A Low-Cost Electronically Controlled Pneumatic Knee with Passive Four-Bar Stance Stability and Semi-Active Swing Damping: A Single-Case Feasibility Study

Abstract

Microprocessor-controlled knee prostheses (MPKs) face limited accessibility in resource-constrained environments due to high implementation costs and excessive power consumption associated with complex actuators. This study examines the technical feasibility of a low-cost electronically controlled pneumatic knee (ECPK) that combines structural mechanics with minimal electronic control. A functional decoupling strategy was implemented: stance-phase stability is provided by passive kinematic locking of a four-bar linkage over the near-extended stance range, while a lightweight feedforward controller driven by a single joint-axis Hall sensor segments the gait cycle continuously, updates its speed estimate once per step, and adjusts the valve only for swing-phase damping. From the stance duration of the preceding steps, this controller presets the pneumatic valve orifice to compensate for mechanical response delays, so that link rotation speed is regulated semi-actively without powered actuation. System integration and control viability were evaluated in a single-case feasibility study (N = 1), in which the ECPK was compared within subject with a commercial mechanical prosthesis after a 4-week adaptation period. Despite a 400 g distal mass penalty, the semi-active control algorithm was associated with a smaller increase in step-length asymmetry at the highest speed tested. Furthermore, net oxygen cost was lower with the ECPK during high-speed walking. Because the conditions were compared at unmatched self-selected speeds and the ECPK condition reached a respiratory exchange ratio (RER) of 1.13, this observation is hypothesis-generating. Coupling passive four-bar stance stability with minimal electronic swing regulation is therefore a viable engineering basis for accessible prostheses, and the present study establishes its technical feasibility rather than its clinical effectiveness.

1. Introduction

Transfemoral amputation results in the loss of knee joint function, imposing severe physical constraints on patient mobility and quality of life [1]. In developed countries, dysvascular disease associated with population aging and diabetic foot complications has recently emerged as a primary cause of amputation [2,3]. In developing countries with limited medical infrastructure and in conflict-affected regions, however, trauma-related amputations among young and middle-aged individuals are reported at markedly higher rates [4,5]. To resume economic activity, these individuals require mobility at or above the K3 functional level with variable-speed gait capability. Achieving K3-level performance at a delivered unit cost below approximately 1500 USD within constrained public-assistance budgets remains a major technical challenge in low-cost prosthesis development [6,7]. Given the cost-effectiveness limitations of existing high-end devices [8,9,10], there is a persistent need for durable, widely accessible rehabilitation solutions capable of withstanding demanding use environments.

Over the past decade, research on knee prostheses has progressed beyond demonstrating the biomechanical benefits of microprocessor-controlled knee systems (MPKs) [11]; current trends are shifting toward active assistive control in powered lower-limb wearable robotics, spanning both exoskeletons and powered prostheses [12,13]. These systems integrate networks of high-precision IMUs and angular sensors [14] with machine-learning-based continuous gait pattern recognition algorithms for variable damping control [15]. They can therefore enhance gait stability during stumble recovery and on uneven terrain; fear of falling and related activity avoidance are recognized outcomes in this population [16]. Such advances, however, are accompanied by increased system weight and higher power requirements arising from complex sensor fusion. Conventional hydraulic MPK systems in particular require continuous power for valve actuation to regulate high-viscosity fluids, and may revert to a fixed safety mode upon battery depletion, potentially disrupting gait continuity [17]. The high acquisition cost of these advanced devices likewise often exceeds the scope of public-assistance programs in developing regions [18], limiting access for the majority of amputees worldwide [19].

To reduce these computational, power, and cost demands, simplified single-sensor schemes have been used for gait-event detection; a single waist-worn IMU, for instance, has proved sufficient [20]. This body-mounted modality differs from the joint-integrated sensing adopted here, in which a single Hall-effect sensor tracks knee flexion–extension to determine gait phase. A closely related low-cost approach, also based on a passive four-bar polycentric knee with a single Hall-effect sensor, has been reported [8]. In that work the sensor was used primarily to trigger stumble-locking, the variable damper was not operated in variable mode, and gait-speed-adaptive variable damping was noted as future work. Building on this direction, the present study uses the single-sensor signal to modulate speed-adaptive semi-active pneumatic swing damping, differing in the actuation medium and in relying on the four-bar geometry itself for passive stance stability.

Under these budgetary and infrastructural constraints, commercially available mechanical prostheses equipped with pneumatic cylinders, such as the OP5, represent one practical option for K2 to K3 patients in resource-limited settings [21,22]. Pneumatic systems offer advantages over hydraulic systems in lower weight and greater compliance. The inherent compressibility of air, however, makes precise link rotation speed control difficult [23] and introduces a risk of knee buckling under load-bearing conditions, particularly when stance-phase pressure fails to reach the threshold required for damping engagement [24]; this limitation contributes to their reduced utilization in the modern MPK market [25]. In addition, such systems typically operate only upon reaching predefined pressure thresholds or exhibit structurally fixed damping at specific walking speeds. Patients who walk slowly or exhibit insufficient weight acceptance during the stance phase may fail to generate adequate pressure to activate variable damping. During high-speed walking, conversely, fixed orifice (FO) structures may be unable to accommodate the elevated compressed-air flow demand, resulting in extension lag.

This mismatch in load and speed adaptability induces asymmetric compensatory movement characterized by excessive recruitment of the hip flexors [26,27]. Such compensations increase the demand for intensive gait training while contributing to mechanical overload of the intact limb [27] and elevated overall metabolic cost [28]. These biomechanical imbalances are recognized as major risk factors for prosthesis abandonment [29] and secondary osteoarthritis in the intact limb [30].

In this study, the kinematic characteristics of pneumatic systems are revisited, and the feasibility of an electronically controlled pneumatic knee (ECPK) architecture is explored as a candidate cost-effective design. The core approach of this work is functional decoupling. To mitigate stance-phase instability, a primary limitation of pneumatic systems, a four-bar linkage is employed to position the instantaneous center of rotation (ICR) posterior to the load line, inducing passive structural locking without power consumption [31,32,33]. Prior kinematic analyses of such elevated-ICR configurations report stability margins consistent with resistance to buckling under typical stance loading [33], providing a basis for the passive locking strategy adopted here; the corresponding margins for the present linkage are quantified in Section 2.1.1. Because high-load stance support is provided by the linkage geometry, no actuator energy is used during stance, and, over the near-extended stance range analyzed in Section 2.1.1, stance security does not depend on the controller functioning correctly. The controller and the Hall sensor nevertheless run continuously throughout the gait cycle, since stance duration is itself the measured quantity; what is confined to the swing-phase transition is valve actuation, not electrical operation. The system integrates anticipatory valve flow-path control according to gait phase with air-compression regulation, enabling semi-active control of the linkage’s rotational velocity and damping characteristics.

Speed-adaptive electronic modulation of pneumatic swing damping at the knee is not new. The first commercially available microprocessor-controlled knee inferred walking speed from onboard sensing and adjusted a pneumatic swing-control valve accordingly, while leaving stance support to a mechanical, weight-activated mechanism [34,35]. Related pneumatic–hydraulic strategies have been demonstrated at the ankle [36], and semi-powered designs have combined microprocessor valve control with a small assist motor at the knee [24]. The present work is therefore positioned within this lineage rather than apart from it. What distinguishes the configuration described here is a combination of design choices, set out column-wise in Table 1, that the structured literature search did not identify together: stance support obtained from the four-bar geometry rather than from the actuator, so that no actuator energy is spent in stance and, over the analyzed near-extended range, stance security does not depend on the controller functioning correctly; gait-phase and speed estimation reduced to a single joint-axis sensing channel; and valve actuation confined to discrete mode transitions, with the valve holding its position without current in between.

The inherent compliance of air is further used as a shock-absorbing mechanism to stabilize gait under external perturbations, and a strategy for reducing metabolic cost through regulation of compensatory movement is also examined [37]. From a control perspective, complex sensor fusion is avoided, as gait-phase and speed estimation rely on a single joint-axis Hall sensor. A motor-integrated encoder and a current-sensing circuit are also present, but they serve only needle-valve position feedback and power-up home calibration, respectively, and do not contribute to gait sensing.

A discrete-state anticipatory feedforward controller estimates the speed of the next step from a two-step moving average of the stance time, taken over the current and immediately preceding gait cycles [38]. While recent active prostheses increasingly adopt machine learning or Kalman filters for gait prediction, historical moving averages remain a robust, rule-based approach validated for real-time prosthesis control [39]. In robotics more broadly, safe real-time motion is often achieved through hierarchical quadratic programming and priority-based multi-objective control [40]. Such formulations offer strong guarantees but assume computational and sensing resources unavailable in a low-cost prosthesis; the present design instead pursues the opposite end of this trade-off with a rule-based, single-channel, anticipatory feedforward controller.

Relying on a single gait-sensing channel, this lightweight control architecture reduces processing latency, sensor-fusion complexity, and power consumption, which are key requirements for resource-constrained environments [38]. The approach presets the needle valve prior to swing-phase entry, thereby bypassing the pressure dependency of conventional pneumatic systems and compensating for the mechanical response delay of pneumatic valves in an anticipatory manner. Although this estimation based on prior-step data may introduce phase lag under rapid acceleration or deceleration, it provides a viable alternative for K2 to K3 users performing level walking and gradual speed transitions, enabling variable-speed extension with minimal computational resources. Even under computational delay or power loss, the closed kinematic chain of the four-bar linkage preserves its geometry independently of controller state [31,33]; within the near-extended corridor analyzed in Section 2.1.1, stance support is therefore not contingent on the electronics. The analysis supporting this is quasi-static and does not cover initial contact. Structural strength was verified to KS P ISO 10328:2016 [41] (see Section 2.1.1).

This study is a single-case feasibility study investigating whether the proposed ECPK system improves gait symmetry and reduces net metabolic energy cost relative to a conventional passive mechanical knee, despite the added distal mass of its electronic components. Following the well-established precedent for single-subject case designs in early prosthetic device validation [42], a within-subject comparative experiment was conducted with a highly experienced transfemoral amputee with 15 years of prosthesis use (N = 1), using a passive commercial mechanical prosthesis (OP5) as the comparator condition. The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Institutional Review Board of the Rehabilitation Engineering Research Institute (Approval No. RERI-IRB-221130: 30 November 2022), and its findings are interpreted as hypothesis-generating rather than generalizable. Following a 4-week adaptation period with the ECPK system, evaluations were performed using the six-minute walk test (6MWT) [43], center-of-pressure trajectory analysis to characterize load-bearing symmetry control and gait symmetry [44,45], and respiratory gas-based metabolic measurement [46] to assess trends in dynamic stability and metabolic efficiency under the weight-penalty condition.

To position the proposed design among existing devices, representative passive, microprocessor-controlled, semi-powered, and powered knees were identified through a structured search of Scopus, PubMed, IEEE Xplore, and Google Scholar (the term “transfemoral prosthetic knee” combined with pneumatic, hydraulic, magnetorheological, semi-active, microprocessor, and polycentric; English-language records, 2000–2026), supplemented by backward citation chaining for earlier seminal work and by manufacturer documentation for commercial devices not described in the peer-reviewed literature; this served to position the present design rather than as a systematic review.

As summarized in Table 1, fully powered and microprocessor-controlled knees offer full speed adaptability and active stance control, but they depend on continuous power, multiple sensors, and considerably higher mass and cost. Fully passive low-cost knees avoid these burdens, although their swing resistance cannot be adjusted electronically. It should also be acknowledged that speed adaptation is not unique to the present design; some commercial passive knees approximate it through flow-dependent mechanical valving [47], and comparable or lower mass and cost have been reported for several recent low-cost prototypes [48,49].

The main contributions of this study are as follows. First, a structure that combines the passive kinematic locking of a four-bar linkage with the compressibility of air is evaluated as a candidate low-cost complement to hydraulic MPK systems. Second, the extent to which single-gait-sensor-based anticipatory control can offset the physical penalty of an additional distal mass of approximately 400 g through kinematic assistance is examined in a single-case study, with net metabolic energy cost as an outcome measure. Third, the effect of anticipatory flow regulation on extension lag and gait symmetry relative to a conventional passive device is preliminarily characterized.

Table 1. Literature-based positioning of the proposed ECPK against representative passive, microprocessor-controlled, semi-powered, and powered transfemoral prosthetic knees.

Category (Representative Device)	Stance-Phase Support	Power in Stance	Swing-Speed Adaptation	Gait-Sensing Channels	Ref.
Passive pneumatic polycentric, manually set (Össur OP5; comparator in this study)	Polycentric geometric	None	Passive rate-dependent only; orifice fixed at fitting and not adjusted automatically or electronically (rated ≈ 5 km/h)	None	[22,50]
Passive pneumatic polycentric, mechanically auto-adaptive (Össur Paso Knee)	Polycentric geometric	None	Automatic, continuous, purely mechanical (≤7 km/h); not programmable or subject-calibrated	None	[47]
Low-cost MPK on a passive four-bar frame (E-Knee; Galey & Gonzalez)	Four-bar geometric + MP-triggered clamp	On demand	Damper not operated in variable mode; speed adaptation stated as future work	Single joint-axis Hall sensor	[8]
Low-cost magnetorheological MPK (i-Inspire; Qadir et al.)	Active MR	Continuous	Full	Multi-sensor (angle, force, tilt)	[49]
Microprocessor pneumatic swing, uniaxial (Blatchford IP/SmartIP)	Uniaxial, Mechanical, weight-activated	None (powered in swing only)	Automatic, continuous	Onboard sensing only (no external gait sensors)	[34,35]
Commercial MPK, hydraulic or MR (Ottobock C-Leg 4; Össur Rheo Knee)	Active microprocessor stance	Continuous	Full	Multi-sensor	[51,52]
Semi-powered stance-control swing-assist (Vanderbilt SCSA; Lee et al.)	Active hydraulic (valve closed in stance)	≈6 W	Closed-loop, cadence-adaptive	IMU, encoders, load cell	[24]
Powered/motorized (Össur Power Knee)	Powered stance support	High (active drive)	Full, incl. stairs and ramps	Multi-sensor	[53]
Proposed ECPK (this work); pneumatic semi-active	Four-bar geometric (passive); independent of the controller	None; no holding current	Discrete three-mode, swing only; subject-calibrated LUT indexed by measured stance time	Single joint-axis Hall sensor	This study

Compiled from peer-reviewed and manufacturer sources and not independently benchmarked here. IMU, inertial measurement unit; LUT, lookup table; MP, microprocessor; MPK, microprocessor-controlled knee; MR, magnetorheological.

Table 1. Literature-based positioning of the proposed ECPK against representative passive, microprocessor-controlled, semi-powered, and powered transfemoral prosthetic knees.

Category (Representative Device)	Stance-Phase Support	Power in Stance	Swing-Speed Adaptation	Gait-Sensing Channels	Ref.
Passive pneumatic polycentric, manually set (Össur OP5; comparator in this study)	Polycentric geometric	None	Passive rate-dependent only; orifice fixed at fitting and not adjusted automatically or electronically (rated ≈ 5 km/h)	None	[22,50]
Passive pneumatic polycentric, mechanically auto-adaptive (Össur Paso Knee)	Polycentric geometric	None	Automatic, continuous, purely mechanical (≤7 km/h); not programmable or subject-calibrated	None	[47]
Low-cost MPK on a passive four-bar frame (E-Knee; Galey & Gonzalez)	Four-bar geometric + MP-triggered clamp	On demand	Damper not operated in variable mode; speed adaptation stated as future work	Single joint-axis Hall sensor	[8]
Low-cost magnetorheological MPK (i-Inspire; Qadir et al.)	Active MR	Continuous	Full	Multi-sensor (angle, force, tilt)	[49]
Microprocessor pneumatic swing, uniaxial (Blatchford IP/SmartIP)	Uniaxial, Mechanical, weight-activated	None (powered in swing only)	Automatic, continuous	Onboard sensing only (no external gait sensors)	[34,35]
Commercial MPK, hydraulic or MR (Ottobock C-Leg 4; Össur Rheo Knee)	Active microprocessor stance	Continuous	Full	Multi-sensor	[51,52]
Semi-powered stance-control swing-assist (Vanderbilt SCSA; Lee et al.)	Active hydraulic (valve closed in stance)	≈6 W	Closed-loop, cadence-adaptive	IMU, encoders, load cell	[24]
Powered/motorized (Össur Power Knee)	Powered stance support	High (active drive)	Full, incl. stairs and ramps	Multi-sensor	[53]
Proposed ECPK (this work); pneumatic semi-active	Four-bar geometric (passive); independent of the controller	None; no holding current	Discrete three-mode, swing only; subject-calibrated LUT indexed by measured stance time	Single joint-axis Hall sensor	This study

Compiled from peer-reviewed and manufacturer sources and not independently benchmarked here. IMU, inertial measurement unit; LUT, lookup table; MP, microprocessor; MPK, microprocessor-controlled knee; MR, magnetorheological.

2. Materials and Methods

2.1. ECPK System Configuration and Mechanism

The proposed ECPK is based on a four-bar linkage mechanism implementing polycentric kinematics, as illustrated in Figure 1, and consists of an upper frame, an embedded controller, and a pneumatic cylinder integrated with a variable-orifice needle valve. The embedded controller comprises a microcontroller (MCU) for real-time computation, a single Hall sensor interface for estimating walking speed by detecting phase transitions between the stance and swing phases, and a valve actuator driver for operating the needle valve. To keep distal mass low and to limit power consumption, a functional decoupling strategy is adopted, in which high-load support is assigned to the linkage geometry while semi-active variable damping is confined to the flexion valve.

2.1.1. Kinematic Stance Stability of the Four-Bar Linkage

Stance-phase stability of the ECPK is provided by the linkage geometry rather than by the controller, and the relevant dimensions and sagittal-plane joint-axis coordinates are listed in

Table 2. Dimensions and sagittal-plane joint-axis coordinates of the ECPK four-bar linkage. The frame origin lies on the anteroposterior mid-line of the shank (ankle center) and at the most distal joint axis (A1); +x anterior, +y proximal.

Link Element	Joint Axes	Length (mm)
Anterior link	A1–A4	70.8
Posterior link	A2–A3	39.8
Distal (shank) link—fixed frame	A1–A2	38.9
Proximal (thigh) link—coupler	A3–A4	33.8
Joint axis	x (mm)	y (mm)
A1 (distal anterior)	19.0	0.0
A2 (distal posterior)	−19.0	8.5
A3 (proximal posterior)	−23.2	48.0
A4 (proximal anterior)	3.3	69.0

. Coordinates are expressed in a shank-fixed frame whose origin lies on the anteroposterior mid-line of the shank at the transverse level of the most distal joint axis A1, with +x directed anteriorly and +y proximally (Figure 2a). The origin is a reference point on the shank mid-line and not the axis A1 itself, which lies 19.0 mm anterior to it, and the maximum knee flexion is 170°.

The instantaneous center of rotation (ICR) was defined as the intersection of the extended anterior (A1–A4) and posterior (A2–A3) links and was evaluated from the CAD model at 1° increments through the stance range and at coarser increments up to the maximum flexion of 170°.

Table 3. ICR position and stability margin as a function of knee flexion angle. $d_{\mathrm{ground}}$ and $d_{\mathrm{hip}}$ are the horizontal offsets of the ICR from the posterior and anterior bounds of the load-line envelope, respectively; positive values indicate an extension moment. The anterior bound (x = +15.3 mm) coincides with the ICR position at 8° and represents an alignment tolerance rather than an independently measured offset.

Knee Flexion (°)	${\mathit{x}}_{\mathbf{ICR}}$ (mm)	${\mathit{y}}_{\mathbf{ICR}}$ (mm)	${\mathit{d}}_{\mathbf{ground}}$ (mm)	${\mathit{d}}_{\mathbf{hip}}$ (mm)
0	−51.27	307.88	+51.27	+66.57
1	−21.48	229.12	+21.48	+36.78
2	−8.09	192.04	+8.09	+23.39
3	−0.12	168.61	+0.12	+15.42
4	5.17	151.88	−5.17	+10.13
5	8.92	139.08	−8.92	+6.38
6	11.68	128.82	−11.68	+3.62
7	13.77	120.33	−13.77	+1.53
8	15.30	113.15	−15.30	0.00
9	16.60	106.95	−16.60	−1.30
10	17.56	101.54	−17.56	−2.26
12	18.88	92.48	−18.88	−3.58
15	19.87	82.00	−19.87	−4.57
20	20.14	69.65	−20.14	−4.84

lists the resulting positions over 0–20°, the range relevant to stance stability, and the full trajectory is plotted in Figure 2b. At full extension the ICR is located 51.3 mm posterior and 307.9 mm proximal to the origin, because the two link lines are then almost parallel, subtending an included angle of only 6.70°, so that their intersection is formed far proximally. As this angle increases with flexion, the ICR descends rapidly and shifts anteriorly, reaching 113.2 mm proximal at 8° of flexion. This behavior, together with the long anterior link and short posterior link, corresponds to the elevated-instant-center configuration described by Radcliffe [31], for which polycentric knees of this type have been analyzed as a distinct performance class [6], rather than to the voluntary-control configuration, and the rapid descent of the ICR is what progressively releases the mechanism for swing.

Geometric locking requires the ICR to remain posterior to the load line, so that the transmitted compressive load produces an extension moment about it (Figure 2a). Since the load line shifts during stance, its position was bracketed by a two-bound envelope. The conservative posterior bound was taken as the ground-referenced line through the ankle center (x = 0 mm), while the anterior bound was placed at x = 15.3 mm, representing a hip-referenced load line under a forward alignment. This value is not an independently measured alignment offset; it coincides with the anterior position of the ICR at 8° of flexion and is retained to express the alignment tolerance implied by the trajectory. Read in this direction, $x_{\mathrm{ICR}}\left(\theta \right)$ is the minimum anterior offset that a load line must have for geometric locking to persist to a flexion angle θ over the stance range, so the anterior bound reports an alignment requirement rather than a measured line. Because the alignment realized in dynamic fitting is not known a priori, the load line is bracketed by this envelope rather than represented by a single line. The stability margin d(θ) was then defined as the horizontal offset of the load line from the ICR, positive when the resulting moment is extending, as given in Equation (1).

$$d\left(\theta \right)=x_{\mathit{LL}}-x_{\mathit{ICR}}\left(\theta \right)$$

(1)

The margin is greatest at full extension but decreases steeply thereafter, by approximately 30 mm over the first degree of flexion alone, so that the meaningful measure of stability is the angular corridor over which locking is maintained rather than the peak offset (Figure 2c). Self-stabilization is preserved up to 3.0° of flexion against the posterior bound and up to 8.0° against the anterior bound, which yields a stance-stability corridor of 0–3.0° that holds for every load line within the envelope; the 8.0° bound is contingent on the load line being aligned at least 15.3 mm anterior, as defined above. Beyond approximately 8°, the ICR lies anterior to the entire envelope and stability is no longer geometric but depends on the voluntary hip extension moment of the user. This trade-off between stance security and swing initiation is characteristic of passive polycentric knees and determines the alignment tolerance required during fitting.

Because d(θ) is a purely kinematic quantity, it is independent of body mass. Body mass scales the extension moment about the ICR without altering the sign of d(θ) or the flexion range over which locking occurs. This moment is given by Equation (2),

M = W · d(θ)

(2)

where W (denoted F in Figure 2) is the transmitted compressive load, so that d(θ) should be understood as a geometric descriptor of the locking range and not as a structural safety factor. The analysis is quasi-static and derived from CAD geometry, with the load line represented as a straight hip-to-ankle line and the foot idealized as transmitting load through the ankle center, an approximation that applies from foot-flat onward. At initial contact the ground-reaction force acts posterior to this line, so that this instant lies outside the analyzed envelope and is governed by alignment and by the hip extensor moment of the user rather than by the linkage geometry. The corridor was defined to encompass the near-extended stance strategy typical of transfemoral users whose prosthetic knees permit no stance flexion. Verifying it against measured knee angles requires goniometry or motion capture, since the Hall sensor resolves only the threshold crossings used for gait-phase segmentation. Direct measurement of the stance-phase knee angle by goniometry or motion capture therefore remains as future work.

The structural strength of the load-bearing assembly was verified independently of the kinematic analysis. At a KOLAS-accredited laboratory (test report K-23-026), the four-bar linkage, the supporting frames, and the pneumatic cylinder were tested to KS P ISO 10328:2016 [41] at test loading level P5 (body mass up to 100 kg) under test loading condition I; the electronic valve actuator and controller lie outside the load path and were excluded from the tested structure. In the principal static ultimate-strength test, the sample sustained the P5-I lower-level ultimate force of 3360 N without loss of structural condition. In the cyclic test it completed 3,000,000 loading cycles at the maximum cyclic force of 1330 N (displacement 1.55 mm) and then sustained the final static force of 2240 N without failure, with a permanent deformation of 0.98 mm against the 5 mm limit.

These tests establish the static strength and fatigue durability of the assembled load-bearing structure at level P5. They are structural tests at a fixed alignment and do not evaluate stance-phase buckling, which is governed by the linkage geometry analyzed earlier in this section; its direct experimental verification, together with a device-specific safety factor and failure-mode analysis, remains future work.

2.1.2. Single-Sensor-Based Gait Speed Estimation Algorithm

Instead of relying on high-cost encoders or complex biomechanical modeling, swing phase damping is controlled through time-domain analysis and empirical mapping using a single Hall sensor. The MCU detects predefined flexion and extension thresholds of the knee joint via the Hall sensor to determine the gait phase, including stance and swing phases, and measures the stance-phase duration (${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}$) of the preceding step. Based on the inverse relationship in which shorter stance duration corresponds to higher walking speed, the controller references an experimentally pre-calibrated lookup table (LUT) to determine the target valve angular position (${\mathrm{\theta }}_{\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{v}\mathrm{e}}$) for the subsequent swing phase. This discrete mapping relationship is expressed as the following control law.

$${\mathrm{\theta }}_{\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{v}\mathrm{e}}\left[\mathrm{n}+1\right]=\mathrm{L}\mathrm{U}\mathrm{T}\left({\overline{\mathrm{T}}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}\right]\right)$$

(3)

Here, ${\overline{\mathrm{T}}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}\right]$ represents the moving average of the stance-phase duration over the two most recent steps, and the LUT is a one-dimensional data array in which the valve motor rotation speed, corresponding to damping intensity, has been pre-optimized based on the subject’s voluntary walking speed variations. The mapping is feedforward and therefore requires neither continuous dynamic computation nor differentiation of the sensor signal, which would amplify noise. It compensates for the actuator response delay and can be executed on hardware with limited computational resources.

2.2. Pneumatic Airflow Dynamics and Control Mechanism

The ECPK system adopts a closed-circuit pneumatic architecture that operates solely through piston motion without requiring an external compressor or exhaust port. Figure 3 illustrates the airflow within the cylinder during knee flexion and extension.

2.2.1. Flexion Phase: Viscoelastic Resistance and Transient Assistance

The control strategy exploits the viscoelastic behavior arising from air compressibility within a sealed volume, without atmospheric venting, to assist gait. During the flexion phase, as the piston compresses the lower cap-end chamber, air within the cylinder is not released to the atmosphere but instead flows into the upper rod-end chamber through the variable-orifice needle valve (FN) and the check valve (FCV).

As walking speed increases, the MCU dynamically closes the FN, causing the piston-induced compression rate to exceed the airflow rate toward the upper chamber, resulting in rapid pressure buildup within the lower chamber. The result is a transient rise in stiffness, similar to that of an internal pneumatic spring. At the flexion-to-extension transition, this pressure differential is expected to push the piston back, assisting rapid knee extension in early swing. Chamber pressures were not instrumented, so this mechanism is inferred from the force–displacement behavior reported in Section 4.1 rather than measured directly.

2.2.2. Extension Phase: Airflow and Impact Dissipation

To minimize distal mass and simplify the control architecture, the proposed system does not actively control extension resistance using a dedicated motor. Instead, it adopts a passive mechanism in which the transient pneumatic rebound effect generated during flexion accelerates knee recovery in early extension, and the resulting accelerated piston motion drives rapid expulsion of air from the upper chamber during terminal extension.

During terminal extension, the narrow flow path of the pre-set extension needle valve (EN) creates a pronounced exhaust restriction. The kinetic energy of the accelerated piston is dissipated through fluid-dynamic friction and the damping force of air passing through the orifice. The restricted orifice therefore acts as an air cushion, attenuating the terminal impact at full extension.

3. System Architecture and Control Strategy

3.1. Hardware Architecture and Embedded System

This section presents the architecture of a custom-designed embedded control unit (ECU) that performs gait phase detection and real-time position control of the flexion needle valve (FN). The system comprises a microcontroller (MCU, STM32F373, STMicroelectronics, Geneva, Switzerland) a power management unit (PMU), an actuation subsystem, a sensing subsystem, and a communication interface, as shown in the overall block diagram (Figure 4).

The sampling and computation cycle, which forms the core of the control system, was designed based on the biomechanical limitations of the target patient population. Assuming a maximum walking speed of 4.5 km/h (approximately 1.25 m/s), corresponding to a step frequency of approximately 2 Hz for transfemoral amputees during daily activities, a control cycle of 100 Hz (10 ms) is applied to manage timing delays during gait phase transitions. However, due to the mechanical time constant of the actuator responsible for valve operation, some delay in damping response is unavoidable. To compensate, the system analyzes the preceding step and incorporates a feedforward control strategy that presets the valve accordingly.

The firmware is implemented using FreeRTOS to ensure stable execution of priority-based multitasking. The sensor data acquisition and gait phase detection loop is assigned the highest priority and operates at 100 Hz, while the Bluetooth transmission task is executed asynchronously at 20 Hz (50 ms) and gait data are recorded to the host at 10 Hz (100 ms) to prevent unnecessary power consumption and control bottlenecks. Direct memory access (DMA) and the nested vectored interrupt controller (NVIC) are used so that peripheral communication does not delay the main control loop.

The PMU is designed around a 3.7 V, 3350 mAh lithium-ion battery (T11-S3350S, LUNAVOLT, Seoul, Republic of Korea) to ensure system portability. To enhance system stability, a decoupled power architecture is adopted in which logic power and actuation power are physically separated. A regulated 3.3 V supply via a low-dropout (LDO) regulator is provided to the noise-sensitive MCU and sensing subsystem, while an independent 6 V supply is delivered to the motor subsystem through a step-up DC–DC converter to support high inductive loads. This topology prevents brownout of the 3.3 V logic circuit under voltage-drop conditions caused by high current draw during valve motor startup and mitigates the influence of battery-level fluctuations on valve control torque.

The actuation subsystem is the core module responsible for regulating flexion damping. It comprises an ironless-core DC motor (RE 10, 0.75 W, 4.5 V nominal, 222 mA maximum continuous current; maxon motor ag, Sachseln, Switzerland) coupled to a 64:1 planetary gearhead (GP 10 A). An H-bridge driver supplied from the boosted 6 V rail actuates the motor to adjust the orifice cross-sectional area of the needle valve, with pulse-width modulation giving an effective terminal voltage of 5.42 V. At this operating point the motor turns at approximately 11,600 rpm, within the gearhead’s maximum continuous input speed of 12,000 rpm, yielding an output-shaft speed of approximately 181 rpm, and draws approximately 63 mA, 28% of its maximum continuous rating. The needle valve has a total travel of 8 turns, of which the settings calibrated for the participant in this study span 1.8 turns; a transition across that span therefore completes in about 0.6 s.

The commanded valve position is retained without holding current: the fine-pitch thread of the needle valve is self-locking against the axial seat reaction, so the setting is held by the valve itself rather than by the drivetrain. Motor current therefore flows only during a mode transition, and the last commanded damping setting persists if power is interrupted. Rather than employing several high-cost actuators, the hardware budget is concentrated on the valve actuation unit, which is the only semi-active element, so that actuation reliability is obtained at low cost.

The sensing subsystem includes a Hall sensor (DRV5056, Texas Instruments, Dallas, TX, USA) for gait-phase detection, a motor-integrated encoder for needle-valve position feedback, and a current-sensing circuit for monitoring motor load. Gait phase and speed are estimated from the Hall sensor alone. The encoder closes the needle-valve position loop and the current-sensing circuit performs power-up home calibration; neither enters the gait-sensing path. The current-sensing circuit detects the stall current generated when the valve reaches its mechanical end-stop during power initialization, enabling automatic calibration of the absolute home position. The “single-sensor” description in this work therefore refers specifically to the single-channel gait-estimation pipeline, not to the total sensor count of the device.

The MCU references a pre-tuned lookup table (LUT) to set the target encoder pulses corresponding to the desired valve opening and performs threshold-based position control by terminating motor drive once the pulse target is reached. Inertial overshoot resulting from high-speed rotation is mechanically suppressed by the resistance of the 64:1 reduction gear, allowing the system to achieve the required damping resolution within the required timeframe without complex feedback computation.

The connectivity and interface subsystem incorporates a low-power Bluetooth module to support wireless communication with a host PC. The dedicated GUI software developed for this system is used to log gait data in real time during clinical experiments and to tune control parameters. User-specific parameters are stored in onboard nonvolatile memory (EEPROM) via I²C communication, ensuring that personalized settings are retained after power cycling.

3.2. Control Algorithm and Safety Interlocks

The control logic is implemented as a deterministic four-layer architecture, each layer corresponding to one block of the flow shown in Figure 5.

The first layer performs initialization and homing. At power-up the controller confirms that the knee is extended, drives the FN motor across its full travel to a mechanical end-stop so that the encoder count can be referenced to an absolute position, and checks the Hall-sensor ADC value to verify sensor connectivity. If either check fails, motor actuation is disabled and the system remains in a standby state after a buzzer alert. On successful initialization the controller enters the normal state with the valve at the Medium setting.

The second layer segments the gait cycle and handles exceptions. The Hall signal is sampled at 100 Hz and compared against a rising threshold of 30% and a falling threshold of 80% of the sensor full scale, which divides the signal into near-extended and flexed intervals; these are used as proxies for the stance and swing phases, since the sensor resolves knee angle and not limb loading. Loaded intervals shorter than 200 ms are discarded as contact bounce at terminal impact. A loaded interval longer than 3 s sets the standing flag and holds the valve at its current position, and a standing state sustained beyond 20 s places the controller in a low-power state, from which a Hall-sensor interrupt restores normal operation. Unloaded intervals longer than 5 s are interpreted not as swing but as user input: 5–10 s arms the rapid mode, which fixes the valve at maximum damping, and more than 10 s arms the auto-switch toggle, which enables or disables stance-time-based automatic mode switching. Prolonged sitting therefore does not enter the low-power state; it is resolved in the third layer.

The third layer arbitrates these user-activated modes. The gesture is a standing knee flexion, which the controller observes as the prolonged unloaded interval defined above, so that no smartphone or button input is required. Because a single sensor cannot separate this gesture from ordinary sitting, an armed gesture is not applied when it is detected: it takes effect only after the standing flag of the second layer has been set, that is, after a loaded interval of at least 3 s. The arbitration block then applies the armed mode and clears both the armed and standing flags. A sit-to-stand transition followed by immediate walking does not produce a 3 s loaded interval, so a gesture armed during sitting is cleared without changing the mode. This pairs a postural gesture with a physical confirmation criterion and avoids additional sensor fusion, although unintended activation remains possible when the user stands still for an extended period after flexing the knee; a secondary interlock, for example a gyroscope, is left to future work.

The fourth layer estimates walking speed and commands the valve. When a special mode is active, the lookup table is bypassed and the corresponding target is applied. Otherwise, two gates are evaluated in sequence. The first is a dwell condition: after each actuation no further transition is admitted for three gait cycles, and while this lockout is in effect, the boundary is not evaluated and the current mode is retained. The transition itself is not delayed—a boundary crossing is committed immediately once the lockout is clear; the lockout stabilizes the newly selected mode by preventing an immediate reversal. The second is a temporal hysteresis of ±200 ms applied to the lookup-table boundaries, so that each boundary is separated into distinct upward and downward switching values; at the Medium–Fast boundary of 700 ms, an upward transition requires a mean stance time below 500 ms and a downward transition a value above 900 ms. The two gates act after a transition to stabilize the newly entered mode—the hysteresis widening the stance-time margin a reversal must clear, and the lockout blocking any transition for three cycles—and were combined because the mode oscillation reported in Section 4.3 was confined to the boundary regions. The candidate mode obtained in this way is mapped to a valve target through the lookup table (Equations (3) and (4)); the motor is driven only if the target differs from the current position and the battery voltage is adequate; the lockout counter is set on each actuation and counts down over the following three cycles.

The ±200 ms band and three-cycle dwell were fixed by offline replay of Section 4.3 log rather than tuned freely. Over the 3.2–3.7 km/h band the two-step mean stance time had a mean of 677 ms and a standard deviation of 109 ms, so a ±200 ms band spans approximately ±1.8 SD of the recorded scatter; the three-cycle dwell matches the two-to-three-step interval over which a genuine speed change persists in the moving-average estimate. These were the smallest values that removed the boundary reversals in that log.

These two gates were introduced in the present revision and were not active during the treadmill and overground experiments reported in Section 4.3 and Section 4.4. Their parameter values were obtained by offline replay of the gait data logged in Section 4.3, and the implemented firmware was subsequently verified against that same recorded input; the resulting change in the number of mode transitions is reported in Section 4.3 and discussed in Section 5.2.

3.3. Signal Processing and Gait Phase Classification

To ensure stable estimation of stance time (${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}$), the primary indicator for gait speed estimation, the proposed system employs dynamic normalization and a multistage filtering approach. Figure 6 illustrates the output characteristics of the Hall sensor in relation to changes in knee joint angle during gait. The sensor produces a maximum output voltage when the knee reaches full extension and the magnet is in close proximity, while the voltage decreases as magnet-to-sensor distance increases during flexion.

Rather than relying on fixed absolute voltage thresholds that may vary due to environmental factors, gait phase detection is normalized based on the full-scale range (FSR) of the sensor output. The system is mechanically designed such that the voltage variation across the full range of knee motion spans at least 60% of the sensor operating range. This ensures a sufficiently high signal-to-noise ratio (SNR) relative to electromagnetic noise generated by the actuation subsystem and provides a clear phase transition margin.

For gait phase detection, dual thresholds are applied at the lower 30% (${\mathrm{L}}_{\mathrm{t}\mathrm{h}}$) and upper 80% (${\mathrm{U}}_{\mathrm{t}\mathrm{h}}$) levels. To improve the accuracy of speed estimation, the system initiates stance-phase detection as soon as the knee begins to extend and the sensor signal rises above the lower threshold (${\mathrm{L}}_{\mathrm{t}\mathrm{h}}$, 30%), whereupon the stance timer is started. Conversely, when the knee begins to flex and the sensor signal falls below the upper threshold (${\mathrm{U}}_{\mathrm{t}\mathrm{h}}$, 80%), the system transitions to swing phase, and the accumulated time at that moment is defined as the final stance time (${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}$).

This threshold separation is intended to suppress spurious phase transitions caused by small fluctuations in the sensor signal. It acts on the raw Hall signal and is distinct from the temporal hysteresis applied to the lookup-table boundaries in Section 3.2. The raw sensor data are first digitized through the MCU ADC and then processed through a low-pass filter (LPF) to attenuate high-frequency noise, followed by a moving average filter to smooth residual noise. Because this multistage digital filtering inherently introduces phase delay, the algorithm requires a trade-off in filter window size selection to preserve real-time responsiveness in gait phase detection. The final gait mode decision is made at the moment of swing phase entry. To reduce stochastic variability within a single gait cycle, the system computes and applies the average of the stance time from the current cycle (n) and the preceding cycle (n − 1), as expressed in Equation (4), in real time.

$${\overline{\mathrm{T}}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}\right]={\displaystyle \frac{1}{2}}{\displaystyle {\sum }_{\mathrm{i}=0}^1}{\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}-\mathrm{i}\right]={\displaystyle \frac{{\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}\right]+{\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}-1\right]}{2}}$$

(4)

This smoothing partly offsets the stride-to-stride variability caused by uneven terrain or brief changes in step length. By avoiding abrupt damping changes, the controller is less likely to overreact to momentary speed fluctuations and instead follows the user’s dominant gait intent.

3.4. ECPK GUI Software for Gait Analysis and Parameter Tuning

A custom GUI software was developed to enable real-time data logging of the ECPK system and subject-specific adjustment of control parameters. Figure 7 presents a schematic diagram illustrating the functional configuration and data flow of the developed software and shows the logical structure of a human–machine interface (HMI) that allows researchers to monitor internal system states and adjust control variables to the experimental conditions during clinical testing. The software architecture consists of two main components: control parameter configuration and real-time monitoring.

The control parameter configuration module shown in Figure 7a defines system responsiveness based on the subject’s gait characteristics. In this module, the researcher sets the stance duration thresholds that determine gait mode transitions, together with the target control value for each mode (Slow, Medium, Fast). The system classifies the gait as Fast Mode when the real-time computed average stance time (${\overline{\mathrm{T}}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}\left[\mathrm{n}\right]$) falls below the Fast–Medium threshold. The target control values are directly linked to the motor target position and determine the extent to which the orifice is closed, thereby increasing damping force. The settings displayed in Figure 7a are firmware defaults shown to illustrate the interface; the thresholds and valve positions applied in the present experiments are those established by the per-user calibration procedure described in Section 4.2.2.

Figure 7b,c present the monitoring and visualization interfaces that process system state feedback. The state monitoring block in Figure 7b displays key variables in real time, including raw ADC data from the Hall sensor, current gait phase, and battery level. The real-time trajectory tracking interface in Figure 7c enables observation of the dynamic tracking behavior between sensor input and actuator output. The plot is a representative snapshot from a bench-top test: the valve motor steps to each target position as the sensor signal cycles. System latency and mode transitions can therefore be observed directly during testing, which supports the parameter tuning described in Section 4.2.2.

3.5. System Implementation and Prototype

The hardware architecture and control algorithm proposed in this study were integrated into a physical prototype to enable mechanical validation and gait evaluation. Figure 8 presents the implemented ECPK system reflecting the design specifications described in Section 3. Figure 8a shows a custom-designed ECU developed to minimize computational bottlenecks and power interference. It integrates the main controller (STM32F373, STMicroelectronics) responsible for computation, a wireless module (BLE) for GUI communication, and a 6 V step-up converter for power decoupling of the actuation subsystem. Figure 8b presents a custom-fabricated variable damping knee module that integrates a coreless motor with the flexion needle valve. To control extraneous variables during subsequent clinical experiments, these core modules were mechanically integrated, as shown in Figure 8c, with the subject’s existing transfemoral socket and prosthetic foot to form a complete transfemoral prosthesis. The integrated system served as the evaluation platform for mechanical impedance bench testing and clinical gait assessment described in Section 4.

4. Experimental Results

The ECPK is evaluated first on the bench and then during gait. First, the dynamic characteristics of the variable damping mechanism are quantitatively assessed using a precision universal testing machine, followed by an exploration of potential improvements in gait symmetry and metabolic efficiency compared with a conventional commercial prosthesis through a within-subject comparative evaluation involving a participant with transfemoral amputation (N = 1).

4.1. Analysis of Mechanical Impedance and Damping Characteristics

The ECPK dissipates the kinetic energy of the swinging shank by throttling airflow between the cylinder chambers, so its damping is set jointly by the needle-valve orifice area and by the piston velocity. To separate these two effects, the pneumatic cylinder was tested on materials testing machines under two conditions: valve position varied at a fixed piston velocity, and piston velocity varied at a fixed valve position.

In the first test (Instron R8511; Figure 9a), the piston was driven at 130 mm/s over a 30 mm compression stroke while the flexion valve was closed from 1.0 (fully open) to 8.0 turns (maximum restriction) in unit steps, with the extension valve fully open. Negative displacement corresponds to flexion (compression) and positive to extension. The force–displacement curves (Figure 9b) follow the expected trend: as the flexion valve closes, the compressive resistance rises, reaching about −280 N at −30 mm for 8.0 turns—roughly 2.3 times the value near the open setting (2.0 turns, ≈−120 N)—and above 6.0 turns the force stiffens nonlinearly with displacement, consistent with air compression in a confined volume. Each valve setting was recorded once; Figure 9b therefore indicates the range of damping the controller can command at this velocity but does not, on its own, establish repeatability or the velocity dependence of the damping.

Because a fluidic damper is inherently rate-dependent, a second test characterized this velocity dependence directly (Instron ElectroPuls, Instron, Norwood, MA, USA). With the flexion valve held at 5.0 turns, the piston velocity was set to 30, 60, 90, 130, 170, and 200 mm/s, and three cycles were recorded at each speed. The analysis is confined to the flexion (compression) stroke, which produces the swing-phase damping of interest; the extension stroke, whose force depends on the extension-valve setting, was not examined here. The results are given in

Table 4. Velocity dependence of the ECPK flexion damping (flexion valve 5.0 turns; Instron ElectroPuls). Values are means over three consecutive cycles; ± denotes SD.

Piston Velocity (mm/s)	Flexion-Stroke Energy (J)	CV (%)	Peak Flexion Force (N)	Compression Stroke (mm)	Eff. Stiffness (N/mm) †
30	1.18 ± 0.01	0.8	63	29.1	2.17
60	1.60 ± 0.00	0.0	80	29.9	2.69
90	2.05 ± 0.00	0.2	106	30.4	3.49
130	2.60 ± 0.01	0.4	143	30.9	4.62
170	3.02 ± 0.01	0.3	173	31.2	5.55
200	3.26 ± 0.01	0.2	188	31.4	5.99

† Effective compression stiffness = secant of the loading branch (|peak flexion force| ÷ compression stroke); velocity-dependent, reported as an indicative value rather than a rate-independent modulus.

and Figure 9c–f.

The flexion force–displacement curve grew with velocity (Figure 9c). Over the compression stroke, the absorbed energy increased from 1.18 ± 0.01 J at 30 mm/s to 3.26 ± 0.01 J at 200 mm/s (Figure 9d), the peak flexion force from 63 to 188 N, and the secant compression stiffness from 2.2 to 6.0 N/mm (Figure 9f). Because this stiffness rises with velocity, it reflects the combined pneumatic-spring and flow-restriction response rather than a rate-independent modulus and is reported as an indicative value. The three cycles at each velocity nearly coincided (coefficient of variation < 1%; Figure 9e). At 130 mm/s the 5.0-turn condition gave a peak flexion force of ≈143 N, agreeing with the 5.0-turn curve of Figure 9b measured at the same velocity.

The two tests describe complementary parts of the same behavior: valve position sets the level of damping available to the controller, while at a fixed valve position the damping scales with piston velocity through the intrinsic response of the cylinder. The lookup table uses this by assigning a valve position to each detected speed, so that faster swing meets greater fluidic resistance. These measurements were confined to the bench; the extension-stroke rebound, the in-cylinder pressures, and any temperature dependence were not measured, and the associated kinematic effects are assessed in the gait evaluation that follows.

4.2. Single-Case Gait Experiments and Protocol

4.2.1. Participant and Experimental Setup

This section presents the single-case feasibility evaluation designed to quantitatively assess the real-time gait assistance performance of the proposed ECPK system. A single-subject, within-subject design (N = 1) was used with an experienced individual with unilateral transfemoral amputation, chosen to minimize confounding variables while establishing initial feasibility and recording baseline kinematic responses to the new control system. The study was conducted in compliance with ethical guidelines, with approval from the Institutional Review Board (IRB) of the Rehabilitation Engineering Research Institute (approval no. RERI-IRB-221130), and written informed consent was obtained from the participant following a full explanation of the study purpose and procedures.

The participant was a female with right-sided transfemoral amputation who had a relatively long residual limb, providing a favorable moment arm for prosthetic control. To minimize between-condition variability, an experienced prosthesis user who had used a passive polycentric mechanical prosthesis (Össur OP5) for more than 15 years was selected. Because the participant’s motor memory and gait pattern were strongly adapted to the comparator, the OP5 serves as a stringent baseline against which any change introduced by the new system must be read. The same 15-year-versus-4-week adaptation asymmetry is, however, a confound that limits interpretation and is treated as such in Section 5.3. Taken together, these characteristics make this a single-case engineering feasibility study intended to establish integration and control viability rather than a clinical-effectiveness trial; the favorable moment arm and single-participant design limit generalizability, and all outcomes are interpreted as hypothesis-generating.

Pre-experimental gait analysis confirmed that the participant was capable of a wide range of walking speeds when using the conventional passive mechanical prosthesis (OP5), from a minimum of 2.3 km/h (75.1 steps/min) to a peak walking speed of 4.3 km/h (120.2 steps/min) over short distances. This indicates that the participant could sustain a broad range of walking speeds, which defined the range over which the ECPK’s variable damping was subsequently evaluated.

The experiment was conducted using a within-subject comparative design comparing the control condition (wearing OP5) and the experimental condition (wearing ECPK). To control baseline conditions, the transfemoral socket, pylon, and prosthetic foot were kept identical to those used by the participant, and only the knee module was replaced to isolate the effects of changes in knee kinematics and control strategy on gait, as summarized in

Table 5. Comparison of system specifications between the control condition (Össur OP5) and the experimental condition (ECPK). To objectively evaluate kinematic and metabolic differences between the two conditions, all lower-limb components except for the knee module, including the socket, pylon, and foot, were matched to the participant’s existing setup.

Specification	Reference System (Össur OP5)	Proposed System (ECPK)
Type	Mechanical Pneumatic (Passive)	Semi-active Electronic Pneumatic
Control Mechanism	Flow Compensation (Mechanical)	Threshold-based Semi-active Damping
Knee Unit Weight	640 g (Module Only)	1040 g (Module Only)
Other Components	Identical (Foot, Pylon, Socket)	Identical (Foot, Pylon, Socket)
Power Source	None	3.7 V Li-ion Battery
Key Feature	Lightweight, Pre-set mechanical damping	Speed-adaptive, Semi-active variable damping

. The experiment was performed on a treadmill (h/p/cosmos Mercury, Nussdorf-Traunstein, Germany) with precise speed control and clinical-grade certification. Ground reaction force and COP data were obtained using an integrated pressure sensor mat (Zebris FDM-T, Isny, Germany) installed beneath the treadmill. Figure 10 illustrates the overall experimental setup used for the clinical gait evaluation.

For each knee module replacement, a certified prosthetist-orthotist (CPO) performed dynamic alignment to optimize kinematic fit. A 4-week adaptation period was implemented prior to data collection to allow the participant to adjust to the dynamic characteristics of the ECPK system. This duration is consistent with reported adaptation timescales for unfamiliar lower-limb prostheses, in which initial kinematic adaptation and the stabilization of steady-state gait parameters have been observed within three to four weeks of continuous use [54]. Although this period may be insufficient to fully eliminate the long-established gait pattern developed over 15 years of using a conventional passive prosthesis, it was deemed sufficient to achieve initial motor learning of the new variable damping control and to extract stable gait parameters for the purposes of this feasibility study.

This study also explicitly reports the weight penalty effect. The OP5 knee module (control condition) weighs 640 g, whereas the ECPK module weighs 1040 g (including the actuator motor and battery) (Table 5). The primary objective of this feasibility study is to investigate whether the proposed functional decoupling design and semi-active variable damping control can offset the biomechanical disadvantage associated with a distal mass penalty of approximately 400 g and whether this approach yields a meaningful improvement in metabolic efficiency compared with a conventional passive mechanical prosthesis.

In terms of implementation cost, the bill-of-materials cost of the ECPK prototype was approximately 1420 USD at single-unit quantity (

Table 6. Bill-of-materials cost of the ECPK prototype at single-unit quantity. Prices are those paid at prototype procurement in 2023, without volume discounts. Assembly labor, socket and foot, clinical fitting, and manufacturing overhead are not included; the total is therefore a component and machining cost rather than a delivered price.

Category	Principal Items	Cost (USD)
Custom-fabricated mechanical assembly	Four-bar linkage, frames, fasteners; pneumatic cylinder, needle and check valves, seals	≈1040
Commercial drive unit	Maxon RE-10 motor, 64:1 gearhead, encoder	≈225
Electronics and power	MCU, Hall sensor, H-bridge driver, LDO, step-up DC–DC, BLE module, PCB, 3.7 V Li-ion cell, charging circuit	≈155
Total	Prototype, single unit	≈1420

). This figure covers the structural, pneumatic, and actuation components, the electronics, and the battery and charging circuit, together with outsourced machining. It excludes assembly labor, the socket and foot, clinical fitting, maintenance and replacement parts, tooling, and manufacturing overhead, and therefore indicates the material burden of the design rather than a delivered price. Custom-fabricated mechanical hardware accounts for approximately three-quarters of the prototype cost, all of it produced at single-unit quantity by outsourced machining; the imported commercial drive unit and the electronics together account for the remaining quarter. The cost is therefore concentrated in items whose unit price is sensitive to production quantity, although the present study does not establish a volume price.

Battery life was estimated from currents measured at the battery terminals with a current probe under three operating states: 45 mA with the firmware loop running and the valve motor idle, 20 mA in the low-power mode entered after a sustained inactive interval, and 150–180 mA in total while a valve transition is in progress, of which 45 mA is the logic supply and 105–135 mA the motor path. Daily consumption was computed from the duty cycle of these states, the device operating at the active current while the prosthesis is worn, in the low-power mode otherwise, and adding a discrete term for each valve transition.

Taking the mean wear time of 12.9 h/day (SD 4.8) reported for proximal (above-knee) prosthesis users, the closest reported population to the present case [55], daily consumption is approximately 809 mAh, giving about 3.5 days per charge from a 3.7 V 3350 mAh cell at 85% usable capacity, or 4.1 days on nominal capacity. Wear time is the variable to which this estimate is sensitive: at one standard deviation above the reported mean, 17.7 h/day, it falls to about 3.1 days. Walking activity is not, because the electronics draw the active current whenever the prosthesis is worn, irrespective of whether the user is walking.

The valve term is correspondingly small: at the settings calibrated here, a transition traverses 1.8 turns of the valve’s 8-turn range in about 0.6 s and contributes under 1% of the daily budget. Bounding it for a more demanding case a step count three times the assumed 2000/day, itself above the mean of 1540 prosthetic steps/day reported for MFCL-2 and -3 transfemoral users [56], combined with a calibration spanning the full 8-turn range so that every transition travels more than twice as far raises the valve term to about 5% of the daily budget and shortens the estimate to about 3.4 days. Battery life is therefore governed by the standing current of the electronics rather than by actuation frequency or valve travel, and would be extended by lowering the active-mode current or by entering the low-power mode more aggressively during standing intervals.

4.2.2. Experimental Protocol

Based on the mechanical damping characteristics identified in the preceding section, the clinical gait evaluation was conducted under controlled conditions in two stages: subject-specific tuning followed by comprehensive evaluation.

Per-user calibration of the LUT parameters: The LUT parameters were set through an explicit protocol applicable to a new user. Because stance-phase support is provided by the four-bar linkage and the valve damping is confined to swing assistance, damping has little direct effect on stance time at a fixed speed. Exploiting this, the stance-time band and valve setting were established together at the medium condition and then used as the reference for the slow and fast modes.

Reference (Medium) setup: With the system running at the firmware default (Medium, 6.0 turns)—a setting located in the nonlinear-hardening region of the force–displacement curves in Figure 9b—the treadmill speed was increased until the participant reported the most comfortable pace, taken as the self-selected walking speed (SSWS) and assigned to the medium condition. At this condition, the stance time (${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}$) was measured by the method in Section 3.3 to define the Medium band, while the valve was concurrently fine-tuned from subjective feedback to minimize terminal impact (6.0 → 5.1 turns).

Slow and fast setup: The participant subjectively selected comfortably sustainable lower and higher speeds relative to the medium as the slow and fast conditions, and their stance-time bands were measured by the same method. The three mode thresholds were defined from these ${\mathrm{T}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}$ values (

Table 7. Stance duration thresholds and valve position settings according to gait mode for the study participant.

Gait Mode	Stance Time Duration (ms)	Flexion Valve Position (Turns) (Range: 0.0–8.0)
Fast	200–700	6.1
Medium	700–1200	5.1
Slow/Standing	1200–3000	4.3

: Fast, 200–700; Medium, 700–1200; Slow/Standing, 1200–3000 ms), and the valve positions were finalized relative to the medium (5.1 turns) by coarse (1-turn) then fine (0.1-turn) adjustment (Table 7: Slow, 4.3; Fast, 6.1 turns). Slow/medium/fast were defined relative to the participant’s self-selected speed range (Section 4.2.1; 2.3–4.31 km/h) rather than by absolute values. Each pace was measured over three bouts of three minutes each, and the mean stance time, taken from the gait log recorded at 100 ms intervals, over steady-state segments—excluding the first and last 30 s of each bout to remove acceleration/deceleration and fatigue-accumulation effects—was used as the representative value. The finalized parameters were stored in onboard EEPROM.

The protocol was designed to be device- and operator-independent, but its multi-site reproducibility was not verified and the final fine-tuning relied on subjective feedback. The values in Table 7 are specific to this participant; it is the procedure, not the values, that is transferable.

The ECPK was evaluated on three outcomes using both kinematic and physiological measures: load-bearing behavior, gait symmetry, and metabolic energy efficiency. Center-of-pressure (COP) trajectories were recorded on the instrumented treadmill (h/p/cosmos with a Zebris FDM-T mat, Germany), from which two descriptive quantities were derived: COP path symmetry, which indexes the left–right symmetry of load bearing, and maximum COP velocity, a descriptive measure of COP excursion rate. As interpreted in Section 4.6, these COP measures did not differ appreciably between the fixed- and variable-orifice conditions and are therefore treated as descriptive; they do not by themselves establish dynamic stability.

Gait symmetry was quantified using the symmetry index (SI) of Robinson et al. [57], applied to spatiotemporal parameters such as step length to compare the intact and prosthetic limbs. SI was computed for both the ECPK and OP5 conditions, so that the two control strategies could be compared directly.

Metabolic energy efficiency was measured during a six-minute walk test (6MWT) using a portable respiratory gas analyzer (K4b²; COSMED, Rome, Italy). The test was performed on a level 100 m track to minimize the acceleration and deceleration associated with turning, and each prosthetic condition was walked at two self-selected paces, Normal and Fast.

Successive walking sessions were separated by at least 30 min of washout, and a session began only after real-time monitoring confirmed that heart rate and oxygen uptake had returned to the resting baseline, which limited any carry-over of fatigue. The two devices alternated in an OP5–ECPK–OP5–ECPK sequence, and within that sequence the three-minute confirmatory bouts always preceded the six-minute bouts used in the metabolic comparison (Section 4.7). Bout duration was therefore fixed within the session sequence while device order alternated, leaving a residual ordering effect that is addressed in Section 5.3. Condition could not be blinded, so expectation effects cannot be excluded; these are also considered in Section 5.3.

Net oxygen cost was defined as the mean oxygen uptake over the final four minutes of walking (minutes 2–6), that is, after the initial oxygen-deficit phase and once the respiratory exchange ratio (RER) had stabilized. Resting oxygen uptake, measured during a 5 min seated rest before each test, was subtracted, and the difference was normalized to walking speed and body weight. Because it is expressed per unit body weight and distance, net oxygen cost permits comparison between the two conditions despite their different self-selected speeds. It does not, however, offset the ECPK’s ~400 g of added distal mass; the metabolic cost of that mass is reflected in the reported value rather than corrected out.

4.3. Real-Time Control Responsiveness

The real-time tracking performance of the ECPK control algorithm in response to changes in treadmill speed was assessed under a single-participant condition. Figure 11 presents the time-series variation in treadmill speed and flexion valve position recorded synchronously while the participant performed a stepwise incremental protocol, in which treadmill speed was gradually increased from 2.5 km/h to 4.5 km/h in increments of 0.1 km/h every 15 s.

The results indicate that as walking speed increased, the system adjusted the valve position from Slow Mode (4.3 turns) to Medium Mode (5.1 turns) and then to Fast Mode (6.1 turns), consistent with the intended design in which falling stance time raises pneumatic damping. However, as shown in Figure 11(b1), the valve position reversed 20 times over the protocol; two of these were the intended Slow → Medium and Medium → Fast changes, and the remaining 18 were spurious Medium ↔ Fast reversals concentrated in the 3.2–3.7 km/h band, where the two-step mean stance time repeatedly straddled the single 700 ms Medium–Fast boundary. These reversals produced the chattering and control oscillation observed for approximately 75 s (red lines).

Once the treadmill speed exceeded approximately 3.7 km/h, the oscillations stabilized and the system consistently maintained Fast Mode. We read this oscillation as a control-design limitation: near the mode boundaries, the participant’s normal stride-to-stride variability repeatedly crosses the algorithm’s single fixed threshold. In particular, the two-cycle moving average of Section 3 does not sufficiently suppress the stance-time scatter near these boundaries. According to the participant’s subjective feedback, a mild sensory disturbance associated with frequent damping changes was perceived in this region, although it did not result in loss of kinematic support or falls. This boundary oscillation is a control-quality limitation of the fixed-threshold logic rather than a loss of support, and it motivated the revised decision logic described in Section 3.2.

The revised logic was evaluated against the stance-time sequence recorded from the participant during the treadmill trial, which had been logged while the fixed-threshold logic was driving the valve. This measured sequence was played back through the controller running the revised firmware, so that the implemented decision logic, rather than a model of it, was exercised against the same stride-to-stride variability that had produced the oscillation. Under this input, the number of valve transitions over the 2.5–4.5 km/h protocol fell from 20 to two—the intended Slow → Medium change near 2.5 km/h and a single Medium → Fast change near 3.5 km/h—so that all 18 spurious Medium ↔ Fast reversals were removed. The Medium → Fast transition that remains within the former oscillation range is committed once, at approximately 3.5 km/h, at the first crossing of the widened upward switching threshold (500 ms). It is not reversed thereafter because, as walking speed continues to rise, the downward switching threshold (900 ms) is only rarely reached: the mode is held by the width of the band rather than by a monotonic fall in stance time. This point lies within the 3.2–3.7 km/h band over which the as-recorded system had chattered, so the single transition retained there is the intended mode change rather than oscillation. Figure 11(b2) is an offline replay: the stance-time sequence recorded in Section 4.3—logged while the fixed-threshold logic was driving the valve, so that the effect of the chattering on the participant’s gait is already embedded in the input—was played back through the implemented firmware. It shows that the revised logic suppresses the recorded stride-to-stride variability; it does not reproduce the closed-loop interaction by which a change in damping would alter the participant’s subsequent gait, and is therefore a design analysis rather than a re-validation with the participant walking.

4.4. Mode-Transition Behavior During Overground Walking

While the preceding treadmill experiment characterized the controller under imposed constant-speed conditions, this section reports a limited observation of the ECPK’s initial mode-transition responsiveness during self-paced overground walking in a single participant. The objective of this experiment is to determine whether the controller can detect variations in stance time and respond appropriately according to the predefined algorithm under real-world conditions. Figure 12 shows the continuously logged Hall sensor signal (input) and valve position data over approximately 30 s of level walking.

Examining the control trajectory in detail, the system remained in a standby state at the initial firmware setting of Medium Mode (5.1 turns) at the start of the experiment (t = 0 s). Shortly after the participant initiated walking from a stationary state (~0.5 s), the relatively long initial stance time was detected by the control system, and the algorithm immediately opened the valve to transition to Slow Mode (4.3 turns). This response follows the intended logic: the prolonged stance of the initial acceleration phase is read as a low walking speed, and damping is reduced accordingly. As the participant voluntarily increased step length and cadence, the interval between successive threshold crossings of the Hall signal shortened, and the system returned to Medium Mode (5.1 turns) at approximately 14 s. In the later phase, as walking speed further increased to a fast walking pace at approximately 26 s, the system exhibited a stepwise transition to Fast Mode (6.1 turns).

Within this single short overground trial, the controller adjusted damping in both directions. This trial was designed to confirm mode-transition behavior outside the treadmill environment, not to quantify tracking accuracy, which would require repeated trials with an independent speed reference (Section 5.3).

4.5. Spatiotemporal Gait Parameters and Kinematic Symmetry

In the preceding control tracking evaluation, short-duration tests were conducted up to 4.5 km/h to verify the operational bandwidth of the control system. However, for the evaluation of kinematic symmetry and stability during continuous walking, the maximum speed was limited to 4.0 km/h to ensure participant safety. At speeds above 4.0 km/h the extension lag of a fixed orifice becomes more pronounced during swing, so continuous walking was capped at 4.0 km/h as a precaution. Toe clearance and knee angle at heel contact were not instrumented; this cap was therefore a precautionary limit rather than a measured threshold, and comparison between conditions above it was not attempted.

In this section, spatiotemporal parameters collected under treadmill conditions are analyzed. Walking speed was gradually increased from 2.5 km/h to 4.0 km/h. The evaluation conditions included a passive polycentric mechanical prosthesis with 15 years of habituation (Passive, OP5), a condition in which the electronic control was disabled and the flexion valve was held at the Medium-mode setting (5.1 turns) for all speeds (Fixed Orifice, FO), and a condition with real-time variable-orifice control using the proposed algorithm (Semi-active Variable Orifice, VO). FO and VO are therefore identical in mass, geometry and alignment, and differ only in whether the valve was re-commanded during walking. Because the FO setting coincides with the Medium Mode, the two conditions are physically identical at speeds for which the controller selects Medium (2.5 and 3.0 km/h in these trials); any difference observed there reflects trial-to-trial variability rather than the control strategy, and serves as a reference for the differences at higher speeds.

Table 8. Comparison of spatiotemporal gait parameters of both limbs according to changes in walking speed and control condition. Passive, OP5; Fixed Orifice, FO; Variable Orifice, VO. (All data are presented as mean ± standard deviation, extracted from 10 consecutive gait cycles under steady-state conditions at each speed. These 10 cycles are repeated measures from a single participant and session; the reported SD quantifies within-trial stride variability only and is not used for statistical inference or to imply population-level reproducibility.).

Speed (km/h)	Control Type	Step Length (cm) [Intact (L)/Prosthetic (R)]	Stance Phase (%) [Intact (L)/Prosthetic (R)]	Calculated SLR (${\mathbf{L}}_{\mathbf{P}} /{\mathbf{L}}_{\mathbf{I}}$)
2.5	Passive (OP5)	45 ± 2/45 ± 2	73.7 ± 1.3/60.4 ± 1.4	1.000
	Fixed Orifice (FO)	47 ± 2/49 ± 2	73.4 ± 1.5/58.8 ± 1.3	1.043
	Variable Orifice (VO)	49 ± 2/50 ± 2	72.7 ± 1.8/58.9 ± 1.6	1.020
3.0	OP5	50 ± 1/50 ± 2	73.1 ± 1.1/59.4 ± 1.3	1.000
	FO	51 ± 2/54 ± 2	71.6 ± 1.1/58.5 ± 1.2	1.059
	VO	52 ± 1/54 ± 1	72.3 ± 1.2/57.8 ± 1.0	1.038
3.5	OP5	53 ± 1/54 ± 2	71.8 ± 1.2/58.5 ± 0.9	1.019
	FO	54 ± 1/60 ± 2	71.2 ± 1.1/57.9 ± 1.1	1.111
	VO	53 ± 2/57 ± 2	71.4 ± 1.0/58.4 ± 0.8	1.075
4.0	OP5	57 ± 1/63 ± 3	70.3 ± 1.0/58.3 ± 0.9	1.105
	FO	55 ± 2/64 ± 2	70.4 ± 0.9/57.5 ± 1.0	1.164
	VO	57 ± 1/61 ± 2	70.8 ± 1.0/58.2 ± 0.7	1.070

summarizes step length and stance-phase ratio of both limbs under each speed and control condition. All values are reported as mean ± standard deviation (SD) over 10 consecutive gait cycles taken from a steady-state segment at each speed. Step lengths of both the intact and prosthetic limbs increased with walking speed under all three conditions. Across all speed conditions the intact limb consistently showed a higher stance-phase ratio (approximately 70–73%) than the prosthetic limb (approximately 57–60%), the load-avoidance pattern commonly reported in transfemoral amputee gait. This stance-phase ratio was similar across the three conditions, as expected, since the ECPK regulates swing-phase damping and does not act on stance-phase load bearing.

The left–right symmetry of step length is considered next. To quantitatively evaluate the speed adaptability of the proposed system from a kinematic perspective, the step length ratio (SLR) was calculated from average step length data and used for comparative analysis. The SLR is defined as shown in Equation (5); values closer to 1.0 indicate symmetric gait with balanced step lengths between the intact and prosthetic limbs.

$$\mathrm{S}\mathrm{L}\mathrm{R}={\displaystyle \frac{{\mathrm{L}}_{\mathrm{Prosthetic}}}{{\mathrm{L}}_{\mathrm{Intact}}}}$$

(5)

Here, ${\mathrm{L}}_{\mathrm{Intact}}$ (intact step length) refers to the linear distance from the preceding prosthetic heel-strike point to the subsequent heel strike of the unaffected limb. ${\mathrm{L}}_{\mathrm{Prosthetic}}$ (Prosthetic step length) refers to the linear distance from the preceding unaffected heel-strike point to the heel-strike of the prosthetic limb.

Figure 13 shows the mean SLR as a function of walking speed under the three conditions. The results indicate that the participant’s long-term adaptation strongly influenced performance in the lower speed range. At 2.5 and 3.0 km/h the OP5 condition gave an SLR of 1.000 at the reported precision, closer to unity than the FO condition (1.043 and 1.059) and the VO condition (1.020 and 1.038). This is consistent with gait patterns well adapted to the OP5 over 15 years of use, although the present data cannot separate device characteristics from long-term adaptation.

As walking speed exceeded 3.5 km/h, this long-term adaptation effect reached the mechanical limits of the system. Under the OP5 condition, the SLR rose to 1.105 at 4.0 km/h, indicating greater asymmetry. The FO condition showed a similar trend, with the SLR rising continuously to 1.164, attributed to the inability of the fixed damping setting to accommodate the increased inertial demands of high-speed walking. This is interpreted as a typical compensatory pattern in which prosthetic step length becomes disproportionately longer than that of the intact limb due to extension lag during the swing phase.

In contrast, under the VO condition the SLR was essentially unchanged between 3.5 and 4.0 km/h (1.075 and 1.070), a difference well below the stride-to-stride spread of the underlying step lengths, while the asymmetry of the other two conditions continued to increase over the same interval.

Although the VO condition did not match the low-speed symmetry of the long-term-adapted OP5, it showed a possible advantage at the higher speeds tested. In this single participant (N = 1), and despite a distal mass penalty of approximately 400 g, the VO condition was the only one of the three tested in which step-length asymmetry did not increase further at 4.0 km/h, the speed at which the two passive configurations (OP5, FO) showed their largest asymmetry.

4.6. Center-of-Pressure Behavior and Dynamic Stability

Beyond apparent kinematic symmetry at the spatiotemporal-parameter level, the dynamic center-of-pressure (COP) trajectory was analyzed to evaluate ground-reaction-force distribution and load transfer. Two independent indices are reported: (b1) the COP butterfly diagram, a qualitative morphological visualization of the COP trajectory, and (b2) the symmetry index (SI) proposed by Robinson et al. [57], computed here from step-length data and defined in Equation (6). The SI is presented alongside, but is not derived from, the COP butterfly trajectories.

$$\mathrm{S}\mathrm{I}\left(\%\right)={\displaystyle \frac{\left|{\mathrm{X}}_{\mathrm{a}\mathrm{c}\mathrm{t}}-{\mathrm{X}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}\right|}{\frac{1}{2}\left({\mathrm{X}}_{\mathrm{a}\mathrm{c}\mathrm{t}}+{\mathrm{X}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}\right)}}\times 100$$

(6)

Here, ${\mathrm{X}}_{\mathrm{a}\mathrm{c}\mathrm{t}}$ and ${\mathrm{X}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}$ represent the measured value of the gait variable for the intact and prosthetic limbs, respectively. The symmetry index equation is that of Robinson et al. [57]; the ~10% band used here to describe acceptable symmetry is a common convention associated with the index rather than a formal cutoff proposed in [57], and is used for description only. This threshold is used here for description only, not as a diagnostic criterion.

Figure 14 presents COP butterfly trajectories and SI values under each speed and control condition. At 2.5 km/h and 3.0 km/h, both the fixed-damping condition (FO) and the variable-damping condition (VO) remained below the 10% reference value. As walking speed increased to 4.0 km/h, the butterfly trajectory under the FO condition became visibly distorted and the SI rose to 15.1%. Under the variable-damping condition (VO), the SI was 6.8% at the same speed, with a more symmetric trajectory than under FO. For reference, the SI computed from the OP5 step lengths in Table 8, a condition not shown in Figure 14, was 0% at 2.5 and 3.0 km/h, 1.9% at 3.5 km/h, and 10.0% at 4.0 km/h.

To characterize the load-transfer behavior accompanying this symmetry result, stride length, COP path symmetry, and maximum COP velocity were extracted across the same speed range and summarized in

Table 9. Stride length, COP path symmetry, and maximum COP velocity across increasing walking speeds under the fixed-orifice (FO) and semi-active variable-orifice (VO) conditions. Stride length is presented as mean ± SD over 10 consecutive cycles, whereas COP path symmetry and maximum COP velocity are single values extracted from the steady-state interval at each speed. As in Table 8, all values are repeated measures from a single participant and session and are reported descriptively, without statistical inference.

Speed Condition (km/h)	Stride Length (cm)		COP Path Symmetry (mm)		Maximum COP Velocity (cm/s)
	FO	VO	FO	VO	FO	VO
2.5	96 ± 3	99 ± 3	2.4	2.9	145.9	144.6
3.0	105 ± 3	107 ± 2	2.1	2.7	153.7	144.0
3.5	114 ± 2	111 ± 3	2.3	2.1	153.2	158.0
4.0	119 ± 2	118 ± 2	2.8	3.2	165.5	165.4

. Stride length increased with walking speed under both conditions, and at the highest tested speed (4.0 km/h) it reached 119 cm under FO and 118 cm under VO, so that the same treadmill speed was covered with essentially the same stride length in the two conditions. COP path symmetry and maximum COP velocity showed no consistent difference between FO and VO either, the two conditions alternating in rank from one speed to the next rather than separating systematically. This near-absence of a between-condition difference is expected rather than anomalous, because stride length, COP path symmetry, and stance-phase loading are governed by the four-bar linkage together with the shared socket, pylon, and foot, none of which differs between FO and VO, whereas the variable-orifice controller acts only on swing-phase damping and therefore leaves these stance-dominated measures largely unchanged.

Maximum COP velocity increased with walking speed under both conditions and did not separate systematically between them, the FO condition being higher at 2.5 and 3.0 km/h, the VO condition being higher at 3.5 km/h, and the two conditions falling within 0.1 cm/s of each other at 4.0 km/h (FO 165.5 cm/s versus VO 165.4 cm/s). Maximum COP velocity is in any case an ambiguous index in the present context, since a higher value is read as reduced postural stability under conventional static-balance criteria but may instead reflect maintained forward propulsion during dynamic level-ground walking, and the single-session data cannot distinguish between these readings. The prosthetic-side vertical loading-response peak was similarly close between the two conditions at 4.0 km/h (FO 512 N versus VO 515 N), which is consistent with stance-phase load bearing being set by the shared linkage and components rather than by the swing-phase controller. Taken together, these COP and loading measures do not by themselves establish any difference in dynamic stability between FO and VO, and the margin of stability, joint moments, trunk acceleration, and three-axis ground-reaction forces that would be needed to establish one are left to future work. The effect attributable to variable-orifice control appears instead in swing-phase step-length symmetry, reported in Section 4.5 and Figure 14, where the symmetry index at 4.0 km/h is held at 6.8% under VO against 15.1% under FO.

4.7. Evaluation of Metabolic Energy Efficiency and Gait Performance

As the final evaluation in this study, a six-minute walk test (6MWT) was conducted on level ground to assess the gait assistance effectiveness of the ECPK system from a physiological perspective. Because the two conditions were compared at self-selected rather than matched speeds, the metabolic values reported in this section are descriptive; see Section 5.3 for the methodological caveats. The participant wore a portable respiratory gas analyzer (K4b² COSMED, Italy) during the test. The experimental setup and participant instrumentation are shown in Figure 15.

The control condition was defined as the passive polycentric mechanical prosthesis (Össur OP5) that the participant had used for 15 years with a high degree of adaptation. The experiment was conducted under two conditions: the participant’s self-selected Normal Walking speed (which activates Medium Mode in the controller) and a fast walking speed. The primary outcome measure was net oxygen cost, which represents walking economy, calculated using Equation (7).

$$\mathrm{N}\mathrm{e}\mathrm{t} {\mathrm{O}}_2 \mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}(\mathrm{m}\mathrm{L}/\mathrm{k}\mathrm{g}/\mathrm{m})={\displaystyle \frac{\stackrel{`}{\mathrm{V}}{\mathrm{O}}_{2,\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}-\stackrel{`}{\mathrm{V}}{\mathrm{O}}_{2,\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}}{\mathrm{W}\mathrm{a}\mathrm{l}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{S}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{d}\times \mathrm{B}\mathrm{o}\mathrm{d}\mathrm{y} \mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}}$$

(7)

Here, $\stackrel{`}{\mathrm{V}}{\mathrm{O}}_{2,\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}$ represents the mean oxygen uptake (mL/min) measured during walking, and $\stackrel{`}{\mathrm{V}}{\mathrm{O}}_{2,\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}}$ represents the oxygen uptake measured during a seated rest condition prior to the test. Walking speed was expressed in m/min, and body weight in kg. Figure 16 and

Table 10. Comparison of physiological gait parameters measured during the six-minute walk test (6MWT). All values are means over the final 4 min (minutes 2–6) of each bout, measured with the K4b² metabolic analysis system, the initial oxygen-deficit period being excluded. Because the two conditions were compared at unmatched self-selected speeds and the ECPK reached RER 1.13 under the Fast condition—where indirect calorimetry underestimates total metabolic cost, preferentially for the more anaerobic condition—the net O₂ cost values are single-case, uncorrected observations and should not be read as a demonstrated efficiency gain (see Section 5.3). Negative values in the last column indicate a lower net O₂ cost with the ECPK than with the OP5.

Speed Condition	Prosthesis Type	6MWD (m)	Walking Speed (m/min)	Heart Rate (bpm)	Respiratory Exchange Ratio (RER)	$\stackrel{`}{\mathbf{V}}{\mathbf{O}}_{2,\mathbf{g}\mathbf{r}\mathbf{o}\mathbf{s}\mathbf{s}}$ (mL/min)	$\mathbf{N}\mathbf{e}\mathbf{t} {\mathbf{O}}_2 \mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}$ (mL/kg/m)	$\mathbf{N}\mathbf{e}\mathbf{t} {\mathbf{O}}_2 \mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}$ Difference vs. OP5 (%)
Normal	OP5 (Passive)	317.30	52.88	98.53	0.87	458.73	0.09	-
	ECPK (Semi-Active)	294.30	49.05	106.55	0.87	374.32	0.06	−33.3%
Fast	OP5 (Passive)	371.70	61.95	115.05	1.04	731.47	0.16	-
	ECPK (Semi-Active)	433.20	72.20	131.59	1.13	593.38	0.10	−37.5%

present the quantitative comparative analysis of physiological gait parameters obtained from the 6MWT.

Analysis of the clinical metrics six-minute walk distance (6MWD) and walking speed showed that under the Normal condition, total walking distance (317.30 m) and speed (52.88 m/min) were greater under the OP5 condition than under the ECPK condition (294.30 m; 49.05 m/min). This may reflect long-term habituation to the OP5 together with a conservative gait strategy adopted in response to the unfamiliar control and the added distal mass of approximately 400 g; the present design cannot separate these contributions. In contrast, under the Fast condition, the ECPK achieved a 6MWD of 433.20 m at 72.20 m/min, whereas the OP5 reached 371.70 m at 61.95 m/min. This corresponds to an approximately 16.5% greater walking distance with the ECPK under the Fast condition—a reversal of the Normal-condition direction that is consistent with the passive damper approaching its mechanical limits at higher speed, although a single-case comparison cannot establish the cause.

For heart rate, a higher value was observed under the Fast condition with the ECPK (131.59 bpm) compared with the OP5 (115.05 bpm). This increase cannot be attributed solely to the added hardware mass. Under the same condition the participant reached an RER of 1.13 with the ECPK, compared with 1.04 for the OP5. An RER at or above 1.10 is conventionally read as evidence of maximal effort, while an appreciable anaerobic contribution is already present once RER approaches 1.0 [58]; both Fast conditions therefore lie at or above that point, the ECPK condition more so. The participant increased voluntary walking speed to a near-maximal 72.20 m/min under the ECPK, which in turn elevated cardiovascular demand; the present measures do not allow this to be attributed to greater confidence or perceived stability.

Gross oxygen uptake under the Fast condition was itself lower with the ECPK (593.38 mL/min) than with the OP5 (731.47 mL/min), although the ECPK condition was walked faster, with approximately 400 g more distal mass and at a higher heart rate. Taken together with the elevated RER, this pattern is consistent with an anaerobic contribution that indirect calorimetry does not capture.

Despite the elevated cardiovascular demand, net oxygen cost, the primary metabolic outcome, was 37.5% lower with the ECPK, uncorrected for that anaerobic contribution. These findings rest on a preliminary single-participant observation and their generalizability is therefore limited. One possible explanation for the direction observed is that speed-adaptive damping reduced compensatory movement during high-speed walking. Given the unmatched speeds and the near-maximal effort reached under the ECPK, this remains a hypothesis to be tested under the matched-speed protocol described in Section 5.3.

The same direction was observed in the shorter three-minute confirmatory bouts, in which the ECPK showed a lower net O₂ cost than the OP5 at both the Normal and the Fast pace. These bouts are not tabulated with the primary results because they do not contain the minutes 2–6 steady-state window used here and, under the Fast condition, reached an RER of 1.28; they therefore indicate only that the direction of the difference was reproduced, not its magnitude.

5. Discussion

5.1. Trade-Off Between Added Distal Mass and Metabolic Cost

Compared with the passive OP5 that the participant had used for 15 years, net oxygen cost during high-speed walking was approximately 37.5% lower with the ECPK, despite an additional distal mass of approximately 400 g. Because this single-case value was obtained at an unmatched self-selected speed and at RER 1.13 (Section 5.3), it is treated here as a hypothesis-generating observation rather than a demonstrated efficiency gain. Added distal mass in lower-limb devices generally raises the metabolic cost of walking, so the direction observed here runs counter to expectation. Beyond the primary mechanisms of functional decoupling and semi-active swing-phase damping, we propose the following hypotheses to account for it.

Hypothesis 1. 

Acute Inhibition of Compensatory Movement.

One plausible mechanical explanation is that the combination of an additional 400 g distal mass and semi-active damping resistance physically suppressed the participant’s long-established compensatory pattern of excessive hip flexion, developed over 15 years of using a passive prosthesis. This is consistent with earlier reports that insufficient swing-phase damping in passive prostheses obliges users to adopt exaggerated hip flexion and vaulting in order to obtain toe clearance [58].

Hypothesis 2. 

Altered Pacing Strategy at the Anaerobic Threshold.

Under the Fast condition the participant reached an RER of 1.13 with the ECPK and 1.04 with the OP5. An RER at or above 1.10 is conventionally read as evidence of maximal effort, while an appreciable anaerobic contribution is already present once RER approaches 1.0 [59], so both Fast conditions represent near-maximal walking, the ECPK condition more so than the OP5. Rather than being held to the pace imposed by a fixed orifice, the participant wearing the ECPK may have exploited the speed adaptability of the variable damping to carry voluntary pacing further into this near-maximal range, and this shift may reflect not purely mechanical efficiency but a change in neuromuscular control strategy adopted under near-maximal walking conditions.

Hypothesis 3. 

Defensive Gait due to Incomplete Adaptation.

A 4-week adaptation period is sufficient to achieve initial motor learning but is biomechanically insufficient to fully supplant 15 years of long-term habituation to a passive prosthesis [60,61]. Consequently, the participant may have adopted a defensive gait strategy to compensate for the uncertainty associated with the unfamiliar dynamic system, characterized by a reduced step length and increased cadence [62]. Such a strategy is a confound rather than a device effect, and its metabolic direction is not determined by the present data.

5.2. Boundary-Condition Oscillation and Revision of the Mode-Decision Logic

The feedforward control algorithm as configured for the experiments in Section 4.3, which compared the mean stance time against a single deterministic threshold, produced control oscillation over the 3.2–3.7 km/h band, and this exposed a limitation of the decision logic. The oscillation arises because the participant’s stride-to-stride variability repeatedly crosses a fixed threshold that carries no deadband, the mode decision being taken once per gait cycle at swing-phase entry (Section 3.3) with no constraint on how frequently successive decisions may differ.

To address this instability at the firmware level, the decision logic of the fourth control layer was revised as described in Section 3.2. A temporal hysteresis of ±200 ms separates each lookup-table boundary into distinct upward and downward switching values, removing the single crossing point at which stride-to-stride variability alternates between adjacent modes. The dwell acts after a transition rather than before it: the valve is driven as soon as a boundary is crossed, and mode evaluation is then suspended for three gait cycles, during which the current mode is held and cannot be reversed by the next stride-to-stride fluctuation. Played back through the revised firmware, the gait log recorded in Section 4.3 yielded two mode transitions in place of the 20 originally recorded, removing all 18 spurious Medium ↔ Fast reversals while retaining the intended Slow → Medium → Fast progression.

Two qualifications bound this result. First, the ±200 ms band and the three-cycle dwell were both fixed from, and then evaluated on, the same recorded stance-time sequence, so the reduction from twenty transitions to two is an in-sample consistency check rather than an independent validation; moreover, because that sequence was generated while the earlier logic was driving the valve, the playback exercises the implemented decision logic against a fixed input and does not reproduce the loop by which a change in damping alters the user’s subsequent gait, and it is therefore not a re-validation with the participant walking. Second, the sequence comes from a single session with one participant, so the revised logic is shown only to suppress boundary chattering for the variability recorded in that session, which is not the same as establishing robust speed adaptability. Because stance-phase support within the near-extended corridor analyzed in Section 2.1.1 is provided passively by the four-bar linkage, and outside that corridor by the user’s hip-extension moment and alignment rather than by the controller, the valve governing swing-phase damping alone, a fault or mistuning in this logic degrades swing regulation rather than stance security; even so, its robustness and safety under conditions not present in this session—rapid speed changes, external perturbations, and uneven terrain—remain unverified, and closed-loop confirmation in a subsequent human-subject session is required.

The two gates affect transition timing differently. The hysteresis is direction-dependent and does not delay a sustained one-way transition—a genuine boundary crossing is committed at the step where the mean stance time durably crosses the widened threshold, and the single Medium → Fast change in Figure 11(b2) occurs at approximately 3.5 km/h—within the 3.2–3.7 km/h band over which the as-recorded system had chattered before settling into Fast. The dwell does not delay the first transition either, since the valve is driven the moment the boundary is crossed; what it holds off is the following evaluation, which is suspended for three gait cycles after each actuation. Under the gradual ramp used here, every mode persists far longer than this window, so the lockout is never exercised; its cost surfaces only when the intended mode changes again within a few steps—as in rapid acceleration or deceleration—where the second change waits until the three-cycle lockout (≈3–4 s) clears, consistent with the prior-step phase-lag limitation already noted in Section 1.

5.3. Study Limitations

This study is a single-case feasibility study of the hardware integration and operational behavior of the ECPK architecture. However, it has several clear limitations.

First, there is a significant asymmetry in adaptation periods between the control condition (15 years) and the experimental condition (4 weeks). The findings are based on a single participant (N = 1) and therefore cannot be generalized to the broader K2 to K3 patient population. In addition, although the two devices were tested in an alternating order, the three-minute bouts preceded the six-minute bouts throughout, so that the six-minute measurements used in Table 10 were all obtained in the later part of the session sequence. The at-least-30 min washout and the confirmed return of heart rate and oxygen uptake to resting baseline restrict any carry-over of fatigue, but a residual effect of increasing familiarity with the test procedure on the six-minute measurements cannot be fully excluded. This ordering applies to the metabolic six-minute walk test; the step-length and COP symmetry results (Section 4.5 and Section 4.6) rest on the fixed-orifice versus variable-orifice contrast, in which mass and geometry are identical and only the swing regulation differs, and are therefore not subject to the same device-order effect.

Second, electromyography (EMG) and three-dimensional motion capture were not included. As a result, the study does not provide direct kinetic and kinematic evidence identifying which joint moment changes or muscle activation reductions contributed to the observed 16.5% increase in high-speed walking distance and the reduction in metabolic cost. Future research should include multiple participants and conduct comprehensive clinical gait evaluations on varied terrain, including slopes and stairs, to validate the overall effectiveness of the system.

Third, the metabolic comparison is subject to two methodological constraints. Under the Fast condition, the ECPK elicited an RER of 1.13. An RER at or above 1.10 is conventionally read as evidence of maximal effort, while an appreciable anaerobic contribution is already present once RER approaches 1.0 [59]. Both Fast conditions therefore lie at or above that point, the ECPK condition (1.13) more so than the OP5 condition (1.04). Because indirect calorimetry captures only aerobic energy expenditure, the net O₂ cost measured under this condition likely underestimates total metabolic cost, and does so preferentially for the more anaerobic ECPK condition; the reported 37.5% reduction in net O₂ cost should therefore be interpreted with caution. Moreover, because measurements were obtained at self-selected rather than matched walking speeds, and the metabolic cost of transport is a nonlinear (U-shaped) function of speed, the isolated effect of the knee module is partially confounded with differences in self-selected speed. Future protocols should compare conditions at matched walking speeds below the anaerobic threshold (RER < 1.0).

Fourth, although the velocity dependence and repeatability of the flexion damping were characterized directly—over six piston velocities from 30 to 200 mm/s at three cycles each, with a coefficient of variation below 1% (Table 4, Figure 9c–f)—the valve-rotation sweep of Figure 9b was recorded only once at each setting, so the repeatability of that particular sweep was not itself quantified, and the bench characterization did not address the extension-stroke rebound, the in-cylinder pressures, or any temperature dependence.

Fifth, two elements of the analysis reported here were not verified experimentally within this study. The stance-stability corridor of Section 2.1.1 was derived quasi-statically from the CAD geometry and does not cover the instant of initial contact, so the passive locking it predicts has not been confirmed against measured stance-phase knee angles; and the revised mode-decision logic of Section 5.2 was fixed and then checked on a single recorded stance-time sequence rather than in closed loop, so its behavior under rapid speed changes, external perturbations, and uneven terrain remains unverified. Both are addressed by the closed-loop, instrumented human-subject session identified as future work.

6. Conclusions

An electronically controlled pneumatic knee prosthesis (ECPK) architecture is proposed for individuals with transfemoral amputation, in which swing-phase damping responds to changes in walking speed. Whether this improves gait symmetry and metabolic efficiency was examined in a single case. The proposed system is based on the kinematic stability of a four-bar linkage and provides speed-adaptive semi-active variable damping through event-driven valve control using real-time estimation of stance time. The assistive potential of the proposed ECPK was explored in a single-case feasibility study with one experienced participant (N = 1) after a 4-week adaptation period. The main findings are as follows.

Step-length asymmetry at higher walking speeds: Step-length symmetry was compared under three conditions: the commercial passive device (OP5), the ECPK with its electronic control disabled at a fixed orifice (FO), and the ECPK under semi-active variable-orifice control (VO). At 2.5 and 3.0 km/h, the OP5 produced the most symmetric gait (SI = 0%), consistent with the participant’s 15 years of use of that device. As walking speed increased, asymmetry under the FO condition grew and reached 15.1% at 4.0 km/h, whereas the VO condition remained at 6.8% and the OP5 at 10.0% at the same speed. Since FO and VO differ only in whether the valve is regulated during swing, this contrast reflects the effect of the semi-active control at constant mass and geometry, while the comparison with the OP5 also carries the adaptation asymmetry between the two devices. In this participant, semi-active control limited the increase in step-length asymmetry at the highest speed tested.

Net oxygen cost during the six-minute walk test: The ECPK was evaluated under a shorter adaptation period than the control condition. Under the high-intensity fast condition (RER = 1.13), net oxygen cost in this single participant was approximately 37.5% lower with the ECPK than with the OP5. The underlying mechanism was not measured; this direction is consistent with, but does not establish, a reduction in inefficient compensatory movement by the semi-active swing-phase resistance (Hypothesis 1, Section 5.1); because this value is uncorrected for the anaerobic contribution at RER 1.13 and was obtained at an unmatched self-selected speed, it is reported as a hypothesis-generating observation rather than a demonstrated efficiency gain, and requires confirmation at matched speeds below the anaerobic threshold.

This single-case feasibility study shows that, over the analyzed near-extended stance corridor, stance-phase stability can be assigned to passive four-bar mechanics while electronic intervention is restricted to swing-phase damping, at a single-unit component and machining cost of approximately 1420 USD, without holding current, and with an estimated battery life of approximately 3.5 days under representative daily use. The gait and metabolic observations reported above point in a favorable direction but come from a single case; whether the architecture improves gait symmetry or walking economy is for a multi-subject study to determine. On the engineering evidence presented here, the approach is a candidate low-cost complement to powered and hydraulic microprocessor-controlled knees rather than a substitute for them.

Although this study is limited by the absence of EMG and joint kinetic data and is based on a single case, these findings provide a documented engineering baseline—linkage geometry, stability margins, structural test results, bill-of-materials cost, and measured current draw—for subsequent multi-subject evaluation. Phase II should evaluate a larger cohort of K2–K3 ambulators (N > 10) across diverse clinical settings and terrains, with speed-matched metabolic testing below the anaerobic threshold, to test the biomechanical efficacy and generalizability of the proposed functional decoupling architecture. The revised mode-decision logic, whose parameters were fixed and checked on a single recorded sequence, should be re-examined in a closed-loop human-subject session covering rapid speed changes and uneven terrain before it is relied on in extended use. Future work should also replace the subjective fine-tuning of the swing-damping lookup table with closed-loop automatic calibration driven by quantitative symmetry indices (e.g., SLR or SI) to improve the objectivity and cross-user consistency of the per-user tuning procedure.