Variable stiffness treadmill

Abstract

A variable stiffness treadmill system is disclosed. An elevated split-belt treadmill has a left treadmill platform assembly and a right treadmill platform assembly, each includes a frame, a belt, and a motor for independently driving the respective belt. A variable stiffness mechanism (VSM) is operatively connected to the treadmill platform assembly and adjusts vertical stiffness of each belt. The VSM has at least one linear actuator adjustable for varying the vertical stiffness of each belt. A counterweight system is operatively connected to each treadmill platform assembly to counterbalance the weight of the treadmill platform assembly acting on the VSM in an unloaded configuration of the treadmill platform. The counterweight system has a pulley system driven by a roller chain and connected to opposite ends of each platform assembly. A plurality of guide rail bearings is operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection.

Description

[0001]2101715-001236 -1- VARIABLE STIFFNESS TREADMILL CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to United States Provisional Application No. 63 / 584,762, filed September 22, 2023, the content of which is incorporated herein by reference in its entirety for all purposes. REFERENCE TO U.S. GOVERNMENT SUPPORT This invention was made with government support under Grant Nos. 2020009, 2015786, 2025797, and 2018905 from the National Science Foundation. The United States has certain rights in the invention. FIELD OF THE INVENTION Aspects of the invention relate generally to simulation devices. More particularly, aspects of the invention relate to a variable stiffness treadmill system. BACKGROUND OF THE INVENTION Locomotion is a crucial component involved in almost all daily activities. Legged locomotion, particularly human-like gait, is complex, especially when considering the variety of environments encountered on a daily basis. Each environment possesses distinct properties, including but not limited to stiffness, damping, friction coefficient, slope, and roughness, with each property or combination of properties requiring specific response(s) to maintain stability and minimize energy expenditure. Such responses have been shown to be highly dependent on robust coordination between the legs. Of these surface properties, walking on low-stiffness environments is valuable for multiple applications, including human rehabilitation as well as training and development of robust controllers for biped and quadruped robots. Previous studies have shown the merit of reduced stiffness environments through walking overground on a variety of different surfaces. Prior art studies have examined how leg stiffness increases in order to maintain stability on low-stiffness terrain while walking, running, hopping, and in the transition from rigid to compliant surfaces, as opposed to steady-state walking on soft ground. Additionally, understanding energetic cost and biomechanics when running on soft surfaces has been examined. However, in said studies, testing was limited to three or fewer different low-stiffness environments due to restrictions of using a collection of different materials to walk on or creating a spring-based platform, which do not allow for an easy change or variation of stiffness. For example, a prior art Variable Stiffness Treadmill (VST) 1.0, as shown in FIGS. 1-3, includes a treadmill capable of altering vertical ground stiffness. This prior 2101715-001236 -2- art treadmill is split-belt (e.g. a left belt and a right belt), where the speed of the belts is tied, but the stiffness of the belts is not. For example, the VST 1.0 has the capability of reducing the stiffness of the left belt while keeping the right one rigid. Variable stiffness was achieved by using a first-class lever system, where the two opposing forces include the weight of a subject on the treadmill and the force of two extension springs in parallel (FIG. 3). As shown in FIGS. 2-3, effective stiffness (the stiffness felt by the subject) was alterable by changing the moment arm of the force applied from the subject (i.e. altering the mechanical advantage). By changing this distance via a linear actuator, stiffness levels ranging from 61.7 N / m to 1 MN / m were achievable on the left belt. Further, the deflection created on this treadmill was angular, not linear. As the treadmill belt deflects, it rotates around a fulcrum at the front of the treadmill. Therefore, to create a constant effective stiffness underneath the walker’s foot throughout a gait cycle, the linear actuator that controls the mechanical advantage between the belt and the springs had to be changing its position as a function of the subject’s foot position on the belt. This undesirably introduced a small delay between the linear actuator position relative to the subject’s foot position. Additionally, the angular deflection generated by the VST 1.0 causes the ankle to either increase dorsiflexion in order for the entire bottom of the foot to remain in contact with the belt or allow the heel to lift off the belt earlier in the stance phase. However, these types of angular deflection is not commonly seen in natural or real-life environments. The VST 1.0 has been used to investigate human gait in a variety of ways. First, the asymmetric environment created by the VST 1.0 has been shown to disrupt interleg coordination and generate responses to these low-stiffness perturbations (see e.g., J. Skidmore and P. Artemiadis, “Leg muscle activation evoked by floor stiffness perturbations: A novel approach to robot-assisted gait rehabilitation,” in 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015, pp. 6463– 6468; J. Skidmore and P. Artemiadis, “On the effect of walking surface stiffness on inter-limb coordination in human walking: toward bilaterally informed robotic gait rehabilitation,” Journal of NeuroEngineering and Rehabilitation, vol. 13, p. 32, 32016; and J. Skidmore and P. Artemiadis, “A Comprehensive Analysis of Sensorimotor Mechanisms of Inter-Leg Coordination in Gait Using the Variable Stiffness Treadmill: Physiological Insights for Improved Robot- Assisted Gait Therapy,” in 2019 IEEE 16th International Conference on Rehabilitation Robotics (ICORR), June 2019, pp. 28–33). In these studies, by perturbing the left leg via low-stiffness perturbations, mainly right- side responses are seen in the ensuing gait cycles. Indications of an evoked inter-leg coordination response have been further validated via brain activity through both 2101715-001236 -3- response delays and the use of electroencephalography (EEG). Additionally, rehabilitation protocols directed toward post-stroke populations have been tested on the VST 1.0 (see e.g., V. Chambers and P. Artemiadis, “Using robot-assisted stiffness perturbations to evoke aftereffects useful to post-stroke gait rehabilitation,” Frontiers in Robotics and AI, vol. 9, 2023; and V. Chambers and P. Artemiadis, “Repeated Robot- assisted Unilateral Stiffness Perturbations Result in Significant Aftereffects Relevant to Post-Stroke Gait Rehabilitation,” in IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2022, pp. 5426–5433.) Specifically, it has been shown that walking in an asymmetric low-stiffness environment leads to aftereffects that could be useful for poststroke gait rehabilitation. Still further, a Treadmill with Adjustable Stiffness (TwAS) is known (see e.g., E. Hernandez, C. Warhmund, K. Lamoureux, E. Lee, I. Sanchez, W. Matthews, and A. Jafari, “A Novel Treadmill That Can Bilaterally Adjust the Vertical Surface Stiffness,” IEEE / ASME Transactions on Mechatronics, vol. 23, no. 5, pp. 2338–2346, Oct. 2018). Prior art variable stiffness treadmills have drawbacks. First, they lack a counterweight to offload the weight of the belt. This causes an initial displacement of the belts at low stiffnesses before any external load is applied. Additionally, they include a small walking surface with respect to length, thereby not giving subjects sufficient space to walk / run or not giving taller subjects sufficient space to walk at the faster speed of the motors used. Also, prior art devices include a large distance or gap between belts which can cause unnatural foot placement, thereby affecting gait. Still further, conventional variable stiffness treadmills lack force sensors, which does not allow for tracking capabilities, such as tracking a foot center of pressure with human subjects. The lack of force sensors also does not allow for effective stiffness calculations over time as a subject walks, making it difficult to verify the magnitude of belt stiffness in dynamic scenarios. Therefore, there remains a desire for improvements in variable stiffness treadmills, particularly of improvements in systems capable of repeatable, accurate, and efficient simulation of walking environments with variable properties (e.g. variable stiffness). SUMMARY OF THE INVENTION According to an aspect of the invention, a variable stiffness treadmill system comprises an elevated split-belt treadmill comprising a left treadmill platform assembly and a right treadmill platform assembly. Each treadmill platform assembly has a frame, a belt, and a motor operatively connected to the belt and configured for independently driving the respective belt. The system also includes a variable stiffness mechanism 2101715-001236 -4- (VSM) operatively connected to the frame of each treadmill platform assembly and configured to independently adjust vertical stiffness of each belt. The VSM includes at least one linear actuator adjustable for varying the vertical stiffness of the belt. The system has a counterweight system operatively connected to each treadmill platform assembly to counterbalance the weight of the treadmill platform assembly acting on the VSM in an unloaded configuration of the treadmill platform. The counterweight system further includes a pulley system driven by a roller chain and connected to opposite ends of each platform assembly. The VSM also has a plurality of guide rail bearings operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection. According to another aspect of the invention, a method of using a variable stiffness treadmill system includes placing a user on the variable stiffness treadmill system. The variable stiffness treadmill system comprises an elevated split-belt treadmill comprising a left treadmill platform assembly and a right treadmill platform assembly. Each treadmill platform assembly has a frame, a belt, and a motor operatively connected to the belt and configured for independently driving the respective belt. The system also includes a variable stiffness mechanism (VSM) operatively connected to the frame of each treadmill platform assembly and configured to independently adjust vertical stiffness of each belt. The VSM includes at least one linear actuator adjustable for varying the vertical stiffness of the belt. The system has a counterweight system operatively connected to each treadmill platform assembly to counterbalance the weight of the treadmill platform assembly acting on the VSM in an unloaded configuration of the treadmill platform. The counterweight system further includes a pulley system driven by a roller chain and connected to opposite ends of each platform assembly. The VSM also has a plurality of guide rail bearings operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection. The method also includes measuring the location of the individual with a force sensor mat positioned below the respective belt of the left treadmill platform assembly and / or the right treadmill platform assembly. The method further comprises adjusting the vertical stiffness of the respective belt of the left treadmill platform assembly and / or the right treadmill platform assembly below the location of the individual with the variable stiffness mechanism. BRIEF DESCRIPTION OF THE DRAWINGS The foregoing summary and the following description will be better appreciated and understood in conjunction with the non-limiting examples illustrated in the attached drawing figures, of which: 2101715-001236 -5- FIG. 1 is a photograph of an exemplary variable stiffness treadmill in accordance with prior art; FIG. 2 is a photograph of an exemplary variable stiffness mechanism in accordance with prior art; FIG. 3 is a schematic diagram depicting an exemplary variable stiffness mechanism in accordance with prior art; FIG. 4 depicts a variable stiffness treadmill system in accordance with aspects of the invention; FIG. 5A is a photograph depicting an elevated split-belt treadmill of the variable stiffness treadmill system of FIG. 4 in accordance with aspects of the invention; FIG. 5B is a photograph depicting a left or right treadmill platform assembly of the elevated split-belt treadmill of FIG. 5A in accordance with aspects of the invention; FIG. 6 is an image depicting a variable stiffness mechanism (VSM) of the variable stiffness treadmill system of FIG. 4 in accordance with aspects of the invention; FIG. 7A depicts a block diagram showing an exemplary control of a position of a sliding joint of the VSM of FIG. 6 in accordance with aspects of the invention; FIG. 7B depicts a block diagram showing an exemplary control of a speed of a respective belt of the treadmill platform assembly of FIG. 5B in accordance with aspects of the invention; FIG. 8 depicts an exemplary method of using the variable stiffness treadmill system of FIG. 4 in accordance with aspects of the invention; FIGS. 9A-9B depict schematic diagrams of simplified kinematics of the variable stiffness treadmill system of FIG. 4 in accordance with aspects of the invention; FIG. 10 depicts a schematic diagram of simplified kinematics of the VSM of FIG. 6 in accordance with validation testing of the variable stiffness treadmill system of FIG. 4; FIG. 11 depicts a performance evaluation of the accuracy of the VSM of FIG. 6 in accordance with validation testing of the variable stiffness treadmill system of FIG. 4, showing a graph that compares the experimental results with theoretical stiffness values; FIG. 12 depicts a performance evaluation of the linear deflection of the split-belt treadmill of FIGS. 5A-5B over time for various stiffness levels in accordance with validation testing of the variable stiffness treadmill system of FIG. 4; and 2101715-001236 -6- FIG. 13 depicts a graph showing a relationship between desired ^^ௗ) and actual stiffness ( ^^) for various stiffness levels in accordance with of the variable stiffness treadmill system of FIG. 4. DETAILED DESCRIPTION OF THE INVENTION Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention. Additionally, various forms and embodiments of the invention are illustrated in the figures. It will be appreciated that the combination and arrangement of some or all features of any of the embodiments with other embodiments is specifically contemplated herein. Accordingly, this detailed disclosure expressly includes the specific embodiments illustrated herein, combinations and sub-combinations of features of the illustrated embodiments, and variations of the illustrated embodiments. In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant design features. However, it should be apparent to those skilled in the art that the present design features may be practiced without such details. In other instances, well known methods, procedures, components, and circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present design. Various terms are used throughout the disclosure to describe the physical shape or arrangement of features. In the description, relative terms such as "horizontal," "vertical," "up," "down," "top" and "bottom" as well as derivatives thereof (e.g., "horizontally," "downwardly," "upwardly," etc.) should be construed to refer to the orientation as then described or as shown in the drawing figure under discussion. These relative terms are for convenience of description and normally are not intended to require a particular orientation. Terms concerning attachments, coupling and the like, such as “connection,” “mounted,” “connected” and “interconnected,” refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise. Finally, the term “individual,” “user,” or “subject” is used herein to refer to the user of variable stiffness treadmill systems. These terms may refer to, for example, an amputee having a prosthesis, a legged robot, an impaired patient, a healthy subject, 2101715-001236 -7- etc.. Finally, although the variable stiffness treadmill systems is described as primarily relating to a biped, the invention is not limited to a subject having any particular number of legs. In general, aspects of the invention relate to variable stiffness treadmill systems and methods of using said variable stiffness treadmill systems. The systems and methods described can include an ability to independently reduce stiffness of both belts of the elevated split-belt treadmill by generating vertical deflection instead of angular deflection, while containing a large treadmill surface with enough space for an individual or subject to walk or run comfortably. Additionally, both treadmill belts are driven independently, and embodiments include high-spatial-resolution force sensors under each belt to allow real-time measurement of ground reaction forces and foot center of pressure. Through validation experiments, the inventive variable stiffness treadmill system (e.g. VST 2.0) displays high accuracy and precision. When setting the VST 2.0 to a desired low-stiffness value, embodiments of the VST 2.0 have an error of less than 1% and standard deviations of less than 2.2 kN / m, demonstrating an ability to reliably simulate low-stiffness environments. The variable stiffness treadmill systems and methods disclosed herein are suitable for non-limiting applications, including research on biped locomotion, athletic training, and rehabilitation of gait after injury or disease. In particular, low ground- stiffness walking is shown to be beneficial for understanding and rehabilitating human gait. Gait dysfunction is known, especially among those who have had a stroke, and implementing ground stiffness perturbations, especially with respect to stroke rehabilitation can therefore assist in relearning motor patterns through the concept of neuroplasticity. Additionally, low ground-stiffness walking can be beneficial to athletes, especially runners, when attempting to prevent overuse injuries or return to activity after an injury, by offering a low-impact environment to train. In this case, a low- stiffness environment allows for reduced hip and knee forces resulting from heel strike, as well as creating a challenging walking environment to promote the muscular adaptations necessary for recovery. Low-stiffness environments are also incredibly useful for the development of robust controllers for biped and quadruped robots. As robots are used for a variety of applications such as industrial inspection, search and rescue, payload delivery, security, mining, and agriculture, having the ability to generate stable locomotion in most real-world environments is crucial. With terrains of sand, mud, snow, and grass all having different mechanical stiffnesses, legged robots aim to be robust in environments ranging from rigid to rather compliant. Thus, testing 2101715-001236 -8- of performance of biped and quadruped robots requires systems that is capable of simulating a multitude of terrains with various properties. Referring generally to the figures, a variable stiffness treadmill system includes an elevated split-belt treadmill, a variable stiffness mechanism (VSM) operatively connected to the elevated split-belt treadmill, a counterweight system, and a plurality of guide rail bearings operatively connected to the elevated split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection. In one example, the subject 200 is a human (FIG. 4). Advantageously, the VSM 500500 (FIG. 7) of system 100 generates linear vertical deflection, which simulates more realistic or natural settings of surfaces found in real-world environments. More specifically, FIG. 4 depicts an exemplary variable stiffness treadmill system 100. The system 100 includes elevated split-belt treadmill 300 comprising a left treadmill platform 310 assembly (FIG. 5A) and a right treadmill platform assembly 320 (FIG. 5A). Each treadmill platform assembly 310, 320 includes a frame 330 (FIG. 6), a belt 312, 322, and a motor 350 (FIG. 6) operatively connected to the belt 312, 322 and configured for independently driving the respective belt 312, 322. As will be explained later below, a variable stiffness mechanism (VSM) 500 (FIG. 7) 0 is operatively connected to the frame 330 of each treadmill platform assembly 310, 320 and configured to independently adjust a vertical stiffness of each belt 312, 322. In a non- limiting example, each belt 312, 322 has a walkable surface area of 0.74 m2and the belts 312, 322 are supported by a 20mm thick particle board for supporting the weight of the mass (e.g. of subject 200) on the treadmill 300. Still further, to increase subject 200 comfort when walking on the treadmill 300, the surface of each belt 312, 322 have dimensions of at least 166 cm by 45 cm, and the treadmill 300 has a height (H, FIG. 4) relative to the ground of 45 cm. These dimensions also facilitate additional simulated conditions relating to higher walking speeds or running speeds that were not previously possible with prior art systems. Additionally or optionally, as shown in FIG. 4, the system 100 includes a body-weight support 400 mounted to a post 410 and capable of supporting the weight of the user 200 relative to the post 410. In an exemplary embodiment, the post 410 is engaged to a rail 420 for mounting the body-weight support 400 and the body-weight support 400 has a harness 430 capable of supporting the weight of the user 200. In one non-limiting example, the harness 430 is a custom- made harness-based body weight support (BWS) from Litegait Inc. of Tempe, Arizona. The harness 430 is fastened to the ground at a rear portion of the system 100 and overhangs directly onto a center portion of the belts 312, 322. The body-weight support 400 is configured to support a maximum subject 200 weight of 140 kg, and the 2101715-001236 -9- amount of support can be adjusted for the specific application, while its height is adjustable through an actuator 430 that moves the support 400 vertically. Turning now to FIGS. 5A-5B and 6, additional details of the variable stiffness mechanism (VSM) 500 (FIG. 7) and other components of the variable stiffness treadmill system 100 is illustrated. As stated above, the elevated split-belt treadmill 300 includes the left treadmill platform 310 assembly and right treadmill platform assembly 320. In an exemplary embodiment, the elevated split-belt treadmill 300 includes a housing or frame 330 made of extruded low-carbon steel or other suitable rigid materials. In one example, frame 330 comprises 50 mm by 25 mm extruded low- carbon steel rectangular tubing of 2 mm thickness that is welded together as a unitary construction of a rigid body. Together with other components of the system 100, frame 300 houses the internal components of system 100, including for example, the variable stiffness mechanism 500 (FIG. 7). For example, frame 330 is configured for attachment with side panels, such as side panels 370a (FIG. 5A) constructed from 6.35 mm aluminum plate and which contain circular cutouts 372 to reduce weight and allow for viewing of the internal components of system 100. An outer surface of inner side panels 370b include countersunk-head fasteners such that in an assembled configuration of the left treadmill platform 310 assembly and the right treadmill platform assembly 320 to form the elevated split-belt treadmill 300, a gap (FIG. 5A) or distance between the respective belts 312, 322 measures 15 mm, for example, thereby mitigating or avoiding unnatural foot placement that could affect the gait or stance of subject 200 during a use cycle of system 100. The side panels 370b interface with frame 330, such that a plurality of guide rail bearings 340 is operatively connected to the split-belt treadmill 300 for constraining the split-belt treadmill 300 to a single degree of freedom. In particular, the plurality of guide rail bearings 340 mitigate angular movement (e.g. due to the lever arm 530 angular motion forces, discussed further below). Thus, unlike prior art variable stiffness treadmill systems, the inventive system 100 constrains the split-belt treadmill 300 to only linear vertical deflection. Additionally or optionally, frame 330 includes multiple (e.g. two) rows of gusset brackets (e.g. four) that each house a single 30 kg-rated threaded rubber bumper of 40A durometer, with the bumpers configured to interact or make contact with components of the elevated split- belt treadmill 300, such as in the event of reaching a maximum linear vertical deflection (e.g. of 10 cm) or during travel or vertical displacement of the treadmill platform assemblies 310, 320 between a resting or equilibrium position and a linear vertical deflection of the treadmill platform assemblies 310, 320. 2101715-001236 -10- In an exemplary embodiment, as can be best seen in FIG. 6, the VSM 500 is a third-class lever-based system that modifies a mechanical advantage between the treadmill platform assemblies 310, 320 and a set of fixed stiffness extension springs. The VSM 500 includes at least one linear actuator 510 that is adjustable for independently varying the vertical stiffness of the belt 312, 322 of the treadmill platform assemblies 310, 320. In one non-limiting example, the at least one linear actuator 510 has a linear track 520 extending for a length between an end portion of the treadmill platform assembly 310, 320 and an opposite end portion of the treadmill platform assembly 310, 320. The at least one linear actuator 510 also includes a spring-loaded lever operatively connected to the linear track 520 and a sliding joint 540. The sliding joint 540 is driven by a motor assembly 550 (e.g. Flipsky motor 6354; peak power: 2450 W; peak torque: 10 Nm as designed by Flipsky Inc.) and is moveable along the linear track 520 that is operatively connected to the spring-loaded lever. In an exemplary embodiment, the spring-loaded lever comprises a lever arm 530 having a first lever arm end 530a pivotable about an axle 532 and a second lever arm end 530b supported by spring webbing 560 that is fixed to frame 330 and attached to a roller (not shown), such as ultra-strength high carbon steel cylinder belt rollers that interface directly with the respective belts 312, 322 and are supported to each side panel 370b via flanged ball bearings. In a non-limiting example, the belt rollers include a front roller acting as a passive idler and includes a threaded tension mechanism 570 through which to the tension of the belts 312, 322 can be adjusted. A rear roller acts as a driver for the belts 312, 322 and is connected with a 20mm solid carbon steel keyed shaft to the motor assembly 350 (e.g. Flipsky motor 63100; peak power: 5500W; peak torque: 7 Nm as designed by Flipsky Inc.) through a geared reduction. One skilled in the art would understand from the description herein that the at least one actuator includes assemblies capable of actuating or moving the treadmill platform assemblies 310, 320 via a gearbox, a worm gear, or like mechanisms. A first spring is fixed at one end to the frame 330 above the second lever arm end 530b, wrapped partially around the roller, and affixed at an opposite end to one or more second springs affixed to a bottom of the lever arm 530, configured such that a vertical downward force (e.g. F arrow in FIGS. 4 and 8) applied to the platform 300 causes deflection of the lever arm 530 to extend the first spring with a corresponding extension in the one or more second springs to generate a spring force that acts at the second end 530b of the lever arm to resist the vertical downward force (e.g. F arrow in FIGS. 4 and 8) applied to the platform 300. In operation, for example, with the VSM 500 in a maximum stiffness configuration, in which the sliding joint 540 is positioned 2101715-001236 -11- (e.g. as driven by motor assembly 550) directly above the first lever arm end 530a, the force (F) applied to the treadmill platform assemblies 310, 320 is transferred directly through the sliding joint 540, axle 532, and into frame 330, resulting in an absence of linear vertical deflection. As the sliding joint 540 travels or is positioned away (e.g. as driven by motor assembly 550) from the first lever arm end 530a, the mechanical advantage between the treadmill platform assemblies 310, 320 and the extension springs increases, thereby resulting in a lower effective stiffness ( ^^^ௗ). In contrast, the mechanical advantage is at its highest when the VSM 500 is in a minimum stiffness configuration, as shown in FIG. 6. In this configuration, the sliding joint 540 is positionable (e.g. as driven by motor assembly 550) to generate a spring force that resists the force (F) applied to the treadmill platform assemblies 310, 320, resulting in an effective stiffness ( ^^^ௗ) that is proportional to the sliding joint 540 position and the spring coefficient of the extension springs. Accordingly, the effective stiffness ( ^^^ௗ) of the elevated split-belt treadmill 300 is variable based on a length of the spring-loaded lever, a position of the sliding joint 540 along the length of the spring-loaded lever, a spring coefficient of the first and one or more second springs, or a combination thereof. Also shown in FIG. 6 is a counterweight system 600. In an exemplary embodiment, a counterweight system (CWS) 600 is operatively connected to each treadmill platform assembly 310, 320 to counterbalance the weight of the treadmill platform assembly 310, 320 acting on the VSM 500 (FIG. 7) in an unloaded configuration of the treadmill platform assembly 310, 320. The CWS 600 is configured to ensure that the forces acting on the VSM 500 is equal or close to zero when the treadmill 300 is in the unloaded configuration. Thus, in operation, the CWS 600 travels in the opposite direction of the treadmill platform assembly 310, 320 during a linear vertical deflection event or displacement of the treadmill platform assembly 310, 320 (e.g. between a rest or neutral position and a linear vertical deflection position). In one non-limiting example, the counterweight system 600 has a pulley system driven by a roller chain (e.g. single-strand American National Standards Institute (ANSI) Number 40 roller chain), which is equal to the weight of the respective treadmill platform assembly 310, 320 and connected to opposite ends of each platform assembly 310, 320. Additionally or optionally, CWS 600 includes four individual chain links containing rigid attachments that connect to a custom steel plate welded tray that holds custom- molded and painted lead weights of 34 kg each to precisely offset the 34 kg weight of the respective treadmill platform assembly 310, 320. 2101715-001236 -12- Additionally or optionally, system 100 includes at least one encoder operatively connected to the split-belt treadmill 300, the variable stiffness mechanism 500, or the CWS 600. In an exemplary embodiment, the at least one encoder includes deflection encoders integrated with the CSW 600 for the measurement of the linear deflection of the split-belt treadmill 300 corresponding to the vertical displacement of the split-belt treadmill 300 in response to the forces (F) applied to across the split-belt treadmill 300 and the effective stiffness ( ^^^ௗ). More specifically, the at least one encoder 700 is attached to the CWS 600 at both a front portion 300a (FIG. 5A) and an opposite rear portion 300b (FIG. 5A) of the split-belt treadmill 300. In operation, an average value may be taken among the at least one encoders 700 to estimate the linear deflection of the split-belt treadmill 300. In one non-limiting example, the deflection encoders include 0.2º resolution, 12-bit absolute encoders (by AMT222A-V as designed by CUI Devices) integrated with CWS 600, thereby providing a direction relationship between rotation of the CWS and the linear deflection of the split-belt treadmill 300. Still further, as shown in FIGS. 5B and 6, in an exemplary embodiment, each treadmill platform assembly 310, 320 comprises a force sensor mat 380 including a plurality of capacitive sensing cells for the measurement of the distribution of forces (e.g. F arrow in FISGS. 4 and 8) applied across the split-belt treadmill 300. Additionally or optionally, the force sensor mat 380 is configured for sensing the location of the user 200 on the split-belt treadmill 300 and in contact with the first belt 312 and the second belt 322. In one non-limiting example, underneath each belt 312, 322 includes a force sensor mat 380 comprising Tekscan 3140 with VersaTek™ Cuffs as designed by TekScan Inc. which has at least 2,000 capacitive sensing cells across the area of the force sensor mat 380, thereby offering a planar resolution of less than 1 cm in both directions. This permits system 100 to observe the distribution of forces from the foot of user 200 and the foot center of pressure, and this data is collected in real time at a frequency of 100 Hz, for example. Turning now to FIGS. 7A-7B, block diagrams depict exemplary controls of a position of the sliding joint 540 of the VSM 500 (FIG. 7A) and a speed of a respective belt 312, 322 of the treadmill platform assembly 310, 320 (FIG. 7B). In an exemplary embodiment, a processor comprising a Python-based control program and Graphical User Interface (GUI) facilitates real-time control or regulation of predetermined parameters related to operation of system 1000. Said predetermined parameters include, but are not limited to, the speed of the movement of the belts 312, 322 and the stiffness of the split-belt treadmill 300. 2101715-001236 -13- In one non-limiting example of a regulation of the stiffness of the split-belt treadmill 300, an input of system 100 includes a new effective stiffness ( ^^^ௗ) value, based on which the processor is configured to determine the required position of the sliding joint 540 and transmits this required position to the motor assembly 550, which in turn, drives the sliding joint 540 along the linear track 520 toward the determined position. In an exemplary embodiment, the motor assembly 550 comprises Odrive v3.6 motor drivers that drive the sliding joint 540 to the calculated position along the linear track 520. In operation, as shown in FIG. 7A, for a given desired effective stiffness ( ^^^ௗ) value, the corresponding position of the sliding joint 540 ( ^^ௗ^^) is determined via Equation 10 (discussed in the Example below), which is represented by function ( ^^^) in FIG. 7A. The motor assembly 550 drives the sliding joint 540 toward the target position ( ^^^^) and the split-belt treadmill 300 has a linear vertical deflection corresponding to a vertical displacement ( ^^ீ^) of first belt 312 and the second belt 322 in response to the forces (F) applied across the split-belt treadmill 300 and the effective stiffness ( ^^^ௗ) value. The vertical displacement ( ^^ீ^) is measured by at least one deflection encoder integrated into the CWS 600 and provide feedback at a frequency of 200 Hz. The applied force ( ^^^) is measured (e.g. at a rate of 100 Hz) by the force sensing mats 380. As a result, the final effective stiffness ( ^^^) is dependent upon the applied force ( ^^^) and the linear vertical deflection ( ^^ீ^) of the split-belt treadmill 300, and said relationship is represented by function ( ^^ଶ) in FIG. 7A as the output of system 100. In this way, regulation or control of the stiffness of the split-belt treadmill 300 is an open- loop system, in which no feedback on the actual effective stiffness is used to optimize the performance of the system 100. Nevertheless, since the effective stiffness is a function of the position of the sliding joint 540, errors or discrepancies between the true effective stiffness and desired effective stiffness is minimized by calibrating the processor with experimental data (as discussed in the Example below). In an exemplary embodiment, the system 100 is configured to independently vary the stiffness of both belts 312, 322 of the treadmill 300 in a range of effective stiffness ( ^^^) between 13 kN / m and 1.5 MN / m. Referring now to FIG. 7B, in an exemplary embodiment of regulating the speed of the movement of the belts 312, 322, regulation is achieved based on velocity control (as opposed to position control described above with respect to FIG. 7A). In one non- limiting example, an input of system 100 includes a speed ( ^^ௗ), from which an angular 2101715-001236 -14- velocity of the motor assembly 350 ( ^^ௗ) is calculated by the processor using function ( ^^ଷ) in FIG. 7B. Motor drivers of motor assembly 350 drive belt motors of the motor assembly 350 to the calculated velocity using pulse-width modulation of 48V and up to 100A of current. The true belt 312, 322 speed (V) is a function of at least the angular motor velocity ( ^^), which is captured by inverted function ( ^^ଷି^) in FIG. 7B. Unlike the control system described in FIG. 7A, the treadmill belt 312, 322 speed is dependent upon only the angular motor velocity ( ^^) and is thus a fully closed-loop system. In an exemplary embodiment, the system 100 is configured to independently vary the speed of both belts 312, 322 of the treadmill 300 in a range of speed between -2.6 m / s and 2.6 m / s, which accommodates a range of normal walking speeds by subject 200. The positive and negative speeds denote the ability of the belts 312, 322 to move in two different directions. Thus, the ability to independently vary the stiffness and speed of both belts 312, 322 advantageously permits system 100 to facilitate more types of environments (e.g. different terrains, such as dirt, sand snow, etc.) and conditions to be simulated. Non-limiting applications for system 100 includes rehabilitation for subjects with gait dysfunction, development and validation of controllers for powered prosthetics and legged robots, research of gait mechanisms, exercises for strength and conditioning, and haptic feedback for virtual reality gaming. Turning now to FIG. 8, an exemplary method 2000 of using a variable stiffness treadmill system is disclosed. In an exemplary embodiment, method 2000 is described in context of the variable treadmill system 100 as discussed above. Generally, method 2000 includes steps of placing a user on a variable stiffness treadmill system; measuring a location of an individual with a force sensor mat positioned below a respective belt of a left treadmill platform assembly and / or a right treadmill platform assembly; and adjusting a vertical stiffness of the respective belt of the left treadmill platform assembly and / or the right treadmill platform assembly below the location of the individual with a variable stiffness mechanism. Step 2100 of method 2000 includes placing user 200 on the variable stiffness treadmill system 100. As shown in FIG. 4, user 200 is placed on the variable stiffness treadmill system 100, such that a vertical downward force (e.g. F arrow in FIGS. 4 and 8) is applied to a treadmill 300 of the system 100. Step 2200 of method 2000 includes measuring a location of a user or individual 200. In one non-limiting example, as shown in FIGS. 5B and 6, a force sensor mat 380 is positioned below a respective belt 312, 322 of a left treadmill platform assembly 310 2101715-001236 -15- and / or a right treadmill platform assembly 320. The force sensor mat 380 has a plurality of capacitive sensing cells for the measurement of the distribution of forces (F) applied across the split-belt treadmill 300. Additionally or optionally, the force sensor mat 380 is configured to sense the location of the user 200 on the split-belt treadmill 300. Further, a motor 350a connected to the belt 312 of the left treadmill platform assembly 310 independently drives said belt 312 of the left treadmill platform assembly 310 at a first speed (V1) and the motor 350b connected to the belt 322 of the right treadmill platform assembly 320 independently drives said belt 322 of the right treadmill platform assembly 320 at a second speed (V2). Additionally or optionally, the first speed (V1) is different from the second speed (V2). Step 2300 of method 2000 includes adjusting a vertical stiffness of the respective belt with a variable stiffness mechanism. In one non-limiting example, system 100 is configured to adjust a vertical stiffness of the respective belt 312, 322 with a variable stiffness mechanism (VSM), such as VSM 500, of the left treadmill platform assembly 310 and / or the right treadmill platform assembly 320. Still further, the vertical stiffness is regulated in a position along the belts 312, 322 below the location of the individual 200. In an exemplary embodiment, the vertical stiffness of the split-belt treadmill 300 is regulated in real time. This may be achieved, as discussed above, by adjusting an effective stiffness ( ^^^ௗ) of the split-belt treadmill 300 via the variable stiffness mechanism 500 based on a length of the spring-loaded lever, a position of the sliding joint 540 relative to the length of the spring-loaded lever, a spring coefficient of the first spring and the one or more second springs, or a combination thereof. In an exemplary embodiment, the VSM 500 provides for selecting a degree of stiffness imparted to the split-beam treadmill 300 throughout a gait cycle of the user 200 and for continuous controlling of the stiffness during a stance phase of the user 200. Additionally or optionally, method 2000 includes attaching a body-weight support to the user and mounting the body-weight support to a frame positioned above the split-belt treadmill. In one non-limiting example, method 2000 includes attaching a body-weight support, such as body-weight support 400, to user 200. Further, the body-weight support 400 is mounted to a frame comprising a post 410 engaged to a rail 420, and the height of support 400 relative to the split-belt treadmill 300 is adjustable through an actuator 430 that moves the support 400 vertically. In this way, the height of the support 400 relative to the split-belt treadmill 300 is adjusted to vary the amount of weight of the user 200 being supported by the body-weight support 400. 2101715-001236 -16- Still further, method 2000 includes measuring a distribution of forces (e.g. F arrow in FIGS. 4 and 8) applied across the split-belt treadmill. In this way, linear vertical deflection of the split-belt treadmill 300 is measured as corresponding to the vertical displacement of first belt 312 and the second belt 322 in response to the forces (e.g. F arrow in FIGS. 4 and 8) applied across the split-belt treadmill 300 and the effective stiffness ( ^^^ௗ). The method 2000 disclosed herein is not limited to a type of user 200. Non- limiting examples include an amputee having a prosthesis, a legged robot, an impaired patient, and a healthy subject. When user 200 is the amputee having a prosthesis, the method 2000 further comprises evaluating a prosthesis controller. When user 200 is the legged robot, the method 2000 further comprises evaluating a robot controller. When user 200 is the impaired patient, the method 2000 further comprises providing rehabilitation to the impaired patient. When user 200 is the healthy subject, the method 2000 further comprises studying a gait mechanism or validating a gait model study. EXAMPLE The co-inventors assessed the exemplary systems and methods as disclosed herein in a clinical or laboratory setting, to validate feasibility and functionality of the components of the subject systems, as well as verified any updates or improvements made. Generally, through these validation experiments, the inventive variable stiffness treadmill system (e.g. VST 2.0) was found to display high accuracy and precision. When setting the VST 2.0 to a desired low-stiffness value, embodiments of the VST 2.0 have an error of less than 1% and standard deviations of less than 2.2 kN / m, demonstrating an ability to reliably simulate low-stiffness environments. In general, the variable stiffness treadmill system includes an elevated split-belt treadmill with a left treadmill platform assembly and a right treadmill platform assembly, a variable stiffness mechanism (VSM) operatively connected to the treadmill platform assembly, a counterweight system operatively connected to each treadmill platform assembly, and a plurality of guide rail bearings operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection. System Design Considerations The inventive variable stiffness treadmill system is designed to be bilaterally- compliant with independently adjustable stiffness levels for each belt (e.g. left treadmill platform assembly and right treadmill platform assembly). In contrast, non-limiting examples of prior variable stiffness treadmill systems were only capable of varying the 2101715-001236 -17- stiffness of one of the treadmill platform assembly (e.g. left belt), while the right treadmill platform assembly (e.g. right belt) would remain at a constant stiffness (e.g. rigid). Thus, the inventive variable stiffness treadmill system has bilateral-compliance, which expands gait research possibilities and allows for testing a host of new hypotheses. For example, selecting a (effective) stiffness range a 1 MN / m to 10 kN / m allows for simulating a variety of surfaces from effectively rigid at 1 MN / m to highly compliant at 10 kN / m. In order to more closely match real-world environments, the linear vertical deflection of the loaded treadmill platforms is designed to be vertical (e.g. as opposed to angular deflection). To achieve this, the system allows for 10 cm of maximum linear travel, thereby allowing for the capacity to handle 1 kN of force at a stiffness of 10 kN / m. The 0.07 N / m average stiffness adjustment resolution and 640 ms travel time between rigid and minimum stiffness was found to permit precise and rapid stiffness changes. Further, incorporating a counterweight system ensures that only VSM forces are transmitted to the subject, and ensuring constant static deflection when set to low- stiffness in absence of external forces. As for the design on the elevated split-belt treadmill, treadmill performance, safety and comfort were considered. For example, to accommodate the range of normal walking speeds, the elevated split-belt treadmill is configured to include an exemplary speed range of -2.6 m / s to 2.6 m / s on each treadmill platform assembly (e.g. belt), with positive and negative speed denoting the ability of the treadmill belts to move in two different directions. Additionally, as split-belt treadmills are most commonly used for speed perturbations (i.e. belts moving at different speeds), the inventive variable stiffness treadmill system implements independent variable belt speed and a velocity resolution of 0.1 mm / s. Then, to ensure subject safety and comfort, the treadmill platform height relative to the ground is configured for 45 cm at the highest (e.g. maximum) position. Additionally, the width and length of the treadmill platform assembly are configured to minimally modify the gait of subjects and accommodate the stride length of taller individuals. This is achieved with width of 45 cm and length of 165 cm. Further, the inter-belt distance is minimized to 15 mm. Still further, the variable stiffness treadmill system can include high-spatial-resolution force sensors disposed under each treadmill platform assembly (e.g. belt), which are designed to sense the location of the user on the split-belt treadmill as well as measure the ground reaction forces of the subject’s feet, as sensed in contact with the first belt and the second belt, throughout a phase (e.g. stance phase). 2101715-001236 -18- Regarding the variable stiffness mechanism (VSM), the VSM is configured to independently adjust vertical stiffness of each belt. In one example, the VSM is a third- class lever-based system that modifies the mechanical advantage between the treadmill platform assemblies and a set of fixed stiffness extension springs. This configuration creates a variable effective stiffness at the treadmill platform assembly that is dependent upon a geometric configuration of the system. Also, as shown in FIG. 6 (showing the variable stiffness treadmill system at a minimum stiffness configuration), the treadmill platform assembly is constrained to move vertically by a plurality of guide rail bearings. The treadmill platform assembly is supported by a carriage or a sliding joint, which serves as a movable connection point between the treadmill platform assembly and the VSM by riding on a linear track. Thus, the VSM includes at least one linear actuator adjustable for varying the vertical stiffness of the belt. This at least one linear actuator includes a carriage, linear track, and a motor assembly (e.g. a leadscrew-motor assembly) that permits the carriage to be positioned along a spring-loaded lever operatively (e.g. a lever arm) connected to the linear track. The spring-loaded lever comprises a lever arm having a first lever arm end pivotable about an axle, a second lever arm end attached to a roller, a first spring fixed at one end to the treadmill platform frame above the second lever arm end, wrapped partially around the roller, and affixed at an opposite end to one or more second springs affixed to a bottom of the lever arm, configured such that a vertical downward force applied to the platform causes deflection of the lever arm to extend the first spring with a corresponding extension in the one or more second springs to generate a spring force that acts at the second end of the lever arm to resist the vertical downward force applied to the platform. The effective stiffness ( ^^^ௗ) of the elevated split-belt treadmill is variable based on a length of the spring-loaded lever, a position of the sliding joint along the length of the spring-loaded lever, a spring coefficient of the first and one or more second springs, or a combination thereof. Maximum effective stiffness is achieved when the carriage is placed directly above the first lever arm end pivotable about an axle. When the carriage is in the maximum stiffness configuration, forces applied to the treadmill platform assembly are transferred directly through the carriage, axle, and into the frame of the treadmill platform assembly, resulting in absence of linear vertical deflection. As the carriage is moved away from the first lever arm end and towards the other (e.g. second) lever arm end, the mechanical advantage between the treadmill platform assembly and extension springs increases, resulting in a lower effective stiffness for carriage positions further from the first lever arm end. Thus, at a minimum 2101715-001236 -19- stiffness, the mechanical advantage is at its highest. Thus, for any carriage position other than the maximum stiffness case, a force applied to the treadmill platform assembly results in a linear deflection of the treadmill platform assembly, thereby creating an angular deflection in the VSM and forcing the extension springs to elongate via the spring webbing. This generates a spring force that resists the force applied to the treadmill platform assembly and results in an effective platform stiffness that is proportional to the carriage position and the spring coefficient of the extension springs. A simplified kinematic diagram is shown in FIG. 9A. The VSM along with the treadmill is shown at equilibrium, where the spring is at its equilibrium or rest length. The mechanism can be simplified as shown in FIG. 9B, where the equivalent spring is at its rest length and shown between points M and H. FIG. 10 shows the deflection of the spring under a force F exerted on the treadmill, causing a vertical deflection of the treadmill by LGD. Throughout this analysis, the notation LXY denotes the scalar representing the Euclidean distance between the points X and Y. At this configuration, setting the sum of the torques around point C equal to zero gives: ^^ ൈ ^^ ^^ ^ ^^^^ൈ ^^ ^^ᇱൌ 0 (Equation 1)where ^^ ൌ^0 െ ^^ 0^், is the force exerted to the treadmill perpendicular to its surfacepointing along the inertial reference axis ^^ with magnitude ^^ ^ 0, ^^ ^^ ൌ^^^^^ cos ^^ െ ^^^^ sin ^^ 0^்and ^^ ^^ᇱ ൌ ^ ^^^ுᇱ cos ^^ െ ^^^ுᇱ sin ^^ 0^் are the vectors CDand CH’ expressed with respect to the inertial reference system at C respectively, and^^ ^ 0, while ^^ గ గ ்^ൌ^^^^cos^ଶെ ^^^ ^^^sin^ଶെ ^^^0^= ^ ^^^sin^ ^^^ ^^^cos^ ^^^ 0^் is theforce exerted by the spring. Substituting these expressions in Equation 1, the total torque along the ^^ inertial axis are െ ^^^^^^ுᇱcos^ ^^ െ ^^^ ൌ 0 (Equation 2) The force ^^ ^^ exerted along the direction of the spring is given by: ൌ െ (Equation 3) where ^^^is the stiffness of the spring, ^^ெுis its rest length shown in FIG. 9B and ^^ெுᇱis elongated length as shown in FIG. 5. As illustrated in FIG. 5, we have: 2101715-001236 -20- ^^ெுᇱൌ^ಾಿୡ୭^^ఈ^(Equation 4) where: ^^ெேൌ ^^ெு^ ^^ுே^^ெேൌ ^^ெு^ ^^^ுᇱsin^ ^^^ (Equation 5) Then, from Equations 3, 4, and 5, we have: ^^^ൌ ^^^ ୡ୭^^ఈ^^ (Equation 6) The total effective vertical stiffness of the treadmill ^^^can be expressed as the ratio of the magnitude of the vertical force ^^ exerted over the vertical displacement ^^ீ^, i.e., 7) where ^^ீ^ൌ Solving Equation 2 for we have: ^^ ൌிೞ^^ಹᇲ ୡ୭^^ఈିఏ^^^ವ ୡ୭^^ఏ^(Equation 8) From Equations 8 and 6, and since ^^ீ^ൌ ^^^^sin^ ^^^, Equation 7 is written as: ^^ ൌ ^^^^ಹᇲ ^^ಹᇲ ^୧୬^ఏ^^^^ ^మ ୡ୭^(Equation 9) ^ವ ^ఏ^ ^୧୬^ఏ^ ୡ୭^^ఈ^If we assume that the angle ^^ is very small, i.e., ^^ ≃ 0, then cos^ ^^^ ≃ 1, and ccos^ ^^ െ ^^^ ≃ cos^െ ^^^ ൌ 9 is simplified to: (Equation 10) Equation 10 shows that since ^^^ுᇱis constant and given by design, controlling the effective vertical stiffness of the treadmill can be done by only controlling the distance ^^^^platform is a function of, for example, spring stiffness, lever arm length and the position of the carriage. With the length of the lever arm set, Equation (10) is used to determine the spring stiffness needed to achieve the specified variable stiffness range of 1 MN / m to 10 kN / m. Based on this calculation, a bank of kN / m extension springs in parallel can be implemented, thereby minimum effective stiffness of 8.6 kN / m. The rest of the VSM 1 m lever arm and the two 4.3 kN / m 2101715-001236 -21- springs in parallel. Still further, a 1 m long, 16 mm diameter leadscrew is chosen, which has an advancement of 35 mm per revolution. Additionally, a motor (e.g. Flipsky 6354 motor), is provided, which has a peak power of 2450 W and a peak torque 10 Nm that is sufficient to reliably and quickly move the carriage to vary or change the vertical stiffness levels. Turning to the elevated split-belt treadmill, each of the treadmill platform assembly includes a frame, a belt, and a motor operatively connected to the belt and configured for independently driving the respective belt. The frame is a 50 mm by 25 mm extruded low-carbon steel rectangular tubing of 2 mm thickness and is welded together as a single rigid body for the entire system (shown in FIG. 6). The frame houses multiple bolted interfaces to several other sub-assemblies in strategic positions, namely the plurality of guide rail bearings and the counterweight system. The frame also holds two rows of four gusset brackets that each house a single 30 kg rated threaded rubber bumper of 40A durometer. The platform interfaces with these bumpers both in the event of reaching the maximal deflection of 10 cm and every time the platform returns to resting position from a deflection. The counterweight system (CWS) is required for ensuring the forces acting on the VSM are equal to zero when the treadmill is unloaded. The CWS is configured to travel in the opposite direction of the platform assembly during platform deflection and return when the platform reaches its neutral position. The CWS includes pulley system driven by a roller chain (e.g. a single-strand American National Standards Institute (ANSI) Number 40 roller chain) and connected to opposite ends of each platform assembly. The CWS is equal to the weight of the elevated split-belt treadmill that rests on the top the VSM carriage, with support from the frame. Four individual chain links contain rigid attachments that connect to a custom steel plate welded tray that holds custom-molded and painted lead weights of 34 kg each to precisely offset the 34 kg platform weight. The CWS is attached on both ends of each belt and is centered laterally relative to each belt, resulting in four counterweights in total. The overall vertical deflection of the platforms is measured by a 0.2◦ resolution, 12-bit absolute encoder (AMT222A-V, CUI Devices) at the CWS bearings, offering a direct relationship between CWS rotation and platform deflection. The CWS is connected to opposite ends of each platform assembly through the side panels, which connect the belt and motor system, as well as interfacing with the CWS and plurality of guide rail bearings. These panels are constructed from a 6.35 mm aluminum plate and contain circular screened cut-outs to reduce weight and allow for the viewing of the internal mechanisms of the inventive variable stiffness treadmill 2101715-001236 -22- system. The outer face of the inner side panels contains only countersunk-head fasteners in order to attain a gap between treadmill belts of only 15 mm. In one example, the two side panels are rigidly connected through ten 20 mm solid t-slotted framing rails and through two ultra-strength high carbon steel cylinder belt rollers of 44.5 mm diameter and 2.5 mm wall thickness. The framing rails interface directly with the VSM through another set of VSM linear rails that are rigidly attached, allowing for a single connection point at the carriage at a 20 mm diameter 1566 carbon steel rotary shaft. The belt rollers interface directly with the belt and are doubly supported to each side panel through flanged ball bearings. The side panels also interface with the frame through four stainless steel linear guideway rail bearings at each corner of each side. These bearings constrain the deflection of the treadmill to a single degree of freedom acting as a vertically-oriented prismatic joint, which ensures only vertical deflection and mitigates angular movement due to the VSM lever arm angular motion forces that are inherent in this system. This linear deflection is the most notable and substantial improvement from prior variable stiffness treadmill systems, which instead employs a revolute joint for only rotational deflection. To achieve this, the roller acts as a passive idler and includes a threaded tension mechanism for which to adjust the belt tension. The rear roller acts as the treadmill belt driver and is connected with a 20 mm solid carbon steel keyed shaft to the treadmill drive motor (Flipsky 63100; peak power: 5500 W; peak torque 7 Nm; Flipsky Inc.) through a geared reduction. The reduction consists of two 1045 carbon steel gears of 15 teeth and 100 teeth, respectively, that are completely enclosed by a custom ABS extruded plastic cover. The treadmill drive motor is similar to the VSM motor (Flipsky 6354; peak power: 2450 W; peak torque 10 Nm; Flipsky Inc.), but with a nearly doubled increase in maximum power output to support the continuous treadmill belt load. Finally, the belts chosen are of custom length for this application and originate from a Precor C956i commercial treadmill (Precor Incorporated of Woodinville, WA). The walkable surface area for each belt is 0.74 m2. Directly under each belt is a 20 mm thick particle board that supports the weight of the mass on the treadmill. Additional components of the variable stiffness treadmill system include force sensor mats (e.g., Tekscan™ 3140 with VersaTek™ Cuffs, TekScan Inc. of Norwood, MA) capable of acquiring vertical force measurements using more than 2,000 individual capacitive sensing cells across the treadmill belts, offering a planar resolution of less than 1 cm in both directions (see FIG. 5B). This gives the unique ability to observe both the distribution of forces from the foot and the foot center of pressure. This data is 2101715-001236 -23- streamed live at a frequency of 100 Hz. Further, the system includes a body-weight support mounted to a post and capable of supporting the weight of the user relative to the post, wherein the post is engaged to a rail for mounting the body-weight support, and wherein the body-weight support comprises a harness capable of supporting the weight of the user. In one example, the harness is a custom-made harness-based body weight support (BWS) from Litegait Inc. of Tempe, Arizona. The harness is fastened to the ground at the rear of the system and overhangs directly onto the center of the belts. This system has a maximum subject weight of 140 kg, and the amount of support can be adjusted for the specific application, while its height is adjustable through an actuator that moves the support vertically. For a control system of the variable stiffness treadmill system (e.g. control of the stiffness during a stance phase of the user or subject or throughout a gait cycle), a Python-based control program and Graphical User Interface (GUI) is provided (e.g. to operate and modify the settings or parameters of the belts’ speeds and stiffness. When a new stiffness is requested ^^^ௗ, the program computes the necessary carriage position ( ^^ௗ^^) via Equation 10 and sends it to the motor drivers via a USB connection. The motor drivers include Odrive v3.6 motor controllers, a closed-loop brushless DC motor driver and an active open-source project. When the motor drivers receive a new carriage position, the motor is moved to the target position according to the path created by a configurable trapezoidal trajectory planner. Beneath the trajectory planner, the drivers run a nested position-velocity current control loop that performs closed-loop position control at a frequency of 8 kHz, providing very accurate and consistent position control with zero steady-state position error. Each VSM is powered by a 2450 W BLDC outrunner motor. The motor drivers feed the VSM motors with 48 V and up to 50 A of phase current, resulting in a peak theoretical power consumption of 2.4 kW. Connected to each motor is a 0.25º resolution, 8192 count incremental quadrature encoder (AMT102-V, CUI Devices) which provides position feedback to the Odrive motor drivers in order to close the motor control loop (see FIG. 7A). For a given desired effective stiffness ^^^ௗ, the corresponding desired carriage position ( ^^ௗ^^) is determined via Equation 10, as represented by the function ^^^in FIG. 7A. When the motor arrives at the desired position, the target carriage position ^^^^is achieved, and the platform has a certain deflection according to the force applied and the effective stiffness. This displacement ^^ீ^is measured by the deflection encoders integrated into the CWS which provide feedback on the platform displacement at a frequency of 200 Hz. The applied force ^^^is measured at a rate of 100 Hz by the force sensing mats 2101715-001236 -24- beneath each belt. The final effective stiffness ^^^is a function of the kinematics and dynamics of the system and is dependent upon the applied force ^^^and the platform deflection ^^ீ^. This relationship is captured by the function ^^ଶin FIG. 7A, which outputs the effective stiffness of the system for a given applied force and displacement. Overall, the stiffness control system is open-loop, with no feedback on the actual effective stiffness being used to optimize the performance of the system. This opens up the possibility for discrepancies between the true effective stiffness and desired effective stiffness. However, since the effective stiffness is only a function of the carriage position, this error is mitigated by calibrating the VSM controller using experimental data, a process that is discussed in the following section, along with the VSM performance evaluation. The treadmill belts are controlled in a very similar way to the VSM, with the primary difference being that the treadmills utilize velocity control as opposed to position control (see FIG. 7B). When a new speed ^^ௗis set in the control program, the needed angular velocity at the motor ^^ௗis calculated using function ^^ଷand is sent to the Odrive motor drivers via USB connection. The motor drivers, which are running closed-loop velocity control on the belt motors at a loop frequency of 8 kHz, then drive the belt motors to the desired velocity using pulse-width modulation of 48 V and up to 100 A of current. As with the VSM motors, feedback is provided to the motor drivers by a 0.25º resolution, 8192 count incremental quadrature encoder (AMT102-V, CUI Devices) connected to each belt motor. The true belt speed V is a function of the system dynamics and the angular motor velocity ^^, a relationship which is captured by the inverted function ^^^in FIG. 7B. Unlike the VSM control system which has no feedback on the value of the true effective stiffness, the treadmill belt velocity is dependent upon only the angular motor velocity and thus is a fully closed-loop and accurate system. System Evaluation and Results The inventive variable stiffness treadmill system was evaluated through two preliminary experiments. First, theoretical stiffness values from 10 were compared to stiffness values found experimentally. Second, the step response of the variable stiffness treadmill system was analyzed. Stiffness Evaluation The accuracy of the variable stiffness mechanism (VSM) was first evaluated by comparing experimental results with the theoretical stiffness curve from (10). The discrepancy between the experimental and theoretical curves resulted in a new 2101715-001236 -25- stiffness that will replace Equation 10 in the areas of “useful” stiffness ranges. and results are explained in more detail below. A known weight of 70 kg was used to evaluate the stiffness of a single treadmill platform with the VSM carriage at many different locations. Barbell plates, the weight of which was verified using a scale, were used for the 70 kg weight. This specific weight was chosen as it represents the average weight of all 12 subjects that partook in a recent study on another variably stiffness treadmill system (see V. Chambers and P. Artemiadis, “Using robot-assisted stiffness perturbations to evoke aftereffects useful to post-stroke gait rehabilitation,” Frontiers in Robotics and AI, vol. 9, 2023). The VSM was tested at 25 different locations, taking the carriage across its full travel in increments of one motor rotation or 35 mm of linear travel. At each of the 25 locations, the 70 kg weight was applied to the center of the treadmill platform three times, and an average vertical deflection was taken between the three trials. Instead of physically dropping 70 kg of weight on the treadmill 75 times, the weight was simply left on the top of the treadmill for the entire experiment. The treadmill platform was manually lifted from the front and back until the rubber stoppers that limit its upward movement were fully engaged, ensuring that the VSM was fully unloaded and there was no vertical deflection. The front and back of the treadmill were then dropped simultaneously, allowing for the platform and weights to deflect and arrive at a new vertical position. The deflection was measured via encoders attached to the counterweight system at both the front and back of the platform. For each trial, an average value was taken between both encoders to estimate the deflection at the center of the treadmill. However, for all trials, the difference between front and back encoders was so small that the platform had a pitch angle of less than a quarter of a degree. The resulting experimental stiffness curve can be seen in FIG. 11. The experimental and theoretical stiffness curves agree quite well at low-stiffness values (< 50 kN / m). However, at high stiffness values, the difference is quite large. This could be due in part to the theoretical calculation not accounting for both friction and binding that can occur in a mechanism of this complexity. Additionally, high stiffnesses are far more sensitive to error, due to the corresponding very small deflection values. While there is a large error between experimental and theoretical curves, consistency, or small standard deviations, is far more important as the control architecture or system will simply use a new mapping between carriage position and stiffness level to accurately simulate surfaces of a certain stiffness. It should also be noted that the five data points corresponding to a carriage position of less than 175 mm were omitted from this analysis. The nearly 1.5 MN / m stiffness created at 175 mm is sufficiently 2101715-001236 -26- rigid, and actually more stiff than the prior variable stiffness treadmill systems (see J. Skidmore, A. Barkan, and P. Artemiadis, “Variable stiffness treadmill (VST): System development, characterization, and preliminary experiments,” IEEE / ASME Transactions on Mechatronics, vol. 20, 2015). Reducing the carriage position farther produced diminishing returns as the stiffness did not significantly increase past 1.5 MN / m. For this reason, the carriage will not be used in configurations of less than 175 mm, reducing the overall travel of the carriage and decreasing the time it takes for the treadmill to switch between rigid to minimum stiffness from 800 ms to 640 ms. In operation, each belt functions in either one of two settings: “rigid” or “low- stiffness.” For the “rigid” setting, the VSM will create a surface of high stiffness, simulating walking on a normal treadmill belt. In this case, a value of about 1.5 MN / m was achieved with a carriage position of 175 mm. This stiffness is sufficiently high and much higher than the maximum stiffness achieved in prior variable stiffness treadmill systems (see Skidmore, 2015 cited above). In the “low-stiffness” setting, the VSM will create a surface with a stiffness of less than 125 kN / m. Stiffness values higher than about 125 kN / m result in deflections so small, that they are indistinguishable from the rigid case described above when walking on the inventive variable stiffness treadmill systems. Therefore, stiffness levels between 1.5 MN / m and 125 kN / m will be unused in human experiments and were not discussed or explored any further. Since the “rigid” case and the carriage position to achieve this stiffness have already been found, the region of “low stiffness” values must be investigated. The inset of FIG. 11 shows all experimental stiffness values less than 125 kN / m compared to theoretical stiffness values. The best-fit curve of the experimental data is also shown. This experiment was performed by setting a carriage position to measure stiffness at each position. However, in practice, the inventive variably stiffness treadmill system will be used in the opposite configuration (i.e. a carriage position will be calculated based on a desired stiffness level). Therefore, a new mapping and a replacement to Equation 10, as well as function ^^^in FIG. 7A, is found to be the inverse of the best-fit curve in the inset of FIG. 11 and can be described as: ^^, if "rigid"^^ ^^ ^^ ൌ ^^^^ ^^ ^^^^ ^^, if(Equation 11)^^ "low െ stiffness"where ^^^^is the carriage position in mm as shown in FIG. 10, a is 175.0, b is 3139, c is -0.6062, d is 182.9, ^^^is the effective vertical stiffness of the treadmill platform in kN / m, “rigid” is the maximum treadmill stiffness of about 1.5 MN / m, and “low- stiffness” represents the stiffness levels useful for human experiments, ranging from 2101715-001236 -27- 13 to 125 kN / m. This fit has very little error with an R2 value of 0.9993 and will allow for the generation of accurate low-stiffness surfaces. Step-Response Analysis Using the same protocol as described above with respect to the Stiffness Evaluation, the treadmill platform deflection was tracked over time for four different stiffness levels. Stiffness levels of 20, 32, and 66 kN / m were evaluated as they span a common range of levels used for experiments regarding variable stiffness treadmill systems. Additionally, a stiffness of 13 kN / m was also evaluated since it is the minimum stiffness level of the inventive variable stiffness treadmill in order system. For each of the four different stiffness levels, the treadmill platform deflects, overshoots, and settles back to its desired steady-state value. All four stiffness levels come to rest within 0.6 s, each approaching a distinct steady-state value with an error of less than 1%. Response specifications can be seen for each stiffness level in Table 1. Table 1: Open-Loop Response ^^ௗ ^^^ ^^^ ^^^^^kN / m^ ^s^ ^s^ ^%^13 0.1909 0.5258 0.9262 20 0.1634 0.4770 0.4085 32 0.1337 0.3939 0.3801 66 0.1155 0.3403 0.3430 Using the deflection data shown in FIG. 12 and the weight of the 70 kg mass, the actual stiffness can be calculated and shown with respect to time. In FIG. 13, the ratio between desired stiffness ( ^^ௗ) and actual stiffness ( ^^) is displayed for 13, 20, 32, and 66 kN / m, depicting the behavior of the inventive variable stiffness treadmill system as an open-loop system. It should be noted that since the stiffness response (FIG. 13) is simply a manipulation of the deflection response (FIG. 12), the values in Table 1 accurately describe both responses. To summarize, the validation of the variable stiffness treadmill system shows that it can simulate a wide range of stiffness values with both high accuracy and consistency. Low stiffness values are accurate to within 1% and have a standard deviation of less than 2.2 kN / m. Future experiments with human subjects will further evaluate the variable stiffness treadmill system. This will specifically focus on the 2101715-001236 -28- human response to the perturbations generated on this device with respect to kinematic, muscle activity, and force mat data. Conclusions The inventive variable stiffness treadmill system generates vertical deflection instead of the angular deflection. Second, the inventive variable stiffness treadmill system includes a split-belt treadmill with the capability of altering the stiffness of both belts independently within a range of 13 kN / m to 1.5 MN / m. Also, the speed of the belts is independent as each belt has a dedicated motor. Next, a large walking surface allows for comfortable walking or running. Finally, high-spatial-resolution force mats underneath the treadmill belts allow for the collection of ground reaction forces and the foot center of pressure. From the above-described validation experiments, an experimental stiffness curve was found by applying a 70 kg mass to the treadmill platform with the carriage at multiple different positions. This allowed for a comparison between the theoretical and experimental stiffness curves. The discrepancy between these curves led to a remapping of the relationship between carriage position and stiffness, by fitting a non- linear curve to the “usable” portion of the experimental data (R2 = 0.9993). This new mapping was then validated through a step-response analysis, showing that the inventive variable stiffness treadmill system generates a desired stiffness with less than 1% error and less than a 2.2 kN / m standard deviation, proving high accuracy and repeatability. With high accuracy and precision, along with the additional upgrades and features, the inventive variable stiffness treadmill system provides significant value in the areas of biomechanics, robotics, rehabilitation, and motor control. More specifically, the wide range of stiffnesses generated by the inventive variable stiffness treadmill system can be used to test rehabilitation protocols involving split-belt stiffness and / or speed perturbations, as well as test legged robots in many of the terrains they would experience in the real world. Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention. 2101715-001236 -29- What is claimed: 1. A variable stiffness treadmill system comprising: an elevated split-belt treadmill comprising a left treadmill platform assembly and a right treadmill platform assembly, each treadmill platform assembly comprising a frame, a belt, and a motor operatively connected to the belt and configured for independently driving the respective belt; a variable stiffness mechanism (VSM) operatively connected to the frame of each treadmill platform assembly and configured to independently adjust vertical stiffness of each belt, the VSM comprising at least one linear actuator adjustable for varying the vertical stiffness of the belt; a counterweight system operatively connected to each treadmill platform assembly to counterbalance the weight of the treadmill platform assembly acting on the VSM in an unloaded configuration of the treadmill platform, the counterweight system comprising a pulley system driven by a roller chain and connected to opposite ends of each platform assembly, and a plurality of guide rail bearings operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection. 2. The variable stiffness treadmill system of claim 1, wherein the at least one linear actuator includes: a linear track; a spring-loaded lever operatively connected to the linear track; and a sliding joint driven by a motor assembly and moveable along the linear track operatively connected to the spring-loaded lever. 3. The variable stiffness treadmill system of claim 2, wherein the spring-loaded lever comprises a lever arm having a first lever arm end pivotable about an axle, a second lever arm end attached to a roller, a first spring fixed at one end to the treadmill platform frame above the second lever arm end, wrapped partially around the roller, and affixed at an opposite end to one or more second springs affixed to a bottom of the lever arm, configured such that a vertical downward force applied to the platform causes deflection of the lever arm to extend the first spring with a corresponding extension in the one or more second springs to generate a spring force that acts at the

Claims

2101715-001236 -30- second end of the lever arm to resist the vertical downward force applied to the platform.

4. The variable stiffness treadmill system of claim 3, wherein an effective stiffness ( ^^^ௗ) of the elevated split-belt treadmill is variable based on a length of the spring- loaded lever, a position of the sliding joint along the length of the spring-loaded lever, a spring coefficient of the first and one or more second springs, or a combination thereof.

5. The variable stiffness treadmill system of claim 4, further comprising: at least one encoder operatively connected to the split-belt treadmill or the variable stiffness mechanism.

6. The variable stiffness treadmill system of claim 5, wherein each treadmill platform assembly comprises a force sensor mat including a plurality of capacitive sensing cells for the measurement of the distribution of forces applied across the split- belt treadmill.

7. The variable stiffness treadmill system of claim 6, wherein the force sensor mat is configured for sensing the location of the user on the split-belt treadmill and in contact with the first belt and the second belt.

8. The variable stiffness treadmill system of claim 5, wherein each treadmill platform assembly comprises deflection encoders integrated with the counterweight system for the measurement of the linear deflection of the split-belt treadmill corresponding to the vertical displacement of the split-belt treadmill in response to the forces applied to across the split-belt treadmill and the effective stiffness ( ^^^ௗ).

9. The variable stiffness treadmill system of claim 1, further comprising a body- weight support mounted to a post and capable of supporting the weight of the user relative to the post, wherein the post is engaged to a rail for mounting the body-weight support, and wherein the body-weight support comprises a harness capable of supporting the weight of the user.

10. A method of using a variable stiffness treadmill system comprising: placing a user on the variable stiffness treadmill system of any one of claims 1- 9;2101715-001236 -31- measuring the location of the individual with a force sensor mat positioned below the respective belt of the left treadmill platform assembly and / or the right treadmill platform assembly; and adjusting the vertical stiffness of the respective belt of the left treadmill platform assembly and / or the right treadmill platform assembly below the location of the individual with the variable stiffness mechanism.

11. The method of claim 10, further comprising regulating the stiffness of the split- belt treadmill in real time.

12. The method of claim 11, further comprising adjusting an effective stiffness ( ^^^ௗ) of the split-belt treadmill via the variable stiffness mechanism based on a length of the spring-loaded lever, a position of the sliding joint relative to the length of the spring- loaded lever, a spring coefficient of the first spring and the one or more second springs, or a combination thereof.

13. The method of claim 12, further comprising: attaching a body-weight support to the user; mounting the body-weight support to a frame positioned above the split-belt treadmill.

14. The method of claim 13, wherein the height of the support relative to the split- belt treadmill is adjusted to vary the amount of weight of the user being supported by the body-weight support.

15. The method of claim 10, further comprising: measuring a distribution of forces applied across the split-belt treadmill.

16. The method of claim 10, further comprising: measuring the linear deflection of the split-belt treadmill corresponding to the vertical displacement of first belt and the second belt in response to the forces applied across the split-belt treadmill and the effective stiffness ( ^^^ௗ).

17. The method of claim 10, wherein the variable stiffness mechanism provides for selecting degree of stiffness imparted to the split-beam treadmill throughout a gait cycle of the user and for continuous controlling of the stiffness during a stance phase of the user.

18. The method of claim 10, wherein the user comprises one of:2101715-001236 -32- an amputee having a prosthesis, wherein the method further comprises evaluating a prosthesis controller; a legged robot, wherein the method further comprises evaluating a robot controller; a impaired patient, wherein the method further comprises providing rehabilitation to the impaired patient; or a healthy subject, wherein the method further comprises studying a gait mechanism or validating a gait model study.

19. The variable stiffness treadmill system of claim 1, wherein the motor connected to the belt of the left treadmill platform assembly independently drives said belt of the left treadmill platform assembly at a first speed and the motor connected to the belt of the right treadmill platform assembly independently drives said belt of the right treadmill platform assembly at a second speed.

20. The variable stiffness treadmill system of claim 19, wherein the first speed is different from the second speed.2101715-001236 -33- ABSTRACT A variable stiffness treadmill system is disclosed. An elevated split-belt treadmill has a left treadmill platform assembly and a right treadmill platform assembly, each includes a frame, a belt, and a motor for independently driving the respective belt. A variable stiffness mechanism (VSM) is operatively connected to the treadmill platform assembly and adjusts vertical stiffness of each belt. The VSM has at least one linear actuator adjustable for varying the vertical stiffness of each belt. A counterweight system is operatively connected to each treadmill platform assembly to counterbalance the weight of the treadmill platform assembly acting on the VSM in an unloaded configuration of the treadmill platform. The counterweight system has a pulley system driven by a roller chain and connected to opposite ends of each platform assembly. A plurality of guide rail bearings is operatively connected to the split-belt treadmill for constraining the split-belt treadmill to linear vertical deflection.

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