US20180339196A1 - Powered machine and control method - Google Patents

Abstract

An exercise system includes a motor, a chain having a first end connected to the motor, and a handle or seat connected to a second end of the chain, and a control system to obtain variable mechanical resistance with continuous variation. The system may enable unrestricted type of resistance, including adjustable ratios of concentric/eccentric power.

Description

• This application claims the benefit of U.S. Provisional Application No. 62/511,426, filed May 26, 2017 and titled “POWERED MACHINE AND CONTROL METHOD WITH PROGRAMMABLE MECHANICAL IMPEDANCE FOR CONCENTRIC-ECCENTRIC HUMAN EXERCISE”, which is hereby incorporated by reference in its entirety.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH
• This invention was made with government support under Grant No. 1544702 awarded by the National Science Foundation. The government has certain rights in the invention.
BACKGROUND
• Conventional rowing machines store part of the user's energy in a flywheel and a return spring and dissipate the rest in an adjustable air damper. The limitations present in current machines are the fixed inertia, limited damping adjustments and an unloaded return stroke.
• The absence of a significant load during the return stroke precludes an important modality known as eccentric exercise. Muscles are able to provide positive and negative power corresponding to contraction and lengthening under load, respectively.
• On one hand, shortening corresponds to muscles delivering work to a load, for example when lifting a weight. On the other hand, lengthening corresponds to the load returning energy to the muscles, for example when lowering a weight in a slow and controlled motion. An effective workout encompasses a combination of exercises that include concentric and eccentric actions.
• It has been suggested that eccentric exercise produces microdamage that can lead to muscle remodeling and growth. Eccentric loading is important in the microgravity environment to make exercise sessions shorter and more effective. One of the greatest challenges to humans operating in space for long periods of time is that they have to deal with the substantial alteration of the musculoskeletal loading and muscle toning which has repercussions on their muscles and bones responding by losing mass proportional to the time of exposition to the microgravity. Weight lifting may not be used to produce significant loading during spaceflight. The detrimental effects of microgravity must be addressed with machines capable of producing controlled concentric and eccentric loading.
• A conventional air resistance rowing machine (also called rowing ergometer) is composed of a flywheel connected to a pull chain through a ratchet mechanism also referred to as one-way clutch or freewheeling clutch. A fan with variable vent openings rotates with the flywheel and provides the only resistance adjustments in these machines. The chain is connected to a return spring with small stiffness, used to facilitate chain rewind during the return phase.
• In the pull phase, the user applies force to add momentum to the flywheel, overcoming air resistance and the restoring force of the spring. The one-way clutch is coupled and the chain, sprocket and flywheel move as a unit. When the end of the stroke is reached, the user reverses motion and the force on the chain is reduced, equaling only the force due to the spring. The clutch becomes decoupled and the flywheel decelerates due to air resistance, while the chain and sprocket rotate in the opposite direction. At the end of the return phase the user reverses motion again, causing the clutch to re-engage and initiate a new pull phase.
• It would be desirable to develop new machines (e.g., rowing-type machines) and methods for exercise.
BRIEF DESCRIPTION
• The new technology addresses the deficiencies discussed above by including a motor, force and position sensors and a control method to obtain variable mechanical resistance with continuous variation and unrestricted type of resistance, including adjustable ratios of concentric/eccentric power. The powered machine can also closely replicate the operation of conventional ergometers.
• The control system may be designed on the basis of the innovative concept of virtual flywheel and clutch and hybrid impedance control.
• Disclosed, in some embodiments, is an exercise system including: a motor; a sprocket; a belt transmission connecting the motor and the sprocket; a control system for controlling the motor; a chain having a first end and a second end, the first end connected to the sprocket; and a handle attached to the second end of the chain.
• The control system may include a controller and at least one of: a first sensor configured to measure handle force and a second sensor configured to measure sprocket velocity.
• In some embodiments, the exercise system further includes a foot pad; a rail; and a seat slidably engaged with the rail.
• The handle may be releasably attached to the second end of the chain; and the seat may be configured to receive the second end of the chain.
• In some embodiments, the exercise system further includes a cover, wherein the cover at least partially encloses the motor, sprocket, and belt transmission.
• The control system may be configured to switch between a concentric phase and an eccentric phase.
• In some embodiments, the control system is configured to provide dynamic variable resistance.
• The exercise system may further include a display unit including a processor, a display, and a user interface.
• In some embodiments, the controller is configured to adjust the resistance depending on a probability of injury at different handle positions.
• The control system may include an impedance controller.
• Disclosed, in other embodiments, is an exercise system including: a motor; a sprocket; a belt transmission connecting the motor and the sprocket; a control system for controlling the motor; a chain having a first end and a second end, the first end connected to the sprocket; a seat attached to the second end of the chain; a rail; and a foot pad. The seat may be slidably engaged with the rail.
• In some embodiments, the exercise system further includes at least one roller between the seat and the rail.
• The exercise system may further include a handle. The seat may be releasably attached to the second end of the chain; and the handle may be configured to receive the second end of the chain.
• In some embodiments, the exercise system further includes a cover, wherein the cover at least partially encloses the motor, sprocket, and belt transmission.
• The control system may be configured to switch between a concentric phase and an eccentric phase.
• In some embodiments, the control system is configured to provide dynamic variable resistance.
• The exercise system may further include a display unit including a processor, a display, and a user interface.
• In some embodiments, the controller is configured to adjust the resistance depending on a probability of injury at different handle positions.
• The control system may include an impedance controller.
• Disclosed, in further embodiments, is a method for retrofitting an exercise machine. The method includes removing a flywheel; and providing a motor and a control system.
• These and other non-limiting characteristics are more particularly described below.
BRIEF DESCRIPTION OF THE DRAWINGS
• The following is a brief description of the drawings, which are presented for the purposes of illustrating the exemplary embodiments disclosed herein and not for the purposes of limiting the same.
• FIG. 1 is a flowchart for visualizing the operation of an exercise system in accordance with some embodiments of the present disclosure.
• FIG. 2 is a side view of an exercise machine in accordance with some embodiments of the present disclosure.
• FIG. 3 is a side view of another exercise machine in accordance with some embodiments of the present disclosure.
• FIG. 4 is a black and white photograph of a portion of an exercise machine in accordance with some embodiments of the present disclosure.
• FIG. 5 is a black and white photograph of an exercise machine in accordance with some embodiments of the present disclosure during use.
DETAILED DESCRIPTION
• A more complete understanding of the systems, methods, and products disclosed herein can be obtained by reference to the accompanying drawings. These figures are merely schematic representations based on convenience and the ease of demonstrating the existing art and/or the present development, and are, therefore, not intended to indicate relative size and dimensions of the assemblies or components thereof.
• Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. In case of conflict, the present document, including definitions, will control. Preferred methods and materials are described below, although methods and materials similar or equivalent can be used in practice or testing of the present disclosure. The materials, methods, and articles disclosed herein are illustrative only and not intended to be limiting.
• The singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise.
• As used in the specification and in the claims, the term “comprising” may include the embodiments “consisting of” and “consisting essentially of.” The terms “comprise(s),” “include(s),” “having,” “has,” “can,” “contain(s),” and variants thereof, as used herein, are intended to be open-ended transitional phrases that require the presence of the named components/steps and permit the presence of other components/steps. However, such description should be construed as also describing compositions, mixtures, or processes as “consisting of” and “consisting essentially of” the enumerated components/steps, which allows the presence of only the named components/steps, along with any impurities that might result therefrom, and excludes other components/steps.
• Unless indicated to the contrary, the numerical values in the specification should be understood to include numerical values which are the same when reduced to the same number of significant figures and numerical values which differ from the stated value by less than the experimental error of the conventional measurement technique of the type used to determine the particular value.
• All ranges disclosed herein are inclusive of the recited endpoint and independently combinable (for example, the range of “from 2 to 10” is inclusive of the endpoints, 2 and 10, and all the intermediate values). The endpoints of the ranges and any values disclosed herein are not limited to the precise range or value; they are sufficiently imprecise to include values approximating these ranges and/or values.
• As used herein, approximating language may be applied to modify any quantitative representation that may vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about” and “substantially,” may not be limited to the precise value specified, in some cases. The modifier “about” should also be considered as disclosing the range defined by the absolute values of the two endpoints. For example, the expression “from about 2 to about 4” also discloses the range “from 2 to 4.” The term “about” may refer to plus or minus 10% of the indicated number. For example, “about 10%” may indicate a range of 9% to 11%, and “about 1” may mean from 0.9-1.1.
• For the recitation of numeric ranges herein, each intervening number there between with the same degree of precision is explicitly contemplated. For example, for the range of 6-9, the numbers 7 and 8 are contemplated in addition to 6 and 9, and for the range 6.0-7.0, the number 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, and 7.0 are explicitly contemplated.
• The efficiency of an exercise regime is based on several aspects such as human dynamics (postures and coordination of body segments) and on the versatility that the machine can provide. The proposed control system attempts to solve the problems of the low versatility on the conventional machines and also to provide additional benefits such as the ability to operate in the microgravity environment.
• The operation of the control system can be summarized as follows: there are two discrete states: coupled (pull phase) and decoupled (return phase). An impedance regulator is used during the pull phase to provide the force-velocity characteristic corresponding to a flywheel, a nonlinear damper and a small spring action. The force along the pull chain is monitored in this mode. Near the end of the pull stroke, when the force crosses a lower threshold, a transition to the decoupled mode is triggered. The target impedance of the regulator is switched to provide a very low inertia and damping, along with the spring action. At the same time, a real-time simulation of the flywheel is started, mimicking a decelerating flywheel in a conventional machine. The user reverses motion and returns to the starting position and initiates a new pull phase. When the velocity of the chain rises above the velocity of the virtual flywheel, the coupled mode is re-engaged, and the entire cycle repeated. The discrete transition law where one transition is dictated by force and the opposite transition by velocity. In the systems of the present disclosure, the operation of a physical one-way clutch may be replicated entirely by means of control.
• One embodiment of a controller was implemented in real time and successfully tested in its ability to reproduce the operation and “feel” (as judged by an experienced rower) of the original machine. Arbitrary impedance settings were also tested for both pull and return phases, giving the machine great versatility.
• The impedance controller may rely on position, velocity and force feedback, along with a nominal mathematical model of the motor and drive system. Because of modeling errors, target impedances can be achieved accurately by incorporating robustness or adaptation in the controller. A variable-structure (sliding mode) impedance controller may be modified for this problem to account for hybrid dynamics and to allow the specification of nonlinear damping in the target impedance.
• The powered exercise machine may permit the same movements (degrees of freedom) as a conventional rowing ergometer. A sliding seat, a foot rest, and a pull handle are used. However, the pull chain may be connected to an electric motor using a belt transmission. The forces and the force-position-velocity characteristics of the systems and methods of the present application may be programmable across a continuous range, a feature not found in any other exercise machine. The motor may be controlled with a torque-mode servo amplifier, using handle force and chain sprocket velocity as sensors.
• The control system can be used to emulate the operation of a conventional rower by digital means, using the innovative concepts of virtual clutch and virtual flywheel. Moreover, eccentric loading can be activated by changing certain operating parameters in the digital control system. Further, the mechanical resistance of the machine can be programmed to enable exercises unlike rowing.
• For instance, the resistance can be adjusted to replicate the action of an elastic band, a deadweight, a mechanical shock absorber or combinations of the same, with proportions adjusted over continuous ranges.
• The machine may include a redundant safety system, including overspeed and excessive force (software-triggered) and/or user-triggered safety stops.
• The frame of the machine may be similar to that of a conventional ergometer. The flywheel, fan and casing found in a conventional machine are removed, leaving only the sprocket, chain and shock cord. The sliding seat and inclined track may be maintained. These components may be redesigned or conventional.
• The system may include the following hardware components: a load cell mounted between the handle and the chain, a servomotor (e.g., a 1 kW servomotor) and bracket mounted on the underside of the seat track, a timing pulley attached to the servomotor, a timing pulley attached to the sprocket shaft and a timing belt. Electrical components may include a load cell signal conditioner, a servo amplifier, ancillary power supplies, switches and relays, a line filter, and/or connecting cables. The servomotor may be fitted with a rotary incremental encoder.
• The control method may be hosted by any suitable data acquisition and control hardware with real-time capability and sufficient number and type of input/output channels.
• The control system may establish the transitions between the pull and return phases of the rowing exercise according to real-time sensor feedback. Within each phase, the control system produces the mechanical impedances that have been programmed. The virtual clutch feature creates mechanical coupling between the user and the virtual flywheel during the pull phase. In the return phase, the virtual clutch decouples the user from the virtual flywheel.
• Starting with the pull phase, the user applies force on the handle and extends his legs, as in a conventional rowing ergometer exercise. The control system produces the mechanical impedance that has been programmed for the pull phase, while monitoring the force on the load cell. When the user reaches the end of the pull phase and the force crosses a lower threshold, the control system transitions to the return phase and produces the mechanical impedance that has been programmed for the return phase. At the time of the transition, a real-time simulation of a flywheel is started, using the sensed sprocket velocity as an initial condition. The simulation allows the virtual flywheel to decelerate under the action of a damping function, which is also programmable. The velocities of the sprocket and virtual flywheel are monitored during the return phase, and a relative velocity is calculated. The user reaches the end of the return stroke and reverses motion. When the relative velocity crosses an upper threshold, the pull phase is established and the cycle is repeated.
• Within each mode, the controller generates motor torque commands through a robust impedance control algorithm. This algorithm may be changed by programming.
• System operation can be visualized with the flowchart of FIG. 1.
• FIG. 2 illustrates a non-limiting embodiment of an exercise machine 100 in accordance with some embodiments of the present disclosure. The machine 100 includes a rail section 110 and a second section 150 supported with supports 101. A seat 120 is slidably engaged with the rail section 110 via rollers 121. The machine 100 is configured for a user to sit on the seat 120 with his or her feet in a feet pad 130. The user can grab a handle 145 which is attached to a chain 140. The chain 140 is connected to a sprocket 160. The sprocket 160 is in communication with a motor 170 via a belt transmission 180. The machine also includes a display unit 190 which may display one or more performance or biometric characteristics. In some embodiments, the chain 140 may be detached from the handle 145 and attached to the seat 120.
• FIG. 3 illustrates another non-limiting embodiment of an exercise machine 200 in accordance with some embodiments of the present disclosure. The machine 200 includes a rail section 210 and a second section 250 supported with supports 201. A seat 220 is slidably engaged with the rail section 210 via rollers 221. The machine 200 is configured for a user to sit on the seat 220 with his or her feet in a feet pad 230. The seat 220 is attached to a chain 240. The chain 240 is connected to a sprocket 260. The sprocket 260 is in communication with a motor 270 via a belt transmission 280. The machine also includes a display unit 290 which may display one or more performance or biometric characteristics.
• The machine 100, 200 may further include a biometric unit for sensing one or more biometric/metabolic characteristics of a user (e.g., heart rate). The machine 100, 200 may include a user-activated stop button. In some embodiments, the system is configured to stop or slow down when the biometric characteristic passes a predetermined threshold value.
• Non-limiting examples of applications for which the systems and methods of the present application may be useful include:
• • Athletic training: eccentric exercise is known to enhance conditioning due to higher force production at smaller energy expenditure.
  • Rehabilitation: resistance can be suited to the needs of injured individuals. Also, eccentric exercise provides protection from injury or re-injury in older populations.
  • Exercise in microgravity: eccentric exercise leads to faster gains in muscle mass and power, which signifies a more efficient use of crew time.
  • Research labs studying exercise physiology.
• Non-limiting examples of the advantages of the systems and methods of the present application include:
• • Infinitely-variable mechanical impedance by programming
  • Adjustable impedance.
  • Redundant safety system, with triggers from user, observer and software.
  • Online calculation and display of human performance indicators such as velocity, force, average and peak eccentric, concentric and total power and average cadence.
  • Extended programmability for autonomous impedance modulation
• The exercise systems and methods of the present disclosure may exhibit enhanced versatility and/or be suitable for use in a microgravity environment.
• The following examples are provided to illustrate the devices and methods of the present disclosure. The examples are merely illustrative and are not intended to limit the disclosure to the materials, conditions, or process parameters set forth therein.
Examples
• Hybrid Dynamic Model
• The ability to replicate the behavior of a conventional ergometer was set as a first design requirement for the powered machine. A mathematical model capturing the force-velocity dynamics of the standard rower as well as the discrete transitions between coupled and decoupled modes was developed.
• A conventional rowing machine mechanism. The system includes of a flywheel joined to a one-way clutch and connected to a sprocket through a chain and a return spring. The clutch is modeled as an ideal element with coupled and decoupled modes and an instantaneous transition between them.
• A discrete state variable was introduced to designate the coupled and decoupled modes present arising due to the one-way clutch. The dynamics of the continuous state variables depend on the discrete state.
• The discrete state corresponding to the coupled mode is labeled “0” (q=0). The system has only one degree of freedom, with two continuous state variables as follows:
• $\begin{array}{cc}{x}_1=\frac{x_2}{M_h}& \left(\mathrm{Eq}.1\right)\\ x_2=\left({\mathrm{Fr}}_s-K_sr_sx_1-\phi \left(\frac{x_2}{M_h·r_s}\right)\right)\frac{M_h·r_s}{M_h·r_s^2+J_F}& \left(\mathrm{Eq}.2\right)\end{array}$
• wherein x₁ is the linear position of the handle and x₂ its momentum. Function Φ represents friction, modeled as a linear and a quadratic damper with the following representation:
• 
  ϕ(w)=C _F w ² +b _F w  (Eq. 3)
• In this mode, the angular velocity of the flywheel is equal to the angular velocity of the sprocket.
• The discrete state in the decoupled mode is labeled “1” (q=1) and the system has an additional degree of freedom, which contributes an additional continuous state variable. The state derivatives are given by:
• $\begin{array}{cc}{x}_1=\frac{x_2}{M_h}& \left(\mathrm{Eq}.4\right)\\ x_2=F-K_sx_1& \left(\mathrm{Eq}.5\right)\\ x_3=-\phi \left(\frac{x_3}{J_F}\right)& \left(\mathrm{Eq}.6\right)\end{array}$
• where x₃ is the angular momentum on the flywheel and f is the same friction function used for the coupled mode. In this mode, the angular velocities of the flywheel and sprocket are no longer the same.
• The torque transmitted by the clutch and the relative speed between flywheel and sprocket are used to dictate the transitions of the discrete state. The transmitted torque in the coupled mode is F_tr_s, where the corresponding force can be derived from the model as:
• $\begin{array}{cc}{F}_t=\frac{\left(F-x_1K_s\right)J_{F}}{M_hr_s^2+J_F}-\phi \left(\frac{x_2}{M_h}\right)\frac{M_hr_s}{M_hr_s^2+J_F}& \left(\mathrm{Eq}.7\right)\end{array}$
• Likewise, the relative speed in the decoupled mode is:
• $\begin{array}{cc}{\omega }_{\mathrm{flywheel}}-{\omega }_{\mathrm{sprocket}}=\frac{x_3}{J_f}-\frac{x_2}{M_hr_s}& \left(\mathrm{Eq}.8\right)\end{array}$
• If the system starts in the coupling mode. When the transmitted torque (Eq. 7) reaches a small threshold value F_TH, the discrete state changes to decoupled. The transition from coupled to decoupled occurs at the end of the pull phase, when the user is about to reverse motion back to the starting point. The flywheel is decoupled and decelerates because of air friction. The user then reaches the end of the return stroke and reverses motion. When the relative speed reaches a small threshold, the clutch is reengaged and the cycle repeats. The transition laws can be summarized as follows:
• $\begin{array}{cc}{q}_{\mathrm{next}}=\{\begin{array}{cccc}1& q_{\mathrm{prev}}=0& \mathrm{and}& F_i<F_{\mathrm{TH}}\\ 0& q_{\mathrm{prev}}=1& \mathrm{and}& \left({\omega }_{\mathrm{flywheel}}-{\omega }_{\mathrm{sprocket}}\right)<{\omega }_{\mathrm{TH}}\end{array}& \left(\mathrm{Eq}.9\right)\end{array}$
• where F_TH and ω_TH are thresholds adjusted by simulation or experiment.
• Parameter Estimation
• A series of experiments were conducted to estimate the parameters of the conventional rowing machine, as well as gather data concerning the human performing the exercise. Parameters were estimated by a direct collocation method. The estimated parameters, including quadratic damping coefficients for three air vent settings (low, medium and high) are listed in Table 1.

• 	TABLE 1
  	Parameter	Value	Units

  	Sprocket radius (rs)	13.5	mm
  	Handle mass (Mh)	1	kg
  	Spring stiffness (Ks)	14.85	N/m
  	FW inertia (JF)	885	kg · cm2
  	FW linear friction (bF)	9.1e−4	N · m · s
  	FW low quadratic friction (CF)	9e−5	N · s2 · m
  	FW medium quadratic friction (CF)	12.75e−5	N · s2 · m
  	FW high quadratic friction (CF)	22.2e−5	N · s2 · m

• Likewise, parameters were identified for the motorized ergometer. FIG. 4 the drive mechanism of the motorized machine. The dynamic model for torque-mode servo amplifier, motor and belt transmission is given by:
• 
  τ=M{umlaut over (x)}+C{dot over (x)}−F  (Eq. 10)
• where x is the linear displacement of the handle (tangential to the sprocket in the direction of motion) and τ is the control torque applied by the motor:
• $\begin{array}{cc}\tau =\left(\frac{K_m}{n}\right)u& \left(\mathrm{Eq}.11\right)\end{array}$
• where K_m is a motor and servo amplifier constant, n is the effective transmission ratio, u is the analog control input voltage to the servo amplifier and M and C are inertia and friction parameter respectively. These parameters are defined as
• $\begin{array}{cc}M=\left(\frac{J_T}{n^2}\right)& \left(\mathrm{Eq}.12\right)\end{array}$
• where J_T is the inertia of motor and pulleys reflected to the linear coordinate; and
• $\begin{array}{cc}C=\left(\frac{b_T}{n^2}\right)& \left(\mathrm{Eq}.13\right)\end{array}$
• where b_T is the damping of motor and pulley bearings reflected to the linear coordinate. Finally, F is the tension force on the chain.
• By using Eqs. 11-13 and computing {umlaut over (x)} from Eq. 10, the linear acceleration can be obtained as:
• $\begin{array}{cc}\ddot{x}=\frac{{\mathrm{Fn}}^2}{J_T}+\frac{K_mn}{J_T}u-\frac{b_T}{J_T}\stackrel{.}{x}& \left(\mathrm{Eq}.14\right)\end{array}$
• Controller Design
• An impedance controller based on direct model inversion was first designed to qualitatively replicate the behavior of the original ergometer and provide a proof of concept. Due to parametric uncertainties associated with the model of the powered machine, the inverse dynamics controller cannot guarantee achievement of the target impedances. Therefore a robust impedance controller was selected from the existing literature and suitably modified for application to this system.
• The controller was developed in order to target the following generic impedance:
• 
  M _d {umlaut over (x)}+B _d {dot over (x)}+C _d {dot over (x)} ² +K _d x=F  (Eq. 15)
• where M_d, B_d, C_d, and K_d are the desired inertia, linear damping, quadratic damping and stiffness respectively. The values of the target impedance parameters are switched between two values, according to q. In particular, the pull phase involves high M_d (replicating the inertia of the flywheel) and a nonzero value for C_d. The return phase, in contrast uses a much smaller value of M_d (replicating the inertia of the sprocket) and C_d=0 (air damping is not felt by the user in the return phase, since the flywheel is decoupled). The stiffness K_d represents the return spring and is active in both modes. Likewise, the linear damping B_d represents friction in the sprocket, active in both phases.
• Computing {umlaut over (x)} from Eq. 15, the linear acceleration associated with the target impedance is:
• $\begin{array}{cc}\ddot{x}=\frac{1}{M_d}\left(F-K_dx-B_d\stackrel{.}{x}-C_d{\stackrel{.}{x}}^2\right)& \left(\mathrm{Eq}.16\right)\end{array}$
• Equating the accelerations of Eq. 16 and Eq. 14 and defining the inertia ratio by Γ=J_τ/(M_dn²), the control law for the motor torque becomes:
• $\begin{array}{cc}\tau =\left(\frac{b_T}{n^2}-\Gamma B_d\right)\stackrel{.}{x}-C_d{\stackrel{.}{x}}^2-K_d\Gamma x+F\left(\Gamma -1\right)& \left(\mathrm{Eq}.17\right)\end{array}$
• Starting in the coupled mode, the corresponding set of target impedance parameters are used. The discrete transition law is implemented on the basis of load cell and velocity feedback. When q transitions to the decoupled mode, a real-time simulation of the flywheel is started using the sensed velocity at the time of transition as initial condition. This is accomplished with a reset integrator triggered by transitions to the decoupled mode. At the same time, the target impedance parameters are switched to the set corresponding to the return phase. Due to the decrease in inertia and damping and the continued use of the spring constant, the user is able to return to the initial position, as the virtual flywheel decelerates under the action of quadratic damping (air) and linear damping (bearings). The user then reverses motion, accelerates and eventually “catches up” with the virtual flywheel. A transition to the coupled mode is triggered and the cycle is repeated.
• Note that C_d=0 in the return phase and that the velocity of the virtual flywheel is always positive. Therefore the quadratic damping term does not require a sign correction to represent energy dissipation.
• Due to errors in modeling and parametric estimation of the powered mechanism the target impedance is not expected to match the target. The controller may include some changes required to allow for a nonlinear target impedance (quadratic damper) which is also switched according to q. Only an outline of the control law calculations is presented here.
• The control torque required to achieve the desired impedance is specified as:
• 
  τ_R ={circumflex over (M)}{umlaut over (x)} _eq +Ĉ{dot over (x)} _eq −T _d −Ds−ε·sgn(s)−F  (Eq. 18)
• where {circumflex over (M)} and Ĉ are estimated (nominal) values for the corresponding parameters in Eq. (10); {dot over (x)}_eq and {umlaut over (x)}_eq are the equivalent linear velocity and acceleration calculated as:
• 
  {dot over (x)} _eq =−F ₁ ·x−F ₂ z  (Eq. 19)
• 
  {umlaut over (x)} _eq =−F ₁ ·{dot over (x)}−F ₂ ż  (Eq. 20)
• where F₁ and F₂ are arbitrary but nonzero and z is a compensator state defined by the dynamics
• 
  ż=Az+K _pz x+K _vz {dot over (x)}+K _qz {dot over (x)} ² +K _fz F  (Eq. 21)
• where A is arbitrary and negative and constants K_pz, K_vz, K_qz, and K_fz will be selected to achieve the target impedance. The sliding function is defined as
• 
  s(x,{dot over (x)},z)={dot over (x)}+F ₁ x+F ₂ x  (Eq. 22)
• T_d is selected as
• 
  T _d=(δM|{umlaut over (x)} _eq |+δC|{dot over (x)} _eq|)sgn(s)  (Eq. 23)
• where δM and δC are upper bounds on the parametric errors on M and C, respectively. Constants D and ε are positive tuning gains.
• The above control law guarantees that s will converge to zero in finite time and a sliding mode is established. If K_pz, K_vz, and K_qz are selected as below, a derivation shows that the target impedance of Eq. 15 is attained once the sliding mode is established.
• $\begin{array}{cc}{K}_{\mathrm{pz}}=\frac{\left(K_d/M_d+{\mathrm{AF}}_1\right)}{F_2}& \left(\mathrm{Eq}.24\right)\\ K_{\mathrm{vz}}=\frac{\left(B_d/M_d-{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="US20180339196A1-20181129-D00001.png"\; state="\{\{state\}\}">F</figure-callout>}}_1+A\right)}{F_2}& \left(\mathrm{Eq}.25\right)\\ K_{\mathrm{qz}}=\frac{\left(C_d/M_d\right)}{F_2}& \left(\mathrm{Eq}.26\right)\\ K_{\mathrm{fz}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="K\; f\; F"\; filenames="US20180339196A1-20181129-D00004.png"\; state="\{\{state\}\}">K</figure-callout>}}_f}{F_{}}& \left(\mathrm{Eq}.27\right)\end{array}$
• For implementation, the sign function is replaced by a continuous approximation, for instance the saturation function or a sigmoid function. Note that a single sliding function is used, with constant coefficients F₁ and F₂. However, the coefficients of the dynamic compensator z must be switched according to q to obtain the target impedances for the pull and return phases.
• Simulations and Real-Time Experiments
• First, an extensive set of data on the rowing exercise was collected, both on human and machine sides. Experiments were conducted at the Parker-Hannifin Human Motion and Control Lab at Cleveland State University. Human data included motion capture, metabolic variables and electromyography at 13 muscle surfaces. Mechanical data included handle force and velocity and flywheel velocity. Tests consisted of a total of 9 workout trials of 2 minutes each after 10 minutes of warm-up. Three different cadences and three different intensity levels set by opening and closing the machine vents. The data repository and report are available in. Next, simulations were conducted with the hybrid model driven by the above experimental data for validation purposes. Using the force recorded from the first test as the input of the system, the position and velocity of the sprocket and the flywheel were predicted. The sprocket and flywheel velocities were predicted by the model with an accuracy which is sufficient for model-based control development.
• The robust impedance controller was simulated with the identified plant model. The target impedances for the coupled and decoupled modes and the control gains are shown in Tables 2 and 3, respectively.

• 	TABLE 2
  	Mode	Kd	Bd	Cd	Md

  	Coupled	15	100	50	500
  	Decoupled	40	5	50	80

• 	TABLE 3
  	Parameter	Value

  	A	−10
  	F1	10
  	F2	10
  	D	350
  	ε	1
  	ϕ	0.01

• The controller used nominal values for M and C that were intentionally mismatched from those used in the plant simulation, as reflected in δM and δC.
• Robust achievement of the target impedance was validated as follows: the switched target impedance was simulated in parallel with the controller, resulting in a predicted sprocket velocity. This velocity was compared with the corresponding controlled plant output. The velocities of the sprocket and the virtual flywheel were converted to linear coordinates, as well as the coupling state. The velocity of the sprocket from the controlled plant converged to the velocity predicted by applying the same force input to the target impedance. This indicates that the target impedance was attained, despite of significant parametric uncertainty.
• The sliding function converged to zero.
• The impedance controller of as tested in real time with two impedance settings, one with high eccentric loading and one with small eccentric loading (conventional rowing machine replication). The dynamic behavior of the rowing machine has been replicated. Tables 4 and 5 show the target impedance parameters for the two settings and the controller gains, respectively.

• 	TABLE 4
  	Mode	Kd	Bd	Cd	Md

  	Coupled, Low Ecc.	40	100	50	200
  	Decoupled, Low. Ecc.	50	0.5	50	6
  	Coupled, High Ecc.	10	20	50	100
  	Decoupled, High Ecc.	150	0.5	50	8

• 	TABLE 5
  	Parameter	Value

  	A	−5
  	F1	−1
  	F2	1
  	D	800
  	ε	1
  	ϕ	0.0035

• The first target impedance was used to replicate the power patterns and “feel” of the conventional rowing machine. This setting emphasizes the inertial and damping components of the target impedance. The sprocket velocity predicted by applying force measurements to the impedance operator closely matches the experimental sprocket velocity, confirming that the target impedance was attained.
• The second target impedance demonstrates the use of the system as a more general exercise machine. The settings were chosen to produce a 1-1 ratio for the peak instantaneous concentric and eccentric power. To achieve this, target damping and inertia are reduced, while the return target spring is increased.
• Because a physical clutch is no longer used, the motor must reverse direction quickly at the discrete transitions. When transitioning to the coupled state, the virtual inertia is switched to a higher value. This, together with the virtual spring and damping actions result in a resonant frequency. At the time of switching, a brief underdamped oscillation may result, according to the target impedance selection.
• Results have also shown that peak eccentric power can match peak concentric power. Probably due to the lack of previous eccentric training on test users, they have experienced a greater effort (as measured by metabolic variables) to support eccentric exercise.
• The robust impedance controller implemented on the powered rowing machine was effective at producing the desired target impedances for the pull and return phases. The control system introduces unprecedented versatility due to the ability to virtually change parameters that were fixed in the original mechanical systems, such as flywheel inertia, damping characteristics and return spring stiffness.
• Impedance Settings
• To achieve a wider range of resistances and speeds, a series of impedance settings were determined and implemented.
• Training Studies
• The machine has been used in the conditions for which it was designed: a group of test subjects performed a series of rowing-like exercises under various levels of resistance and various cadences. The machine enabled the production of eccentric loading and a programmable resistance.
• A population of 10 subjects, male and female, of different ages and fitness levels were tested. A total of 20 experiments were successfully performed. Each subject participated in 2 different sessions, which focused on either full-body rowing or lower-body exercise (i.e., by attached the chain to the seat). Each trial specified a constant cadence for 12 minutes and the resistance was changed every three minutes.
• To show the benefits of eccentric training, trials were performed by only varying a parameter that determines the intensity of this type of muscular contraction. FIG. 5 is a photograph of a test being conducted with the machine.
• The exemplary embodiment has been described with reference to the preferred embodiments. Obviously, modifications and alterations will occur to others upon reading and understanding the preceding detailed description. It is intended that the exemplary embodiment be construed as including all such modifications and alterations insofar as they come within the scope of the claim(s) or the equivalents thereof.

Claims (20)

1. An exercise system comprising:

a motor;

a sprocket;

a belt transmission connecting the motor and the sprocket;

a control system for controlling the motor;

a chain having a first end and a second end, the first end connected to the sprocket; and

a handle attached to the second end of the chain.

2. The exercise system of claim 1, wherein the control system comprises a controller and at least one of: a first sensor configured to measure handle force and a second sensor configured to measure sprocket velocity.

3. The exercise system of claim 1, further comprising:

a foot pad;

a rail; and

a seat slidably engaged with the rail.

4. The exercise system of claim 3, wherein the handle is releasably attached to the second end of the chain; and wherein the seat is configured to receive the second end of the chain.

5. The exercise system of claim 1, further comprising a cover, wherein the cover at least partially encloses the motor, sprocket, and belt transmission.

6. The exercise system of claim 1, wherein the control system is configured to switch between a concentric phase and an eccentric phase.

7. The exercise system of claim 1, wherein the control system is configured to provide dynamic variable resistance.

8. The exercise system of claim 1, further comprising a display unit comprising a processor, a display, and a user interface.

9. The exercise system of claim 1, wherein the controller is configured to adjust the resistance depending on a probability of injury at different handle positions.

10. The exercise system of claim 1, wherein the control system comprises an impedance controller.

11. An exercise system comprising:

a motor;

a sprocket;

a belt transmission connecting the motor and the sprocket;

a control system for controlling the motor;

a chain having a first end and a second end, the first end connected to the sprocket;

a seat attached to the second end of the chain;

a rail; and

a foot pad;

wherein the seat is slidably engaged with the rail.

12. The exercise system of claim 11, further comprising:

at least one roller between the seat and the rail.

13. The exercise system of claim 11, further comprising:

a handle;

wherein the seat is releasably attached to the second end of the chain; and

wherein the handle is configured to receive the second end of the chain.

14. The exercise system of claim 11, further comprising a cover, wherein the cover at least partially encloses the motor, sprocket, and belt transmission.

15. The exercise system of claim 11, wherein the control system is configured to switch between a concentric phase and an eccentric phase.

16. The exercise system of claim 11, wherein the control system is configured to provide dynamic variable resistance.

17. The exercise system of claim 11, further comprising a display unit comprising a processor, a display, and a user interface.

18. The exercise system of claim 11, wherein the controller is configured to adjust the resistance depending on a probability of injury at different handle positions.

19. The exercise system of claim 11, wherein the control system comprises an impedance controller.

20. A method for retrofitting an exercise machine, the method comprising:

removing a flywheel; and

providing a motor and a control system.

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