer safety constraints. First, axial force was monitored in real time (with torque recorded for reference); exceeding predefined hard limits (Fx > Fmax) immediately halted feed motion and commanded spindle stop. Hard limits were set a priori based on pilot testing to remain below levels associated with wire bending, bone cracking, or fixture slippage. Second, travel/time limits were applied to prevent uncontrolled advancement if breakthrough was missed. For each planned trajectory, the maximum allowed travel was defined as Lmax = Lbone + ΔL (ΔL = 5 mm), and the maximum allowed drilling time was tmax = Lmax/vfeed + Δt (Δt = 5 s), where vfeed is the prescribed feed rate. Lbone was measured for each planned hole as the trajectory length from the outer surface of the near cortex to the outer surface of the far cortex along the drilling axis. If the breakthrough criterion was not met within either limit, the controller halted feed motion and commanded spindle stop as a fail-safe. Hardware and software emergency stops were available throughout, and the operator could manually override the system at any time. All safety events (trigger type, timestamp, and force/position, torque recorded for reference) were logged for traceability.

The primary outcome measure was post-penetration overdrill depth (mm). Using the outer surface of the far cortex as the reference endpoint, overdrill depth was calculated as the difference between (1) the depth from the outer surface of the near cortex at the entry point to the deepest point of the drill channel and (2) the actual cortical thickness, defined as the distance between the outer surfaces of the near and far cortices along the same drilling axis. Measurements were obtained with a vernier caliper (resolution 0.01 mm) and recorded to 0.01 mm. Each hole was measured twice, and the mean of the two readings was used. If burrs or collapse were present at the channel edge, the entrance was gently cleaned with a deburring tool before measurement.

To assess measurement reliability, two investigators independently measured each hole. If the absolute difference between their readings exceeded 0.20 mm, a third measurement was performed, and the final value was taken as the mean of all three measurements. Before each testing day, the depth rod of the caliper was calibrated to zero and across a reference span using gauge blocks, with an acceptance tolerance of ±0.02 mm. All measurements were performed in a temperature-controlled laboratory at 24 °C.

Adverse events were recorded for each hole according to predefined categories: K-wire jamming (requiring reverse withdrawal), overload shutdown (device protection triggered), obvious deviation from the intended trajectory or loss of guidance (drilling axis deviating from the planned angle), and measurement interference (e.g., entrance collapse affecting depth readings). The corresponding management and whether the hole was included in the final analysis were documented.

The primary outcome variable was post-penetration overdrill depth (mm). For the parameter sensitivity tests (repeated measures), a one-factor, three-level design (k = 3; factor: spindle speed or feed rate) was used. Within-subject residuals were first assessed for normality using the Shapiro–Wilk test and inspection of Q–Q plots. When assumptions were met, one-way repeated-measures ANOVA was applied, followed by Tukey post hoc comparisons. If variance or sphericity assumptions were violated, Greenhouse–Geisser (G–G) correction was used. In cases of markedly non-normal distributions or clear outliers, the Friedman test was used instead, with Dunn's multiple comparisons and Holm adjustment for pairwise tests. For the main tests, F statistics F(df1,df2), p values, and partial η2 were reported; for pairwise comparisons, mean differences (mm), 95% confidence intervals (CI), and adjusted p values (p_adj) were presented.

For the paired comparison between the robotic and manual groups, adjacent hole sites on the same bone formed a paired block. Within each block, one robotic value (Ri) and one manual value (Mi) were obtained, and the paired difference was defined as Di=Mi−Ri. A two-sided paired t-test (α = 0.05) was used to compare groups, with mean difference, 95% CI, p value, and effect size (Cohen's d_z) reported. The normality of Di was evaluated with the Shapiro–Wilk test; if the distribution deviated from normality, a Wilcoxon signed-rank test was additionally performed. All analyses were conducted using GraphPad Prism version 10.12. All statistical tests were two-sided, with a significance level of α = 0.05.

For the repeated-measures parameter tests (one factor, three levels), sample size was estimated based on a pilot standard deviation of paired differences of σ_d = 0.20 mm and a minimal clinically important difference (MCID) of Δ = 0.30 mm, yielding an effect size of d=Δ/σd=1.5. With α = 0.05 and power = 0.80, G*Power estimated that n = 5 paired blocks were required. To account for potential data loss or exclusions, the planned sample size was increased to n = 6 blocks (18 holes per experiment).

For the robotic vs. manual paired comparison, a pilot series of six pairs yielded a mean paired difference and a standard deviation SDD=0.63mm, corresponding to an effect size of . With α = 0.05 and power = 0.80, G*Power indicated that a minimum of n = 3 pairs would be sufficient. Given the likelihood that the pilot effect size was overestimated and to allow for potential exclusions due to adverse events, the target sample size was increased to n = 10 pairs (20 holes in total).

Blue curve: raw Fx; green curve: filtered Fx. Between 5 and 7 s, initial contact with the thin near cortex (orange arrow) causes a rise in Fx, followed by a mildly fluctuating steady cutting phase. Around 53–54 s, Fx increases again, indicating approach to the far cortex. At 58–59 s, cortical breakthrough occurs (red arrow), producing an abrupt drop in Fx that satisfies the force-drop criterion and triggers the control algorithm to terminate feed motion and stop the spindle, thereby limiting overdrilling. Horizontal axis: time (s); vertical axis: Fx (N).

Post-penetration overdrill depth at feed rates of 0.5, 1.0, and 1.5 mm·s⁻¹ (n = 6 hole blocks derived from 3 specimens; each specimen contributed two blocks, and each block contributed one hole per level; total 18 holes). Dots represent individual holes; Bars indicate group means, and error bars represent standard deviations (SD). Data were analyzed with one-way repeated-measures ANOVA (Geisser–Greenhouse correction where appropriate), followed by Tukey post hoc pairwise comparisons. A p value < 0.05 was considered statistically significant; “ns” denotes non-significant pairwise differences.

Distribution of post-penetration overdrill depth at spindle speeds of 900, 1,200, and 1,500 r·min⁻¹ ((n = 6 hole blocks derived from 3 specimens; each specimen contributed two blocks, and each block contributed one hole per level; total 18 holes). Dots represent holes; lines (if shown) connect repeated measures within the same specimen. bars indicate group means, and error bars represent standard deviations (SD). Brackets indicate pairwise Tukey post hoc comparisons and their significance. Statistical analysis was performed using one-way repeated-measures ANOVA (with Geisser–Greenhouse correction where appropriate). A p value < 0.05 was considered statistically significant; “ns” indicates non-significant pairwise differences.

The feed-rate test included 3 specimens and 6 hole blocks (18 holes; n = 6 per level). A one-way repeated-measures ANOVA (Geisser–Greenhouse corrected) showed a significant main effect of feed rate on overdrill depth, F(1.992, 9.958) = 6.382, p = 0.016, with a large effect size (partial η² = 0.56). The mean  ± SD overdrill depths were 0.733 ± 0.111 mm at 0.5 mm·s⁻¹, 0.797 ± 0.137 mm at 1.0 mm·s⁻¹, and 0.985 ± 0.100 mm at 1.5 mm·s⁻¹. Tukey post hoc comparisons showed that 1.5 mm·s⁻¹ produced significantly greater overdrilling than 0.5 mm·s⁻¹ (mean difference +0.252 mm; 95% CI, 0.0065–0.497; p_adj = 0.0456). The differences between 0.5 and 1.0 mm·s⁻¹ (mean difference −0.063 mm; 95% CI, −0.3017–0.1750; p_adj = 0.6832) and between 1.0 and 1.5 mm·s⁻¹ (mean difference −0.188 mm; 95% CI, −0.4200–0.04335; p_adj = 0.0981) were not statistically significant (Figure 3).

The spindle-speed test included 3 specimens and 6 hole blocks (18 holes; n = 6 per level). One-way repeated-measures ANOVA with Geisser–Greenhouse correction (ε = 0.6786) indicated no significant main effect of spindle speed on overdrill depth, F(1.357, 6.786) = 0.0459, p = 0.8998, with a negligible effect size (partial η² ≈ 0.009). The mean ± SD overdrill depths were 0.8217 ± 0.0962 mm at 900 r min⁻¹, 0.8200 ± 0.1455 mm at 1,200 r min⁻¹, and 0.8050 ± 0.1297 mm at 1,500 r min⁻¹. None of the Tukey post hoc pairwise comparisons reached significance:

900 vs. 1,200 r min⁻¹, Δ = 0.0017 mm (95% CI, −0.1641–0.1675; p_adj = 0.9994);

900 vs. 1,500 r min⁻¹, Δ = 0.0167 mm (95% CI, −0.1370–0.1704; p_adj = 0.9345);

1,200 vs. 1,500 r min⁻¹, Δ = 0.0150 mm (95% CI, −0.2410–0.2710; p_adj = 0.9802).

These findings indicate that, within the tested range, overdrill depth was essentially insensitive to spindle speed (Figure 4).

The paired comparison included 5 specimens and 10 paired blocks (20 holes). Compared with manual drilling at adjacent sites on the same bone, the force-sensing robotic system substantially reduced post-penetration overdrill depth. Mean overdrill depth was 0.865 ± 0.121 mm in the robotic group and 6.595 ± 1.525 mm in the manual group. The paired mean difference (Manual−Robot) was 5.730 mm (95% CI, 4.665–6.795). A paired t-test showed a highly significant difference, t(9) = 12.17, p < 0.0001, with a very large effect size (Cohen's d_z = 3.85; partial η² = 0.943), indicating a marked and highly consistent advantage of the robotic system (Tables 1, 2, Figure 5). In practical terms, overdrilling was controlled to <1 mm with the robotic system, whereas manual drilling resulted in overdrill depths of approximately 6.6 mm (Figure 5).

No K-wire jamming, overload-related shutdown, or noticeable trajectory deviation/loss of guidance was observed in either group. No fail-safe events (force/torque limit stop, travel/time-limit stop, or emergency-stop activation) occurred. No holes were excluded from the analysis due to adverse events.