2.1.1. Orthosis system

The knee orthosis is based on a commercially available brace (Genu CI Step Thru, Sporlastic, Nürtingen), modified with an active motor module (Sporlastic, 2023). An AK80-9 actuator (CubeMars, Nanchang) (CubeMars, 2023) and an MD80 motor controller (MAB Robotics, Poznań) (MABRobotics, 2025), providing a nominal torque of 9 N m (peak torque 22 N m), drive the polycentric knee joint. The polycentric design replicates the physiological shifting center of knee rotation, requiring an additional translational degree of freedom between the actuator and brace. This is achieved through our custom-designed, 3D-printed lateral bracket, publicly available in standard sizes (S, M, L) for both left and right braces (Scheidl et al., Reference Scheidl, Akarsu, Mehrkens, Schuh and Castellini2025). Interchangeable plastic inserts allow setting fixed limits to knee flexion and extension angles. The actuator’s high backdrivability (0.51 N m) ensures minimal resistance during passive joint motion, preserving natural gait characteristics (CubeMars, 2023). The entire active orthosis assembly weighs approximately 1.1 kg for size S (1.2 kg for size L); roughly 0.55 kg stem from the passive brace and 0.55 kg from the motor module. The motor housing and bracket have approximately the size of 40 cm  $ \times $ 15 cm  $ \times $ 13 cm. At the current prototype scale, orthosis hardware and electronics each cost on the order of 800 EUR.

2.1.2. Sensors and setup

Muscle activity was recorded using wireless Trigno Avanti sEMG sensors (Delsys Inc., Massachusetts), with eight channels placed bilaterally over the rectus femoris, biceps femoris, gastrocnemius medialis, and tibialis anterior (see Figures 1a and 1b). Because of the spatial constraints imposed by the orthosis shell, electrode positions deviated slightly from the SENIAM recommendations. They were positioned as close as practicable to the targeted muscle bellies while avoiding direct contact with the brace (Hermens et al., Reference Hermens, Freriks, Disselhorst-Klug and Rau2000).

Figure 1.

Sensor placement and hardware overview: (a) Anterior view with the powered knee orthosis on the right leg and sEMG electrodes placed over rectus femoris and tibialis anterior. (b) Posterior view with the sEMG electrodes placed over biceps femoris and gastrocnemius medialis. (c) Participant walking at the DIERS 4D High Performance Lab with the active orthosis on the right leg. (d) Lateral close-up of the powered knee orthosis showing the actuator module and brace assembly (Scheidl et al., Reference Scheidl, Akarsu, Mehrkens, Schuh and Castellini2025). Panels (a) and (b) are adapted from (Z-Anatomy, 2025).

Figure 1. Long description

(a) Anterior illustration of both legs with the knee orthosis on the right leg; numbered electrode sites 1 and 2 lie over rectus femoris on the thighs and 5 and 6 over tibialis anterior on the shins. (b) Posterior illustration with electrode sites 3 and 4 over biceps femoris on the back of the thighs and 7 and 8 over gastrocnemius medialis on the calves. (c) Photograph from behind of a participant walking on an instrumented treadmill in a motion laboratory, wearing the black powered knee orthosis on the right leg. (d) Lateral close-up photograph of the powered knee orthosis on a leg, showing the round actuator module at the knee joint mounted on the brace frame with straps.

2.2.1. Controller structure

The controller defines a normalized ramp region that begins at $ {\theta}_{\mathrm{ramp}} $ and ends at the passive mechanical safety boundary $ {\theta}_{\mathrm{lim}} $ . Within this region, the normalized proximity $ \rho $ to the safety boundary is computed:

(1) $$ \rho =\mathrm{clip}\left(\frac{\theta -{\theta}_{\mathrm{ramp}}}{W},0,1\right),\hskip1em W=\left|{\theta}_{\mathrm{lim}}-{\theta}_{\mathrm{ramp}}\right|. $$

Here, $ {\theta}_{\mathrm{ramp}} $ marks the beginning of the normalized ramp region and $ {\theta}_{\mathrm{lim}} $ the passive mechanical safety boundary. The operator

$$ \mathrm{clip}\left(x,0,1\right)=\min \left(1,\max \left(0,x\right)\right), $$

saturates the normalized proximity variable to the interval $ \left[0,1\right] $ . Importantly, $ {\theta}_{\mathrm{ramp}} $ does not mark the hard onset of perceptible braking, because actual controller engagement additionally depends on the gate thresholds $ {\rho}_{\mathrm{on}} $ and $ {v}_{\mathrm{on}} $ . A binary gating mechanism $ G $ (Figure 2) ensures the impedance only engages during meaningful movement toward the limit:

(2) $$ G=\left\{\begin{array}{ll}1,& \rho \ge {\rho}_{\mathrm{on}}\wedge \dot{\theta}>{v}_{\mathrm{on}},\\ {}0,& \rho \le {\rho}_{\mathrm{off}}\vee \left|\dot{\theta}\right|<{v}_{\mathrm{off}}.\end{array}\right. $$

Thresholds $ {\rho}_{\mathrm{on}}>{\rho}_{\mathrm{off}} $ and $ {v}_{\mathrm{on}}>{v}_{\mathrm{off}} $ create hysteresis to prevent unwanted activation, ensuring smooth transitions without jitter. Intuitively, the gate turns on only when the knee is close enough to the flexion limit ( $ \rho \ge {\rho}_{\mathrm{on}} $ ) and still moving into flexion above a small velocity threshold ( $ {v}_{\mathrm{on}} $ ). It turns off when the knee moves away from the limit ( $ \rho \le {\rho}_{\mathrm{off}} $ ) or slows down below $ {v}_{\mathrm{off}} $ , and retains its previous state between the separate on- and off-thresholds. The two threshold pairs ( $ {\rho}_{\mathrm{on}},{\rho}_{\mathrm{off}} $ ) and ( $ {v}_{\mathrm{on}},{v}_{\mathrm{off}} $ ) provide hysteresis and prevent chattering when the motion oscillates around the switching point.

Figure 2.

Sequence-of-operation diagram for the soft-stop controller. The outer panels schematically summarize the gating logic based on proximity and angular velocity. The middle panel shows the resulting gain factor $ g\left(\rho \right) $ as a function of knee flexion angle, multiplying the base proportional and derivative gains.

Figure 2. Long description

A box labelled Gating Mechanisms splits into three branches. Left branch: conditions rho < rho_on and v < v_on lead to “Gate stays OFF” and “Controller OFF” with k_d = k_p = 0. Middle branch: conditions rho > rho_on and v > v_on lead to “Gate turns ON,” then to “Calculation of gain factors depending on flexion angles,” illustrated by a small inset plot of gain factor versus flexion angle in degrees, and finally to “Controller ON” with K_p = K_p,base times g(rho) and K_d = K_d,base times g(rho) times k_d. Right branch: conditions rho < rho_off, v < v_off and v < 0 lead to “Gate turns OFF” and “Controller OFF” with k_d = k_p = 0.

2.2.2. Gain scheduling

The impedance envelope $ g\left(\rho \right) $ smoothly increases stiffness and damping as the knee approaches the flexion limit, shaped by a polynomial ramp:

(3) $$ g\left(\rho \right)=\min \left({\rho}^k,{f}_{\mathrm{max}}\right). $$

Here, $ k>0 $ is a dimensionless shape exponent controlling how strongly the gain increase is concentrated near the flexion boundary. For $ k=1 $ , the uncapped envelope increases linearly, whereas $ k>1 $ shifts more of the gain increase toward the boundary. The value used in this study was $ k=4 $ (Table 1). This envelope is exponentially smoothed to mitigate sensing noise and abrupt changes:

(4) $$ {g}_s(t)=\alpha g\left(\rho (t)\right)+\left(1-\alpha \right){g}_s\left(t-\varDelta t\right), $$

with a soft-start mechanism after gate activation. Gains are finally scaled using the smoothed envelope, ensuring higher damping at higher velocities and minimal resistance at lower speeds:

(5) $$ {K}_p(t)={g}_s(t)\;{K}_{p,\mathrm{base}},\hskip2.00em {K}_d(t)={g}_s(t)\;{\kappa}_d(t)\;{K}_{d,\mathrm{base}}, $$

(6) $$ {\kappa}_d(t)=\min \left(1,\left|\dot{\theta}(t)\right|/{v}_{\mathrm{damp}}\right),\hskip1em {v}_{\mathrm{damp}}=0.60\;\mathrm{rad}/\mathrm{s}. $$

Figure 3 illustrates the controller operation and the reference thresholds over a representative mean gait cycle. The left panel shows the knee angle together with the normalized gain envelope, whereas the right panel shows the corresponding scheduled controller targets. As knee flexion increases in late swing, the scheduled stiffness and damping rise and operate within the prescribed boundary before the knee reverses direction.

Figure 3.

Controller operation during an averaged gait cycle (mild stop preset). Left: knee flexion angle (blue dashed) and normalized gain envelope $ g\left(\rho \right) $ (green). Reference thresholds $ {\theta}_{\mathrm{ramp}} $ , $ {\theta}_{\mathrm{on}} $ , $ {\theta}_{\mathrm{lim}} $ , and the virtual target ( $ {45}^{\circ } $ ) are shown as horizontal lines. Right: scheduled stiffness $ {K}_p\;\left(\mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1}\right) $ (grey) and damping $ {K}_d\;\left(\mathrm{N}\;\mathrm{m}\;\mathrm{s}\;\mathrm{ra}{\mathrm{d}}^{-1}\right) $ (black) over the same gait cycle. Background shading denotes gait phases (LR, MS, PS, TS).

Figure 3. Long description

Both panels plot knee angle (blue dashed line, 0 to 65 degrees) against gait cycle (0 to 100 percent), with background bands for loading response, mid stance, pre swing and terminal swing. Horizontal lines mark theta_ramp (15 degrees), theta_on (about 28.5 degrees), the virtual target (45 degrees) and theta_lim (60 degrees). The knee angle has a small peak of about 21 degrees in early stance and a main peak of about 62 degrees at roughly 75 percent of the cycle. Left: the normalized gain envelope g(rho) (green, right axis 0.30 to 0.70) starts at about 57 percent of the cycle, rises steeply in pre swing and levels off near 0.61 in terminal swing. Right: scheduled stiffness K_p (grey) and damping K_d (black) rise between about 62 and 72 percent of the cycle, with K_d peaking just before the knee angle maximum.

Table 1.

Summary of gain presets and shared controller parameters

Table 1. Long description

Rows: mild stop and firm stop. Base proportional and derivative gains are 10 and 20 for the mild stop and 50 and 70 for the firm stop; maximal scheduled gains K_p max and K_d max are 7 and 14 (mild) and 35 and 49 (firm). Shared by both presets: theta_on 28.5 degrees, theta_off 21.8 degrees, v_damp 0.60 rad/s, shape exponent k 4.00, f_max 0.70, smoothing factor alpha 0.25, theta_ramp 15 degrees, theta_lim 60 degrees, v_on 0.25 rad/s and v_off 0.07 rad/s. Proportional gains in Nm/rad, derivative gains in Nm s/rad.

Note: The proportional and derivative gains are given in $ \mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1} $ and $ \mathrm{N}\;\mathrm{m}\;\mathrm{s}\;\mathrm{ra}{\mathrm{d}}^{-1} $ respectively, $ \theta $ in degree and velocities in $ \mathrm{rad}/\mathrm{s} $ .

The gain-scheduled soft-stop controller generated torque $ {\tau}_{\mathrm{ss}} $ is defined as:

(7) $$ {\tau}_{\mathrm{ss}}(t)=G(t)\left[{K}_p(t)\left({\theta}_{\mathrm{ref}}(t)-\theta (t)\right)+{K}_d(t)\left({\dot{\theta}}_{\mathrm{ref}}(t)-\dot{\theta}(t)\right)\right]. $$

Here, knee flexion and flexion velocity are defined as positive, and the reference velocity was set to $ {\dot{\theta}}_{\mathrm{ref}}(t)=0 $ . When the knee continues to move into flexion relative to the active reference, the resulting soft-stop torque is extension-directed and opposes further flexion. Independent of the gain-scheduled soft-stop law, the actuator used an internal transparency controller to reduce reflected friction from the motor and gearbox. This internal friction compensation was not a separately tuned term of the soft-stop controller. In the ortho plus condition, the soft-stop contribution was disabled, and only the internal transparency compensation remained active. In the firm and mild soft-stop conditions, the scheduled impedance gains were activated relative to this transparent actuator baseline.

2.3.1. Biomechanical rationale

Human knee mechanics vary substantially across gait phases. Perturbation-based identification during walking reported swing-phase knee stiffness of $ 0 $ – $ \approx 3.5\;\mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1} $ and damping of $ \approx 0.02 $ – $ 0.14\;\mathrm{N}\;\mathrm{m}\;\mathrm{s}\;\mathrm{ra}{\mathrm{d}}^{-1} $ (van der Kooij et al., Reference van der Kooij, Fricke, van’t Veld, Vallinas Prieto, Keemink, Schouten and van Asseldonk2022). Separate gait analyses reported phase-dependent knee quasi-stiffness values up to $ \approx 176\;\mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1} $ and an average peak knee moment of $ \approx 0.46\;\mathrm{N}\;\mathrm{m}\;\mathrm{k}{\mathrm{g}}^{-1} $ (Huang et al., Reference Huang, Zhang, Yu, MacLean, Zhu, Di Lallo, Jiao, Bulea, Zheng and Su2022). Published knee-moment data provide an additional order-of-magnitude reference (Zhang et al., Reference Zhang, Liu, Han, Wang, Yan, Ma and Wei2020). These values informed the initial controller scale, whereas the final gains were tuned empirically on the device. The mechanical rationale concerns the external brace-limb interaction rather than direct ACL or graft loading. Decelerating knee flexion requires negative mechanical work. For a comparable reduction in rotational kinetic energy, distributing this work over a larger angular excursion lowers the mean resisting torque and avoids concentrating deceleration at a single rigid end-stop event. The soft-limit controller therefore targets low impedance through most of the gait cycle and increases stiffness and damping only as the configured flexion region is entered, before contact with the passive $ {60}^{\circ } $ safety stop. ACL force depends on the combined tibiofemoral loading state, muscle forces, and joint kinematics (Markolf et al., Reference Markolf, Burchfield, Shapiro, Shepard, Finerman and Slauterbeck1995). These internal tissue loads were not estimated in this study. The present analysis therefore addresses flexion-limiting performance and external user interaction, not tissue-protection efficacy.

2.3.2. Implemented parameters and presets

The controller parameters were chosen by combining literature-derived order-of-magnitude estimates for swing-phase knee impedance and physiological knee moments (Zhang et al., Reference Zhang, Liu, Han, Wang, Yan, Ma and Wei2020; Huang et al., Reference Huang, Zhang, Yu, MacLean, Zhu, Di Lallo, Jiao, Bulea, Zheng and Su2022; van der Kooij et al., Reference van der Kooij, Fricke, van’t Veld, Vallinas Prieto, Keemink, Schouten and van Asseldonk2022), as well as hardware constraints, and pilot tuning on the actual device. The passive boundary $ {\theta}_{\mathrm{lim}}={60}^{\circ } $ was retained as a hardware fail-safe and aligned with the clinical partner’s early-phase practice, whereas the intended virtual flexion bound was approximately $ {45}^{\circ } $ . The rigid-stop comparator was therefore set to $ {45}^{\circ } $ to ensure measurable engagement during healthy treadmill walking, while the soft-stop conditions retained the $ {60}^{\circ } $ passive stop as a safety layer. The ramp onset $ {\theta}_{\mathrm{ramp}}={15}^{\circ } $ was chosen to allow gain buildup over late swing rather than a late abrupt rise. The hysteresis thresholds $ \left({\rho}_{\mathrm{on}},{\rho}_{\mathrm{off}}\right) $ and $ \left({v}_{\mathrm{on}},{v}_{\mathrm{off}}\right) $ were selected to prevent chatter around onset and release. The polynomial exponent $ k=4 $ keeps the gain envelope low over most of the ramp and increases resistance primarily near the boundary. The cap $ {f}_{\mathrm{max}}=0.70 $ was selected empirically as an independent, quick-to-scale parameter that limits end-range interaction intensity without changing the ramp geometry or gating logic. The smoothing factor $ \alpha =0.25 $ reduced jitter without introducing excessive delay. The damping scale $ {v}_{\mathrm{damp}}=0.60\;\mathrm{rad}/\mathrm{s} $ preserved natural interaction at low velocities while allowing stronger damping during faster flexion. The base gains $ {K}_{p,\mathrm{base}} $ and $ {K}_{d,\mathrm{base}} $ were chosen such that the mild preset prioritized low interference and the firm preset prioritized stricter braking. Literature on physiological swing-phase knee impedance and knee flexion moments provided the target order of magnitude, but the final values were tuned empirically on the present orthosis to achieve stable, smooth interaction without an overly abrupt hard-wall sensation. We evaluated two distinct impedance presets (see Table 1): Mild stop ( $ {K}_{p,\mathrm{base}}=10 $ , $ {K}_{d,\mathrm{base}}=20 $ ) yields maximal scheduled gains $ {K}_p^{\mathrm{max}}=7\;\mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1} $ and $ {K}_d^{\mathrm{max}}=14\;\mathrm{N}\;\mathrm{m}\;\mathrm{s}\;\mathrm{ra}{\mathrm{d}}^{-1} $ . Firm stop ( $ {K}_{p,\mathrm{base}}=50 $ , $ {K}_{d,\mathrm{base}}=70 $ ) results in maximal gains $ {K}_p^{\mathrm{max}}=35\;\mathrm{N}\;\mathrm{m}\;\mathrm{ra}{\mathrm{d}}^{-1} $ and $ {K}_d^{\mathrm{max}}=49\;\mathrm{N}\;\mathrm{m}\;\mathrm{s}\;\mathrm{ra}{\mathrm{d}}^{-1} $ . These presets differ primarily in late-swing braking strength; mild prioritizes minimal interference while adhering to the lower boundaries of physiological flexion demands, whereas firm emphasizes stricter flexion capping and explores upper-boundary impedance gains. For the soft-stop conditions, we did not add a second mechanical stop at $ {45}^{\circ } $ . Instead, the impedance profile was tuned so that the knee was typically decelerated toward an effective virtual bound near $ {45}^{\circ } $ , while the passive $ {60}^{\circ } $ stop remained as a fail-safe. This leaves approximately $ {15}^{\circ } $ of headroom between the intended virtual bound and the passive safety stop, accommodating inter-subject variability and helping avoid mechanical impacts. Table 1 summarizes these parameters. Controller commissioning was performed once at device level before participant testing. Both presets shared the same ramp geometry, gate thresholds, hysteresis, smoothing, and velocity scaling, which remained fixed for all participants. The mild and firm presets differed only in their base proportional and derivative gains. No participant-specific gain optimization was performed during the experiment. Compared with a passive compliant stop, this approach requires more parameters during initial setup. However, the restriction level can be adjusted dynamically in software without replacing a spring, bumper, damper, or stop insert. Because this research is at the prototype stage and exploratory, tuning time and operator workload were not formally compared between the two approaches.

2.4.1. Design and conditions

A counterbalanced crossover design with six gait conditions was used (see Table 2):

• • Physiological gait (physio): walking without the orthosis.

• • Orthosis only (ortho only): the brace worn without the motor assembly, representing the passive effects of the shell and strapping.

• • Orthosis plus motor (ortho plus): the brace worn with the motor active and the soft-stop controller disabled. The actuator’s internal transparency controller reduced reflected friction from the motor and transmission, minimizing resistance to voluntary knee motion.

• • Rigid stop (rigid stop): the orthosis with the mechanical 45° flexion stop in place, without the motor assembly, representing the current rehabilitation standard.

• • Firm soft stop (firm stop): the orthosis with both the mechanical 60° safety stop and the firm impedance gain preset active, targeting a strict virtual flexion limit around 45°.

• • Mild soft stop (mild stop): targeting the same flexion limit as in the firm condition but with a milder impedance gain preset.

Each condition was recorded three times, with each trial lasting approximately 6 s (2–3 complete strides per leg). Condition order followed Williams-design sequences intended to balance order and first-order carryover. Participants 1–6 formed one complete six-sequence block, whereas participants 7–8 received two repeated sequences; the complete $ n=8 $ allocation was therefore counterbalanced but not perfectly balanced (Williams, Reference Williams1949). The complete condition presentation order is listed in the Supplementary Table 7. The rigid-stop comparator used a mechanical $ {45}^{\circ } $ flexion stop. In the soft-stop conditions, the intended virtual flexion bound was approximately $ {45}^{\circ } $ , while an additional passive mechanical stop at $ {60}^{\circ } $ was retained as a safety layer.

Table 2.

Condition overview

Table 2. Long description

Physiological gait: no orthosis, no motor, no stop. Orthosis only: orthosis without motor or stop. Orthosis plus: orthosis with motor, no stop. Rigid stop: orthosis without motor, with a rigid stop at 45 degrees. Firm stop and mild stop: orthosis with motor, a rigid safety stop at 60 degrees and a soft stop at 45 degrees.

2.4.2. Task

Participants walked on the instrumented treadmill at a constant speed of 3 km/h, slightly below the average preferred walking speed of healthy adults. This reduced speed was selected to simulate potential gait performance in individuals undergoing early rehabilitation. For each condition, three repetitions consisting of 2–3 complete strides were recorded per leg. Five-minute breaks between repetitions minimized fatigue. Afterward, a questionnaire was completed for subjective user feedback.

2.4.3. Synchronization, gait segmentation, sEMG preprocessing and feature extraction

All data streams (motor encoder, DIERS 4D High Performance Lab kinematics, treadmill force plates, and sEMG) were synchronized using UNIX timestamps. Gait events were identified bilaterally as initial-contact (IC) and toe-off (TO) events from the instrumented treadmill force plates and processed in the DIERS pedogait/DICAM export. Each right gait cycle extended from ipsilateral IC to the subsequent ipsilateral IC and was divided into four consecutive intervals: loading response (LR; ipsilateral IC to contralateral TO), mid stance (MS; contralateral TO to contralateral IC), pre swing (PS; contralateral IC to ipsilateral TO), and terminal swing (TS; ipsilateral TO to the subsequent ipsilateral IC) (Perry and Burnfield, Reference Perry and Burnfield2010). The DIERS export label terminal swing is retained here.

Surface EMG was processed at 3705 Hz. Signals were notch-filtered at 50 Hz, zero-phase band-pass filtered from 20 to 450 Hz using a fourth-order Butterworth filter, and full-wave rectified. Confirmed signal-quality exclusions were applied before participant-sensor standardization. For each participant and sensor, the mean and standard deviation of all retained gait-cycle samples were calculated, and the signal was normalized to reflect $ \left|z\right| $ .

Within each cycle and event-defined interval, values below $ {Q}_1-1.5\times \mathrm{IQR} $ or above $ {Q}_3+1.5\times \mathrm{IQR} $ were clipped to the corresponding fence (Tukey, Reference Tukey1977). Mean standardized ARV was defined as the arithmetic mean of the clipped $ \left|z\right| $ samples, and $ {q}_{95} $ as their 95th percentile.

For the exploratory peak-timing descriptor, $ \left|z\right| $ was additionally low-pass filtered at 6 Hz using a fourth-order zero-phase Butterworth filter. Peak timing was defined as the relative location of the within-interval maximum, expressed from 0% at interval onset to 100% at interval end.

2.4.4. Outcome variables and stride-level summaries

Primary knee kinematics were obtained from the actuator encoder. The knee-angle signal from the DIERS 4D High Performance Lab (DIERS International GmbH, 2025) was used only as a secondary optical plausibility comparison and did not enter the controller calculation. Figure 4 shows the optical trajectory for the unrestricted motorized (ortho plus) condition, because this condition served as the motorized reference and allowed the encoder trajectory to be compared with an optical measurement without an active flexion limit. DIERS-derived ankle, pelvic, and trunk kinematics were analyzed separately as secondary outcomes.

Figure 4.

Knee joint angles during an averaged gait cycle under ortho plus, firm stop, and mild stop conditions. The solid blue trace shows the optical reference from the DIERS 4D High Performance Lab for ortho plus; dashed traces show motor-encoder measurements for ortho plus, firm stop, and mild stop. Shaded bands indicate group mean $ \pm $ 1 SD. Background colors denote the gait phases.

Figure 4. Long description

Knee angle (5 to 65 degrees) versus gait cycle (0 to 100 percent), with background bands for the gait phases and shaded bands of plus/minus 1 SD. The solid blue line is the optical (DIERS) reference for ortho plus; dashed lines are motor-encoder measurements for ortho plus (blue), firm stop (orange) and mild stop (yellow). All curves are similar during stance, between about 10 and 20 degrees. In swing, ortho plus peaks at about 57 degrees (encoder) to 62 degrees (optical) at roughly 77 percent of the cycle, whereas the mild stop levels off at about 41 degrees and the firm stop at about 33 degrees. All curves return to about 10 degrees at the end of the cycle.

For gait-compensation analysis, we additionally used DIERS-derived ankle angle as a metric for ground clearance and push-off range of motion (Schulz, Reference Schulz2011; Bartlett et al., Reference Bartlett, Shepherd and Lawson2023), pelvic obliquity to observe hip-hike compensation (Akbas et al., Reference Akbas, Prajapati, Ziemnicki, Tamma, Gross and Sulzer2019), and sideways trunk deviation to monitor spinal compensation (Christensen et al., Reference Christensen, Quammen, Rigby, Christiansen and Stevens-Lapsley2021). To obtain robust subject-level summaries, we computed for each outcome and condition the 95th percentile ( $ {q}_{95} $ ) or 5th percentile ( $ {q}_{05} $ ) over all strides in the relevant phase (e.g., $ {q}_{95} $ flexion angle in TS, $ {q}_{05} $ extension velocity in PS).

2.4.5. Primary endpoints and outcome families

To keep inference aligned with the hypothesis structure (H1–H3), we grouped outcomes into three primary endpoint sets: (H1, efficacy) terminal swing knee flexion limitation and braking dynamics: $ {q}_{95} $ knee flexion angle in TS, $ {q}_{95} $ flexion velocity in TS, and resistive torque in TS (with PS values reported as a check for unintended interference outside late swing): (H2, function) compensatory kinematics relevant to clearance and push-off: ankle metrics (e.g., TS plantarflexion and PS push-off ROM) and proximal compensations (pelvic obliquity and trunk deviation in TS); and (H3, muscle activity) phase-specific EMG demand proxies, with primary focus on biceps femoris activity in terminal swing (mean ARV and $ {q}_{95} $ ARV). The contrasts evaluated rigid stop versus soft stops. All 15 pairwise condition contrasts of this endpoint formed the H3 multiplicity family. The $ {q}_{95} $ and peak-timing descriptors were exploratory and were adjusted within their corresponding endpoint families.

For multiple-comparison control, we applied false discovery rate correction within outcome families. Kinematic families were defined as joint  $ \times $  phase $ \times $  metric, and EMG families as muscle  $ \times $ side $ \times $ phase $ \times $  metric.

2.4.6. Statistical analysis

For the kinematic and actuator-torque endpoints, we fitted linear mixed-effects models with condition as a fixed effect (treatment-coded, reference = physiological gait) and participant random intercepts (Bates et al., Reference Bates, Mächler, Bolker and Walker2015). Models were fitted using restricted maximum likelihood (REML) for parameter estimation, and for likelihood-ratio tests of overall condition effects, models were refitted using maximum likelihood (ML) while keeping the same random-effects structure. Pairwise contrasts between conditions were evaluated with Wald $ z $ -tests. To control for multiple comparisons, $ p $ -values were adjusted within each family using the Benjamini-Hochberg false discovery rate (FDR) procedure (Benjamini and Hochberg, Reference Benjamini and Hochberg1995). Results are reported as group means with 95% confidence intervals, Hedges’ $ g $ , and FDR-adjusted $ {p}_{\mathrm{adj}} $ -values with: ^† $ .05\le {p}_{\mathrm{adj}}<.10 $ ; * $ {p}_{\mathrm{adj}}<.05 $ ; ** $ {p}_{\mathrm{adj}}<.01 $ ; *** $ {p}_{\mathrm{adj}}<.001 $ . For H3, cycle-level endpoint values were first averaged within trial. The retained trial means were analyzed using a linear mixed-effects model with condition as a fixed effect and participant as a random intercept. All 15 two-sided Wald $ z $ contrasts were adjusted using the Benjamini-Hochberg procedure.

2.4.7. Quality control and exclusions

For analysis, minor adjustments were necessary due to sensor or marker dropouts. Due to sweating, sensor and marker adhesion were compromised in subject four. This led to the loss of markers and sensors, resulting in the exclusion of the ankle angle, the right leg gastrocnemius, and the left leg rectus femoris from analysis. Due to similar circumstances, subject two was excluded from the left leg tibialis anterior and right leg rectus femoris analysis. Additionally, marker occlusion resulted in one firm and two mild stop trials from subject five being excluded. One technically invalid subject eight right-biceps-femoris rigid-stop trial was excluded.

2.4.8. Questionnaire

After the experimental trial, participants completed a custom-designed questionnaire evaluating their comfort, perceived effort, and overall experience across the different test conditions. Clinical literature suggests that brace-related effects may extend beyond mechanics, including psychological confidence and potential proprioceptive trade-offs, which can ultimately influence acceptance and adherence (Heyworth et al., Reference Heyworth, Berube, Gossman, Milewski and Bixby2025). The questionnaire consisted of nine items, each rated for each condition. An additional free-text field allowed participants to provide open-ended feedback. Responses were recorded using scales ranging from $ 0 $ to $ 10 $ . Depending on the question, the scale direction varied: in some items, $ 0 $ indicated low agreement or minimal perception, whereas in others, it indicated strong agreement. The questionnaire was developed using validated instruments and established literature, incorporating elements from the Orthotics and Prosthetics User Survey (OPUS) (Heinemann et al., Reference Heinemann, Bode and O’Reilly2003), System Usability Scale (SUS) (Brooke, Reference Brooke, Jordan, Thomas, Weerdmeester and McClelland1995), and the Return to Sport after ACL Injury Scale (ACL-RSI) (Müller et al., Reference Müller, Schmidt, Krüger-Franke and Rosemeyer2014), among others. The complete questionnaire is provided in the Supplementary Figure 9.