Improving interlimb coordination and paretic limb use after stroke using a novel robotic split-crank pedaling device: a cross-sectional study

Abstract

Background

Many stroke survivors cannot walk effectively, even after rehabilitation. Causes include impaired muscle activation, poor interlimb coordination, and limited restorative interventions. To address this, we developed CUped (pronounced “cupid”), a motorized split-crank pedaling device designed to compel use of the paretic limb and retrain interlimb coordination. We examined its within-session effects, comparing three proportional control schemes—assist (A), resist (R), and assist plus resist (A + R)—to identify which best promotes recovery-related movement.

Methods

Nineteen individuals with stroke and eleven controls pedaled in 5-min bouts, one per control scheme. Each bout included pre-test, exposure, and post-test periods. Participants were instructed to maintain a 180º interlimb phase relationship. Interlimb coordination and paretic limb use were quantified as the mean and standard deviation of phasing error (µE, σE) and net mechanical work (Wₙₑₜ), respectively. ANOVA was used to assess the effects of group, time, and control scheme; regression examined relationships between variables and conditions. Between-limb differences in pedaling velocity (V_dif) were also calculated and served as interpretive measures.

Results

In stroke, all control schemes reduced µE, with the largest reduction observed under A + R (p ≤ 0.019; ES: A − 15º, R − 11º, A + R − 21º). Only A + R reduced σE (p = 0.039; ES: −10º). Effects diminished with sustained exposure to control schemes (p < 0.001) and exceeded pre-test when they were terminated (p ≤ 0.027; n_p² µE = 0.24, n_p² σE = 0.49 ). This “rebound” was associated with an increase in V_dif from pre- to post-test (p < 0.001. n_p²≥0.53). There was an inverse relationship between baseline phasing error and changes in µE and σE during exposure, where greater baseline error was associated with larger improvements (p < 0.001, R² µE = 0.74, R² σE = 0.69). The R scheme increased Wₙₑₜ, whereas A and A + R reduced it (p ≤ 0.026; ES: A − 8.8 J, R 2.9 J, A + R − 5.8 J). These changes were inversely related to changes in µE (p = 0.002, R²: 0.69). Responses to CUped were similar in controls.

Conclusion

CUped improved interlimb phasing and paretic limb use, though effects were not enduring, and gains in one reduced the other, with the A + R scheme performing the best overall. Results support CUped’s potential to enhance recovery-related movement and provide insight into motor adaptation post-stroke.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12984-026-01934-7.

Background

Stroke is a leading cause of adult disability [1], and loss of mobility is a major contributor to this problem. Nearly half of stroke survivors discharged from inpatient rehabilitation are unable to walk in the community, and among those who can, more than 80% require supervision [2–6]. Loss of mobility often leaves individuals homebound, socially isolated, unhappy, embarrassed, and stigmatized [6]. Even “well-recovered’’ individuals rarely regain normal walking. Use of walkers, canes, orthotics, and other adaptive equipment is common [7]. Gait is typically marked by compensatory movements and abnormal biomechanics—such as hip hiking, circumduction, knee hyperextension, and stiff-legged gait—that make walking slow, energetically inefficient, inflexible, cosmetically unacceptable, and prone to joint pain, deformity, and injury [8–23].

Poor walking outcomes after stroke arise largely from the serious, persistent nature of stroke-related movement impairments and the limited availability of therapies that restore lost movement. In non-disabled individuals, walking depends on exquisitely timed muscle activity that is reciprocally coordinated across both limbs and multiple joints. After stroke, muscle output is diminished [24–26], timing is inappropriate [18, 27–29], and interlimb coordination is impaired [30, 31]. Although restoration of movement is possible [32–34], it requires high-repetition practice with forced use of the paretic limb and progressive shaping to ensure the task remains tractable yet challenging [34–39].

State-of-the-art approaches to lower limb rehabilitation—such as harness- and treadmill-based interventions for gait training—can provide high-repetition practice [35]. However, therapists are still required to guide and adjust limb movements to reduce compensation, promote paretic-limb activation, and help patients rediscover effective movement patterns. These methods are staff-intensive, physically demanding for therapists, and difficult to scale. Machine-assisted solutions, including robotic exoskeletons, can correct kinematic errors and facilitate high-repetition training [40–42]. Yet these devices are not well suited for individuals with severe impairment, obesity, or poor trunk control because set-up is lengthy and safe execution is cumbersome. Moreover, when exercise tolerance is low—as is true for most Americans [43]—the benefits of gait training, with or without such devices, may not justify the effort required to implement them. As a result, some patients who might benefit never receive these therapies, while others receive doses too small to be therapeutic [36].

Pedaling devices used in therapy, including conventional cycling ergometers and motorized pedaling machines, address several of these limitations. The seated form factor eliminates the need for balance and body-weight support, reducing physical demands on both patients and therapists and improving feasibility. Enhanced feasibility may allow a larger exercise dose that—while not walking—still provides continuous, reciprocal, multijoint lower limb movement. This increased dose may help explain why several groups have reported improvements in gait speed, lower extremity muscle strength, posture, balance, trunk control, and activities of daily living following pedaling interventions in people post-stroke [44–49]. However, existing rehabilitation pedaling devices use a unitary crankshaft, in which the left and right pedals are mechanically linked. As a result, they suffer from the “free-rider problem,” where the nonparetic limb performs most of the mechanical work, even when the paretic limb is capable of contributing more [30, 50]. Some devices mitigate this issue by providing visual feedback of pedal force, work, or power [44, 46, 51], but they do not address interlimb coordination because the unitary crankshaft enforces a fixed 180° phase relationship. This is a critical limitation, as impaired coordination contributes to poor lower limb function in stroke [52].

To address these challenges, we developed CUped (pronounced “cupid”), a motorized pedaling device designed to compel use (CU) of the paretic limb during pedaling (ped) while retraining interlimb coordination. CUped is a split-crank device, meaning the pedals are not mechanically connected. It is equipped with motors that apply torque independently to each crankshaft. Users are instructed to pedal forward with both limbs while maintaining a 180° interlimb phase relationship. When phasing errors occur, the motors apply torque according to one of three control schemes: assist (A), resist (R), or assist plus resist (A + R). In the A scheme, torque is applied to the lagging limb in the forward direction. In the R scheme, torque is applied to the leading limb in the opposite direction. The A + R scheme combines both approaches, applying torque to each limb with the direction determined by whether the limb is leading or lagging.

CUped’s design is grounded in a mechanistic framework, and its control schemes are informed by motor learning principles. Prior work comparing split-crank, conventional, and unilateral pedaling has shown that both abnormal motor output of the paretic limb and impaired interlimb coordination contribute to non-use of the paretic limb [30]. These impairments, although distinct, interact to create a cycle of non-use and compensation that hinders recovery. As for the three control schemes, the A scheme is a guidance-based approach intended to reduce phasing errors and enable practice of a target movement that might otherwise be intractable [53]. The R scheme is a challenge-based approach designed to increase energetic demands, discourage non-use, and provide an error cue to the leading limb [53]. The A + R scheme combines the features of both approaches, providing tractability, error cues, and encouraging increased use of the paretic limb.

Methods

The aim of this study was to examine the within-session effects of CUped on interlimb coordination and paretic limb use, and to compare outcomes across three control schemes (A, R, and A + R). To this end, we examined the initial effects, aftereffects, and effects of sustained exposure to CUped on interlimb phasing error and paretic limb work. We hypothesized that the A + R scheme would be most effective in improving phasing and work, as it promotes increased use of the paretic limb while providing both tractability and error cues. Portions of this work have been presented previously in abstract form [54].

Equipment and software

As shown in Fig. 1A, CUped consisted of a left and a right pedal, each of which was mechanically independent from the other. The pedals were custom fabricated and instrumented with force transducers and rotary optical encoders. An aluminum crank arm connected each pedal to the crankshaft of a motor with a built-in resolver for position feedback. Each motor was coupled to a 20:1 gearbox. All components were mounted on an aluminum frame. The motors were controlled using custom LabVIEW software deployed on a National Instruments cRIO with two input/output modules.

Fig. 1.

A CUped comprises two force sensitive pedals that are mechanically disconnected. Gearboxes connect the crank arms to crankshafts of the motors. B Participants are seated in front of CUped with their feet secured to the pedals. C CUped operates under feedback control to command torque (T_cmd) proportional to interlimb phasing error (E) which is computed from the position of each crankshaft. The magnitude of T_cmd is the product of a proportional gain constant (K_p) and the difference between E and its setpoint of 0°. D Participants were exposed to each of three proportional control schemes: assist (A), resist (R) and assist + resist (A + R). The order in which A and R were presented was randomized, and each of these schemes were preceded by a “Ramp” protocol to identify K_p. The A + R scheme was presented last and used the K_p from the A and R conditions. Before and after each exposure, participants pedaled for 60 s with no proportional control scheme activated (Pre-test, Post-test)

Three scripts were used to actuate the crank assembly: a control scheme script that generated the A, R, and A + R control schemes tested in this study, a virtual contralateral torque script that simulated the mechanical interaction between limbs that is present in conventional pedaling but eliminated by a split-crank device, and a viscous damping script that prevented overshoot that can occur at high proportional gains. As shown in Fig. 1C, the control scheme script utilized a proportional feedback controller. The error signal for the feedback loop was the difference between interlimb phasing error (E) and its setpoint of 0°, where E was defined as the difference between the ideal (180°) and the actual interlimb phase relationship. The control signal was the product of the error signal and a proportional gain constant (K_p) identified experimentally for each participant as described in Procedures. Additional details about the hardware and software comprising CUped can be found in Supplemental Material; see Additional File 1.

Participants

Participants included 19 individuals with chronic stroke and 11 age-matched controls. All were free from orthopedic and cardiovascular contraindications to pedaling and from neurological disease or injury other than stroke. Individuals with cortical, subcortical, ischemic, or hemorrhagic strokes affecting either side of the brain were included. Thirteen participants had cortical lesions affecting the parietal lobe (n = 6), temporal lobe (n = 4), frontal lobe (n = 8), and/or insular cortex (n = 2). Some participants had cortical lesions that extended into subcortical regions of the basal ganglia (n = 2), external capsule (n = 2), or thalamus (n = 1). Six participants had subcortical lesions affecting the internal capsule (n = 1), thalamus (n = 1), cerebellum (n = 1), basal ganglia (n = 2), corona radiata (n = 2), or pons (n = 1). See Table 1 for details.

Table 1.

Participant demographics. Values are mean (SD). FMLEtot Fugl-Meyer lower extremity total score, FMLEmotor motor score, FMLEsens sensory score, FMLEbal balance score, FMLErom range of motion score, FMLEpain pain score, BMI Body mass index

Variable	Stroke (n = 19)	Control (n = 11)
Age (years)	67 (10)	65 (6)
Sex (male/female)	9/10	5/6
Height (cm)	168 (9)	175 (11)
Mass (kg)	85 (13)	80 (14)
BMI	30 (5)	26 (4)
Time since stroke (years)	11 (8) range: 1–25
Stroke type (ischemic/hemorrhagic)	16/3
Stroke location (cortical/sub-cortical)	13/6
Paretic limb (left/right)	11/8
Walking velocity (m/s)	1.05 (0.5)
FMLEtot (max: 96)	80 (13)
FMLEmotor (max: 34)	25 (7)
FMLEsens (max: 12)	10 (3)
FMLEbal (max: 10)	7 (2)
FMLErom (max: 20)	18 (3)
FMLEpain (max: 20)	19 (2)

Procedures

Participants with stroke completed two experimental sessions. The first session included clinical assessments and a setup test to ensure that participants could be positioned properly to use CUped. In the second session, participants performed split-crank pedaling with and without the application of the three control schemes: A, R, and A + R. Control participants completed only one session because clinical tests were not necessary. All procedures were approved by the Institutional Review Board at Marquette University (IRB: HR-3063), and all participants provided written informed consent according to the Declaration of Helsinki prior to engaging in study activities.

Clinical assessments

Clinical measures included the 10-m comfortable walk test for walking velocity [55] and the lower extremity portion of the Fugl-Meyer Assessment (FMLE) [56, 57]. The total FMLE score was computed along with its five subcomponents: motor, sensory, balance, range of motion, and pain. Height and weight were recorded to calculate body mass index (BMI).

Pedaling with CUped

As shown in Fig. 1B, participants were seated with their back supported and their feet secured to the pedals with a toe cage, heel clamps, and straps. First, they were asked to relax while procedures were conducted to identify the virtual contralateral torque for each limb. Next, participants performed a 1-min bout of unilateral pedaling, from which we computed the net mechanical work (W_net) produced by the paretic limb (right limb for controls), as described in Work. The value of W_net was stored and used later to select K_p, as described below. Finally, split-crank pedaling began, wherein participants were asked to perform one 5-min trial for each control scheme (Fig. 1D). Each trial consisted of a 1-min pre-test (Pre), a 3-min exposure to the control scheme, and a 1-min post-test (Post). During Pre and Post, no proportional control scheme was active. The A and R control schemes were presented before A + R, with the order of A and R determined by block randomization based on FMLE motor and sensory scores.

Procedures to identify K_p for the A and R control schemes were completed immediately before the respective trial. Such procedures were not conducted for A + R because the values used for this control scheme were the same as those used for A and R, which is also why A + R was presented last. In selecting values for K_p, we sought to apply as little torque as possible to enable split-crank pedaling, reduce interlimb phasing errors, and compel participants to use their paretic limb. Participants were asked to perform split-crank pedaling while K_p increased from 0 to 0.3 Nm/deg in increments of 0.05. At each increment, K_p was held constant for 30 s while we recorded the position of each crankshaft and pedal, as well as the forces applied to the pedals. These data were used to compute the mean of the absolute value of E (µE) and the W_net produced by the paretic limb at each K_p. The µE at each K_p was compared to values obtained from pilot work wherein age-matched controls pedaled at K_p=0. The W_net at each gain was compared to each participant’s W_net during unilateral pedaling. The K_p values selected were the smallest non-zero values at which the participant: (1) performed at least three revolutions without one limb lapping the other, (2) achieved µE within two standard deviations of control values, and (3) maintained W_net within two standard deviations of the value recorded during paretic unilateral pedaling. On some occasions, W_net was not recorded due to technical difficulties. In these cases, criteria 1 and 2 were applied. Two stroke participants could not pedal under the R scheme even at the minimum K_p, so we did not test R. They did, however, complete A + R using the minimum non-zero K_p for R.

Instructions

Participants were aware that CUped was a motorized device designed to improve limb function. They were informed that, during pedaling, they would likely feel the motors moving their limbs or changing the difficulty of the task. However, we did not share any information about the control schemes, the order in which they were presented, or their anticipated effects. During all split-crank pedaling procedures, participants were instructed to pedal forward at a comfortable rate, keeping their feet 180° out of phase. We emphasized, and occasionally reminded them, that they did not need to pedal quickly or push hard but should focus on maintaining proper phasing.

Data recording, processing, and dependent variables

Crankshaft positions, pedal positions, and pedal forces, were sampled at 1000 Hz with a National Instruments C-series input module and recorded in LabVIEW. Position and force data were low-pass filtered offline in MATLAB at 10 Hz and 55 Hz, respectively. These signals were used to compute the dependent variables described below.

Interlimb phasing error

Errors in interlimb phasing were quantified by µE and the standard deviation of E (σE), representing errors in phase accuracy and consistency, respectively. To calculate these variables, we partitioned values for E into individual cycles using the position of the non-paretic crankshaft (left for controls). Each cycle was down sampled and interpolated to a length of 500 points after which µE and σE were computed for each cycle. The mean of all the cycles was calculated for each participant and control scheme at five different intervals: Pre, Min 1, Min 2, Min 3, and Post. Pre and Post represented the 60-s pedaling intervals before and after activating a control scheme. Min 1, Min 2, and Min 3 represented each 60 s interval of pedaling during the 3-min exposure to a control scheme. Note that for participants with stroke, E was calculated from Eq. 1 (see Supplemental Material) such that values were positive when the non-paretic limb led and negative when the paretic limb led.

Work

W_net produced by the paretic limb during pedaling was computed offline as described previously [27]. Briefly, the forces oriented tangential to the crankarm (i.e., those that produce angular rotation of the crank) were computed from the pedal forces, pedal position, and crankshaft position. Force data were referenced to the angular position of the crankshaft in 1° increments. The total area under the resulting curve represented W_net. Values were extracted for each cycle, and the mean across all cycles was calculated for each participant and control scheme at Pre, Min 1, Min 2, Min 3, and Post. Due to technical problems, work data were available for only 14 of 19 participants with stroke.

Statistics

SPSS Statistics 28 (IBM, New York, NY) was used for all analyses, with significance set at p < 0.05. Data were tested for normality (Shapiro-Wilk) and equality of variance (Levene’s test). As no violations were found, parametric tests were used. We used a hierarchical testing approach in which an a priori omnibus test was performed first; follow-up comparisons were conducted only when the global test was significant, ensuring that no unnecessary tests were performed and that statistical decision rules were not violated.

Group and condition effects

Initial effects, aftereffects, and the effect of sustained exposure to CUped’s control schemes on µE and σE were examined using analysis of variance (ANOVA). The omnibus models included two within-subject factors—control scheme (A, R, A + R) and time—with time varying by analysis: Pre and Min 1 for initial effects, Pre and Post for aftereffects, and Min 1, Min 3 and Min 3 for sustained effects. A between-subject factor of group (control, stroke) was also included and reached significance in all models (p < 0.001). Accordingly, the control and stroke groups were analyzed separately with two-way ANOVA (factors: control scheme, time). When significant interactions were detected, one-way ANOVA was used for interpretive purposes, followed by t-tests with Bonferroni corrections. Absolute effect sizes (ES), Cohen’s d (d), and partial eta squared (ηp²) were also computed. Where data were missing from the R scheme, mean imputation was used. Analysis of W_net was conducted in the same manner except that there was no omnibus test for the between group effect (control, stroke) because W_net was only assessed in the paretic limb. In examining the effects of sustained exposure (Min 1–3), linear contrast trend analysis was also used to assess whether values changed linearly as a function of time.

Relationships

In the stroke group, regression was used to determine whether the effects of control scheme varied as a function of initial pedaling performance. To this end, changes in µE and σE from Pre to Min 1 and from Pre to Post were computed and plotted against respective values at Pre. Data were fit with a two-factor model that treated µE and σE at Pre as continuous variables and control scheme as a categorical variable. The continuous factors were modeled as quadratic functions. Analogous procedures were used to examine the relationship between changes in µE and W_net from Pre to Min 1. This model also treated µE and W_net as continuous variables and control scheme as a categorical variable. However, the continuous factors were modeled as linear functions.

Additional Interpretive Analyses

To further assess the aftereffects of CUped’s control schemes in stroke, we created average time-relative velocity profiles for the Pre and Post data for each scheme. Pedaling velocity was computed as the derivative of crankshaft position. Data were segmented into individual cycles and normalized to the duration of the non-paretic cycle (left limb for controls). Each cycle began when the non-paretic crank arm (left for controls) was horizontal to the floor with the pedal closest to the participant. Ensemble averages were generated for each participant. From these profiles, we calculated the between-limb velocity difference (V_dif) during the first and second halves of the cycle for each participant and condition. A two-way repeated-measures ANOVA (control scheme: A, R, A + R; time: Pre, Post) tested whether V_dif changed from Pre to Post in either half of the cycle. V_dif was positive when the non-paretic limb moved faster than the paretic limb, and negative for the opposite pattern. For visualization, traces were averaged across participants, as in Fig. 6.

Fig. 6.

A, B Time-relative velocity profiles during pre-test (Pre) and post-test (Post) for the stroke group. Solid lines represent the paretic limb (PAR), and dashed lines represent the non-paretic limb (NPAR). A, R, and A + R represent assist, resist, and assist+resist control schemes and are distinguished by color as shown in the legends. C Mean (SD) V_dif in the first and second 50% of the pedaling cycle at Pre and Post for each control scheme. Asterisks signify a significant main effect of time (Pre vs. Post)

Results

Participant demographics are shown in Table 1, and representative examples of pedaling performance are in Figs. 2 and 3. Group results are presented in Fig. 4, with means (SD), p-values, and effect sizes shown in Tables 2 and 3. Interpretive analyses are in Figs. 5 and 6.

Fig. 2.

Representative example of pedaling performance in a control participant at pre-test (Pre), during exposure to control schemes (Exposure), and at post-test (Post). Assist (A), resist (R), and assist + resist (A + R) control schemes are shown from top to bottom in black, red, and blue, respectively. For each condition, the position (Pos) of the left and right crankshafts, interlimb phasing error (E), and time-relative velocity profiles (Vel) are shown. Pos and E are plotted with respect to time in seconds. Vel is plotted with respect to the time it took the left limb to complete one cycle, after normalizing cycle time to 100%. Thick and thin lines represent the left and right limbs, respectively. Note that the sawtooth shape of the position traces is due to resetting of the resolver with each revolution of the crank

Fig. 3.

Representative examples of pedaling performance in two participants with stroke—each with notably different pedaling performance. The horizontal line separates the two participants, with a less impaired participant shown on top and a more impaired participant on the bottom. Data from the pre-test (Pre), exposure to each control scheme (Exposure), and post-test (Post) are shown. Assist (A), resist (R), and assist + resist (A + R) control schemes are shown from top to bottom in black, red, and blue, respectively. For each condition, the position (Pos) of the left and right crankshafts, interlimb phasing error (E), and time-relative velocity profiles (Vel) are shown. Pos and E are plotted with respect to time in seconds. Vel is plotted with respect to the time it took the non-paretic limb (NPAR) to complete one cycle, after normalizing cycle time to 100%. Thick and thin lines represent the paretic and non-paretic limbs, respectively. Note that the sawtooth shape of the Pos traces is due to resetting of the resolver with each revolution of the crank

Fig. 4.

A–D Interlimb phasing error for each control scheme at pre-test (Pre), minutes one, two, and three of exposure (Min 1–3), and post-test (Post). Group means (SD) for µE and σE are shown for stroke participants (A, C) and controls (B, D). E Mechanical work (W_net) produced by the paretic limb during pedaling. Group means (SD) are shown. F Change in W_net from Pre to Min 1 plotted as a function of the change in µE from Pre to Min 1. In all panels, control schemes—assist (A), resist (R), and assist + resist (A + R)—are distinguished by color as shown in the legend. Asterisks indicate a significant effect of time (Pre vs. Min 1 or Pre vs. Post), and daggers represent significant differences among control schemes. Lowercase letters (a, b, c) indicate significant differences between control schemes during the three-minute exposure. The p-values within panels A–E represent linear effects across Min 1–3, and in panel F, they represent the relationship between the change in W_net and the change in µE. When no interaction was detected, a single p-value is shown; when an interaction was present, separate p-values are shown for each control scheme

Table 2.

Interlimb phasing error associated with each control scheme (A = assist, R = resist, A + R = assist+resist) is shown for stroke and control groups at pre-test (Pre), minute one of exposure (Min 1), and post-test (Post). Values are mean (SD). When p-values differ by control scheme, there was a significant time × control scheme interaction, and p-values are from pairwise comparisons (Pre to Min 1, Pre to Post) within each control scheme. Cohen’s d (d) and absolute effect sizes (ES) are shown. Where one p-value is shown for all control schemes, there was no interaction. The p-value represents the main effect of time, and the partial eta squared (η_p²) is shown. Pre-test values were averaged across control schemes to simplify presentation

	Pre	Min 1			Post
		A	R	A + R	A	R	A + R
Stroke
µE (º)	56(25)	38(14)*	41(17)*	32(10)* †	64(20)*	59(23)*	63(24)*
p-value		0.006	0.019	< 0.001	0.027
d, ES		−0.7, −15	−0.6, −11	−0.9, −21	ηp²=0.24,
σE (º)	44(20)	40(16)ns	41(15)ns	36(13)*	58(24)*	58(26)*	57(21)*
p-value		0.121	0.882	0.039	< 0.001
d, ES		−0.4, −6	−0.04, −0.5	−0.5, −10	ηp²=0.49
Control
µE (º)	24(7)	21(7)*	20(7)ns	17(8)* †	30(10)*	28(9)*	31(12)*
p-value		0.032	0.237	< 0.001	0.005
d, ES		−0.6, −5	−0.4, −2	−1.1, −6	ηp²=0.56
σE (º)	21(7)	22(10)ns	22(8)ns	18(9)ns	29(12)*	25(11)*	29(15)*
p-value			0.529		0.045	0.031	0.002
d, ES			ηp²=0.041		0.5, 5.5	0.5, 4	1.0, 10

^*p < 0.05 vs. pre-test, ^†p < 0.05 vs. other control schemes, ^nsp > 0.05

Table 3.

Net mechanical work (Wₙₑₜ) of the paretic limb. Values are mean (SD) for each control scheme (A = assist, R = resist, A + R = assist+resist) at pre-test (Pre), minute one of exposure (Min 1), and post-test (Post). When p-values differ by control scheme, there was a significant time × control scheme interaction, and p-values are from pairwise comparisons (Pre to Min 1) within each control scheme. Cohen’s d (d) and absolute effect sizes (ES) are shown. Where one p-value is shown for all control schemes, there was no interaction. The p-value represents the main effect of time, and the partial eta squared (η_p²) is shown. Pre-test values were averaged across control schemes to simplify presentation

	Pre	Min 1			Post
		A	R	A + R	A	R	A + R
Wnet(J)	21(8)	13(11)* †	24(10)* †	17(14)* †	24(9)ns	23(9)ns	23(9)ns
p-value		0.001	0.002	0.026		0.398
d, ES		−1.3(−8.8)	1.1(2.9)	−0.7(−5.8)		ηp²=0.06

^* p < 0.05 vs. pre-test, ^†p < 0.05 vs. other control schemes, ^nsp > 0.05

Fig. 5.

A Change in µE from pre-test (Pre) to minute one of exposure (Min 1) plotted against µE at Pre. B Change in µE from pre-test (Pre) to post-test (Post) plotted against µE at Pre. C Change in σE from pre-test (Pre) to minute one of exposure (Min 1) plotted against σE at Pre. D Change in σE from pre-test (Pre) to post-test (Post) plotted against σE at Pre. Control schemes—assist (A), resist (R), and assist + resist (A + R)—are distinguished by color as shown in the legend. The gray line is the line of best fit for all control schemes, with its associated R² and p-value shown in each panel. Colored lines are the best fit for individual control schemes

Between-group differences in pedaling performance

Regardless of the condition examined, µE and σE were larger in the stroke group than in the control group. These between-group differences are evident in the representative examples shown in Figs. 2 and 3 and the group data in Fig. 4. They are supported by a significant effect of group in the omnibus models examining the initial effects of CUped, the effects of sustained exposure, and aftereffects group (all p < 0.001), with ηp² values for µE of 0.470, 0.414, and 0.466, respectively, and for σE of 0.395, 0.380, 0.396, respectively.

Effects of CUped on interlimb phasing

As shown in Fig. 4A, exposure to all three of CUped’s control schemes reduced µE in the stroke group, with A + R producing the largest effect. Effects diminished with sustained exposure. When control schemes were turned off, µE “rebounded”, exceeding pre-exposure levels. These findings are supported statistically, as documented in Table 2; Fig. 4. Briefly, µE decreased significantly from Pre to Min 1 for all control schemes, with a significantly larger reduction under A + R than under A or R alone. During sustained exposure (Min 1–3), µE increased linearly over time. Despite this time-dependent increase, µE remained significantly lower during the exposure period with A + R than with A or R. From Pre to Post, µE increased significantly, with no difference in the magnitude of change among control schemes.

A similar pattern of responses was observed for σE in the stroke group (Fig. 4C; Table 2). However, A + R was the only control scheme to produce a significant reduction in this measure from Pre to Min 1. As with µE, σE increased linearly over time during sustained exposure (Min 1–3) and rebounded when the control schemes were turned off, with Post values significantly higher than at Pre.

In the control group, the A and A + R control schemes significantly reduced µE from Pre to Min 1, with A + R producing a significantly larger effect than A (Fig. 4B; Table 2). There was no significant change in σE from Pre to Min 1 (Fig. 4D; Table 2). Both µE and σE increased linearly during sustained exposure (Min 1–3). When the control schemes were turned off, both measures increased, with Post values significantly higher than at Pre.

These effects are also evident in the representative examples shown in Figs. 2 and 3, where visual inspection of the position and error (E) traces reveals a shift from larger to smaller interlimb phasing errors when the control schemes were activated, particularly in stroke survivors with large initial phasing errors.

Relationships between baseline performance and effects of CUped

Post hoc interpretive analyses of interlimb phasing error in the stroke group showed that the initial effects of CUped’s control schemes on both µE and σE were related to initial performance. As shown in Fig. 5A and C, there was a significant inverse relationship between values at Pre and the changes observed at Min 1: participants with larger phasing errors at Pre showed greater reductions for both measures.

A similar relationship with baseline performance was observed for aftereffects, at least for µE. As shown in Fig. 5B, this relationship was inverse and significant: participants with smaller baseline µE values showed larger increases after the control schemes were turned off, whereas in those with larger baseline errors, values remained below those recorded at Pre. This relationship was observed for all three control schemes. As for σE, there was no significant relationship between values at Pre and the change from Pre to Post.

Effects of CUped on velocity modulation

Post hoc interpretive analyses of time-relative velocity profiles in the stroke group (Fig. 6A, B) showed that pedaling velocity was modulated across the cycle, with the non-paretic limb moving faster than the paretic limb in the first half and slower in the second half. In contrast, the paretic limb showed the opposite pattern—moving slower when the non-paretic limb moved faster, and faster when the non-paretic limb moved slower. These effects were more pronounced at Post than at Pre, as evidenced by a significant main effect of time on V_dif in both halves of the pedaling cycle (first half: p < 0.001, n_p² =0.53; second half: p < 0.001, n_p² =0.56). This effect was consistent across control schemes, with no significant time × control scheme interactions (first half: p = 0.779, n_p² =0.02; second half: p = 0.853, n_p² =0.01).

Effects of CUped on mechanical work

Exposure to the R control scheme increased Wₙₑₜ of the paretic limb, whereas the A and A + R control schemes reduced it. These findings are supported statistically, as documented in Table 3 and illustrated in Fig. 4E. Briefly, Wₙₑₜ increased significantly from Pre to Min 1 for the R control scheme and then increased linearly with sustained exposure (Min 1–3). Wₙₑₜ decreased significantly from Pre to Min 1 for the A and A + R control schemes, with a significantly larger effect for A than A + R. Values for Wₙₑₜ during A and A + R did not change significantly during sustained exposure (Min 1–3), as evidenced by no significant linear trend. There was no significant Pre-to-Post effect for any control scheme examined.

Relationships between changes in mechanical work and interlimb phasing

Post hoc exploratory analyses revealed significant linear relationships between changes in Wₙₑₜ and µE from Pre to Min 1 for all control schemes. For the A and A + R schemes, larger reductions in µE were associated with larger reductions in Wₙₑₜ, whereas for the R scheme, larger increases in Wₙₑₜ were associated with smaller reductions—or even increases—in µE. However, considerable inter-individual variation was also apparent, such that in some cases the R scheme increased Wₙₑₜ while reducing µE, and the A and A + R schemes reduced Wₙₑₜ while also increasing µE.

Discussion

This study investigated the effects of a novel motorized split-crank pedaling device, CUped, designed to compel use of the paretic limb and retrain interlimb coordination after stroke. We evaluated the within-session effects of three proportional control schemes—A, R, and A + R—and found that each initially reduced interlimb phasing error. However, improvements diminished with continued exposure and did not persist once the schemes were turned off. In fact, we observed aftereffects characterized by interlimb phasing errors that exceeded baseline values. As for limb use, the R scheme increased the mechanical work produced by the paretic limb, whereas A and A + R decreased it, revealing a tradeoff between improved coordination and work. Nevertheless, we conclude that the A + R scheme was the most effective, as it reduced phasing error more than the other schemes while producing a smaller decrease in paretic limb work than A alone. Moreover, unlike the R scheme, all stroke survivors could pedal with A + R. Although not an a priori objective, we also found that CUped’s effects were related to baseline split-crank pedaling performance: participants with larger initial phasing errors demonstrated greater improvement. This observation suggests that, as a recovery tool, CUped may be more helpful for stroke survivors with moderate to severe motor dysfunction than for those who are already well recovered. Below, we discuss the implications of these findings for understanding motor impairments and adaptive capacity after stroke. We also examine how neuromuscular control mechanisms and task mechanics interact to produce and modify pedaling behavior. Finally, we consider CUped’s clinical application and ways in which its effects could be enhanced.

CUped reveals stroke-related impairments and preserved adaptive capacity

The results of this study reinforce that impaired interlimb coordination is a robust, stroke-related deficit with functional consequences. Large baseline differences in interlimb phasing error between stroke and control groups mirror findings from our prior work using a non-motorized split-crank device [30]. In both studies, phase error in controls rarely exceeded ~25°, whereas participants with stroke routinely exhibited errors at or above 60°. Although CUped reduced phasing error in the stroke group, their errors remained larger than those of controls even when control schemes were active. Consistent between-group differences across devices—motorized and non-motorized, with and without externally applied torques—provides converging evidence that interlimb coordination deficits are not artifacts of a particular device, control scheme, or experimental protocol, nor are they unique to a specific sample. Rather, they reflect a stable feature of post-stroke motor impairment.

With respect to functional implications, continuous antiphase movement of the lower limbs is fundamental to walking, and coordination deficits observed during pedaling are similar to those in walking [58–60]. Our prior work has shown that phasing errors observed during split-crank pedaling directly relate to phasing errors in walking [31]. Additionally, other biomechanical and neuromuscular features of pedaling are correlated with post-stroke lower-limb sensorimotor function, including gait, balance, and motricity outcomes [61], underscoring the relevance of these findings for post-stroke mobility.

The results of this study also suggest that maintaining consistent interlimb phasing during split-crank pedaling is disproportionately difficult for stroke survivors compared with producing an accurate average phase relationship. Evidence for this comes from the differential effects of CUped on µE and σE: all three control schemes reduced µE, but only A + R reduced σE. The reason for this discrepancy is unclear, but consistent interlimb phasing requires both limbs to move reciprocally and simultaneously at a constant velocity. Stroke survivors, however, employed a turn-taking strategy, in which one limb slowed while the other advanced, followed by the previously slower limb advancing while the other slowed. This phenomenon, also observed in our prior work with a non-motorized split-crank device [30], suggests that stroke survivors can produce coordinated consecutive movements of the paretic and non-paretic limbs but struggle to generate coordinated simultaneous movements.

The physiological basis for the differential effect on phase accuracy versus consistency is unclear, but reduced functional connectivity in global brain networks may play a role. Prior work suggests that global network function is more important for bilateral than unilateral movements [62], and that functional connectivity in global networks is more affected by stroke than connectivity in local networks [63, 64]. With impaired global network function, stroke survivors may struggle to produce simultaneous lower limb movements, yet still engage local networks consecutively to generate non-simultaneous movements. Even if global networks are preserved post-stroke, they may be more difficult to activate than local networks and therefore make a smaller contribution to motor output. This explanation aligns with other physiological explanations for interlimb coordination deficits in pedaling and walking, including disrupted neural coupling between the legs, impaired control of spinal locomotor circuits, and degraded integration of sensory feedback required to maintain reciprocal timing – all of which have cortical contributions [52].

In addition to revealing stroke-related lower limb movement impairments, the results of this study suggest that the neuromuscular system affected by stroke retains considerable adaptive capacity, exhibiting rapid and appropriate adjustments to novel task demands. Although the aftereffect—an increase in interlimb phasing error—was not a desired outcome, its presence indicates that stroke-related deficits during split-crank pedaling are not fixed but can be modified by externally applied torques. Moreover, because the aftereffect was observed in controls, it appears neither unique to stroke nor inappropriate. The fact that it emerged after only a brief, three-minute exposure further suggests that the adaptive systems of stroke survivors remain as responsive as those of controls. This conclusion is reinforced by the observation that the basic pattern of response to CUped during exposure did not differ between groups: both showed reduced interlimb phase error with the initial application of each control scheme, and in both groups, the effect diminished with sustained exposure.

Persistent adaptive ability after stroke is not a new finding. Previous studies have shown that individuals with stroke can increase force and muscle activity when pedaling against external loads of increasing magnitude [65]. They can also modify the timing of muscle activity in response to changes in pedaling rate or direction (forward vs. backward) [27, 29], adjust the magnitude of stretch-mediated reflex responses during static versus dynamic contractions [66, 67], and modify motor output in response to both assistive [68–70] and resistive external torques [71–74]. As in this study, these adaptations did not differ from those of neurologically intact individuals. However, this is the first demonstration of such behavior when the movement of each limb was modified by separate motors to control a single variable—interlimb phasing—which depends on the coordinated movement of both limbs. Together, these findings suggest that the chief obstacle to effective movement post-stroke does not lie in the ability to adapt to task demands but in the residual motor pattern itself.

Mechanical factors contributing to pedaling behavior

The way in which participants adapted to CUped was probably strongly influenced by its mechanical properties. The proportional controller, in particular, likely had an important impact on both the aftereffects and the response to sustained exposure. For example, when the A and A + R schemes were active, larger phasing errors would have produced larger assistive torques, which may have led participants to reduce their voluntary effort and let the motors do more work—a phenomenon known as slacking [75–77]. Slacking would have made the task less strenuous, especially during portions of the cycle where participants had to work against gravity. Participants might also have learned that pedaling with inconsistent velocity (faster downstroke, slower upstroke) generated greater assistive torques, potentially reinforcing their reliance on the device and increasing phasing error with continued exposure. When assistance was removed, these tendencies could have caused greater velocity differences between limbs, resulting in larger phasing errors during the aftereffect.

As for the mechanics of the R strategy, it was designed to cue—or even penalize—forward progression of the leading limb and encourage greater motor output from the lagging limb to achieve the desired phase relationship. It offered no energetic reward for phase error. However, the opposing torque may have been too small to discourage the error, and participants may have simply “pushed through” the resistance instead of adjusting their coordination. Stroke survivors are known to scale their muscle activity in response to increased load [73]. Once they became accustomed to pushing through the extra resistance, its removal at the post-test could have led to greater differences in limb velocity and larger phasing errors in the aftereffect. Had we anticipated this response, we might have used a higher proportional gain to make the resistance more noticeable—or a more meaningful obstacle to success—thereby improving performance, at least during exposure.

Alternatively, the effects of the R control scheme may have been influenced by stroke-related sensory deficits that prevented participants from detecting changes in workload. The work of Chu et al. suggests that dynamic load perception is impaired after stroke, whereas static perception is not [78]. We did not instruct participants that increased workload indicated elevated phasing error, nor did we encourage them to maintain a low workload. If we had, the R control scheme might have been more effective at keeping phasing error low. These findings suggest that participants may need explicit cues to attend to load changes and keep workload low to achieve appropriate phasing.

Finally, we cannot rule out the possibility that the virtual contralateral torque module influenced the adaptation. Because it was present in all conditions, it may explain why all three proportional control schemes produced similar effects. Participants may have learned to anticipate the virtual contralateral torque, especially during antigravity portions of the cycle, and reduced their voluntary effort, leading to increased phasing error with sustained exposure. To address this potential confound, future studies could include a condition in which participants pedal with the virtual contralateral torque but no control scheme for the same duration as the exposure conditions.

Future directions and clinical implications

Given the adaptive capacity of the stroke-affected neuromuscular system and its responsiveness to task mechanics, we suspect that the effects of CUped could be improved with exercise protocols and control schemes that further promote active engagement of the paretic limb, as well as with explicit performance feedback. To this end, we are currently testing an exercise protocol in which the magnitude of motorized assistance and resistance is gradually reduced during exposure, encouraging participants to rely less on externally applied torques and more on their own volition to produce the desired behavior. We expect this approach to enhance motor learning by continually increasing challenge, and it may also reduce undesirable aftereffects by avoiding the abrupt removal of torques to which participants have become accustomed.

We are also considering new control schemes that (1) apply opposing torques to prevent the leading limb from advancing until the lagging limb begins to catch up, (2) withhold assistance from the lagging limb until it produces a specified level or increase in torque, or (3) exacerbate errors to reverse the aftereffect. Prior work [79, 80] supports these ideas, demonstrating that effort-contingent robotic control reduces slacking and that error augmentation—despite degrading performance during training—produces better performance once the augmentation is removed.

As for explicit feedback, we have already developed methods to display the magnitude of interlimb phasing error in real time and are considering displaying pedal forces. Given that explicit visual feedback improves motor performance in other therapies, including pedaling-based ones [81–83], we expect it to benefit CUped as well.

Assuming such modifications work as anticipated, inducing sustained improvements in paretic limb use and interlimb coordination, CUped may have clinical utility. Its seated form factor makes it feasible even for those most impaired by stroke, which is also the group most likely to benefit. In this study, individuals with larger interlimb phasing errors experienced the greatest reductions when using the control schemes and were less likely than their less-impaired counterparts to show rebound effects. Pedaling devices are already widely available in clinics, which means that CUped should integrate well with existing workflows and meet clinician and patient expectations for a therapeutic experience.

While interventions that include pedaling have already been shown to be effective [48, 49, 84], the split-crank feature is novel and adds value. To our knowledge, such a feature has only been used in research settings [30, 50, 58, 59, 65, 85–87], and in those instances, it has been used to examine interlimb influence on motor control rather than to challenge or retrain interlimb phasing. Here, we have shown for the first time the technical feasibility of a motorized split-crank system that modifies interlimb phasing. We also demonstrate that, with only two exceptions involving participants who were unable to pedal with the R scheme, all individuals with stroke were able to interact effectively with CUped. This point is important because one cannot assume that people with hyperreflexia, abnormal synergies, or sensory-processing impairments—common after stroke—will respond to externally applied torques in a way that produces the intended kinetic or kinematic effects. These observations suggest that CUped could be used to support motor learning and recovery in the lower limbs, as robotic devices have been shown to do in upper-limb rehabilitation [88, 89]. Given that efforts to improve lower limb motor function during pedaling are likely to influence walking and other aspects of mobility, our findings support further efforts to optimize CUped as a recovery tool.

Limitations

The observations reported here may not generalize to the broader population of stroke survivors with impaired lower-limb function. Although there was a range of Fugl–Meyer scores and walking speeds, participants were relatively well recovered—a characteristic common among individuals able to visit a research laboratory. More impaired individuals may be unable to pedal with CUped at all, whereas less impaired individuals may pedal as well as controls regardless of the control scheme, deriving little benefit. We were also unable to record work data in 5 participants, further compromising external validity.

Additionally, we provided only 3 min of exposure to each control scheme. We do not know what would have occurred with longer exposure. The effects may have eroded further, or additional time may have allowed participants to improve. We also did not test retention across days, so it remains unknown whether any of these effects carry over from one session to another—an important consideration if CUped is to be used as a rehabilitation tool.

Conclusions

This study demonstrates that CUped, a motorized split-crank pedaling device, can reduce interlimb phasing errors and modulate paretic-limb work in stroke survivors. It revealed both stroke-related motor impairment and the preserved adaptive capacity of the neuromuscular system. Among the three control schemes tested, A + R proved most effective overall, decreasing phasing error while minimizing reductions in paretic-limb work, though individual responses varied, according to baseline impairment. The findings indicate that interlimb coordination deficits after stroke are robust but modifiable. They suggest that performance can be shaped by both neural and mechanical factors, including sensory perception, proportional control, and other device dynamics. Importantly, CUped’s ability to compel use of the paretic limb and retrain coordinated movements—combined with its seated format—positions it as a promising adjunct to existing rehabilitation approaches. Future refinements, such as tailored control schemes and explicit performance feedback, may enhance its therapeutic potential and enable more individualized interventions for stroke survivors with varying levels of motor impairment.

Abbreviations

A

Assist control scheme

R

Resist control scheme

A + R

Assist plus resist control scheme

E

Interlimb phasing error

K_p

Proportional gain constant

T_cmd

Torque commanded to motors

VCT

Virtual contralateral torque

FMLE

Fugl-meyer lower extremity assessment

BMI

Body mass index

W_net

Net mechanical work

Pre

Pre-test

Min 1

Minute 1 of exposure

Min 2

Minute 2 of exposure

Min 3

Minute 3 of exposure

Post

Post-test

µE

Mean of the absolute value of E

σE

Standard deviation of E

V_dif

Difference in mean velocity

Author contributions

TR and SSI made substantial contributions to the conception and design of the work. TR conducted data acquisition, processing, and creation of figures. All authors contributed to data analysis and interpretation. All authors made substantial contributions to the written text of the work. All authors read and approved the final manuscript.

Funding

This work was funded by the National Center for Medical Rehabilitation Research in the Eunice Kennedy Shriver National Institute of Child Health and Human Development through grant number R21HD108585, the National Center for Advancing Translational Sciences in the National Institutes of Health through grant numbers UL1TR001436 and TL1TR001437, the Advancing Healthier Wisconsin Endowment, and the Rev. John P. Raynor, SJ Fellowship. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the funding sources.

Data availability

The datasets used and/or analyzed in the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was approved by the Marquette University Institutional Review Board (HR-3063). All participants gave written, informed consent prior to participation.

Consent for publication

Not applicable.

Competing interests

The authors declare the following competing interests: SSI and BDS are named inventors on the patent for the CUped device. SSI is the founder of Venus Rehabilitation Technologies, LLC, which seeks to commercialize the device. These relationships may be perceived as a conflict of interest. However, all aspects of study design, data collection, analysis, and interpretation were conducted with scientific rigor to ensure objectivity and transparency.