Patent Publication Number: US-8109859-B2

Title: Bilaterally actuated sculling trainer

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/115,211 filed May 5, 2008, which claims priority from U.S. Provisional Patent Application Ser. No. 60/916,037, entitled: Sculling Apparatus, filed May 4, 2007. Both of the aforementioned applications are incorporated by reference herein. 
    
    
     BACKGROUND 
     Rowing or sculling on water are enjoyable forms of recreation and exercise. In terms of exercise, the rower or sculler benefits from a full body exercise, as rowing and sculling involves exercising numerous muscle groups of the torso and upper and lower extremities. However, those who enjoy this outdoor activity are limited by proximity to a large body of water or by ambient weather conditions. 
     In order to have rowing or sculling always available, regardless of weather or geography, machines attempting to simulate the rowing or sculling experience have been developed in the past. However, these machines remain limited because of their use of spring based or dashpot based resistance to motion, unilateral actuation or they are cumbersome. A user may experience a semblance of rowing by moving members simulating oars; however, rowing loads as reflected to the user by the machine may not be realistic or predictable. Accordingly, the rowing experience, provided by prior designs, may not simulate well the sensation of rowing or sculling on water. 
     SUMMARY 
     The disclosed subject matter provides an apparatus and method that simulates rowing or sculling on water. The disclosed subject matter simulates the sensation of rowing on water, as it models the inertial and damping properties of water. The simulation is provided by linear and non-linear dampers, working in conjunction, to provide resistance at the oars, similar to the resistance provided by water. 
     The disclosed subject matter is directed to an apparatus for simulating sculling or rowing on water. The apparatus includes a support frame with foot rests, a sliding seat, bilateral oars that are rotationally coupled to a set of actuators, integrated input velocity and torque sensors, computer and computer display. Each actuator incorporates a mechanical transmission, a rotational inertial mass, a variable linear and a variable non-linear damping element. The damping elements can be controlled manually or automatically by computer programs under user control. 
     The disclosed subject matter is directed to a bilateral sculling trainer. The sculling trainer includes a main frame supporting a pair of first and second simulated oars. The oars respectively rotate about first and second rotational axes that are defined by the rotational axis of first and second transmissions or actuators. The first and second transmissions transmit respective rotations of the first and second simulated oars around the first and second rotational axes. Incorporated within the transmissions are first and second inertial members that are respectively rotatable around the first and second rotational axes. Additionally, the first and second transmissions include corresponding first and second speed changers that convert relatively high-torque, low-angular-speed rotation of the first and second simulated oars into relatively low-torque, high-angular-speed rotation of the first and second inertial members around the first and second rotational axes. 
     The sculling trainer also has first and second variable dampers for respectively resisting rotation of the first and second inertial members. These first and second variable dampers include first and second variable non-linear dampers, for example, air dampers, and first and second variable linear dampers, for example, magnetic dampers. 
     There is disclosed an apparatus for simulating sculling, rowing or the like. The apparatus includes a main frame for supporting first and second simulated oars that are rotatable about respective first and second rotational axes, and an actuator for receiving each of the first simulated oar and the second simulated oar. Each actuator includes a drive assembly for transmitting the rotations of the corresponding oar about the respective rotational axis; at least one angular velocity sensor for detecting the angular velocity of each oar; at least one torque sensor unit for determining the torque on each oar; and a damping system. The damping system is electronically coupled with the angular velocity sensor and the torque sensor. The damping system provides linear and non-linear damping to create a damping load on the drive assembly based on the detected angular velocity and the torque on the first and second simulated oars. Non-linear damping is provided, for example, by non-linear dampers, such as variable air, fluid or viscous dampers, while linear damping is provided, for example, by linear dampers, such as magnetic dampers. 
     The apparatus may also include a processor, for example, a microprocessor. The processor is programmed to receive signals corresponding to the sensed angular velocities of each oar and to receive signals corresponding to the torque on each oar, determine damping output for the damping system from these received signals, and send signals to the damping system for controlling the linear and non-linear damping. 
     Also disclosed is an actuator apparatus for an object, for example, an oar or simulated oar, rotating about a rotational axis. The actuator includes a drive assembly for transmitting the rotations of the object about the rotational axis, at least one angular velocity sensor for detecting the angular velocity of the object, at least one torque sensor unit for determining the torque on the object, and a damping system. The damping system is electronically coupled to the angular velocity sensor and the torque sensor. The damping system provides linear and non-linear damping to create a damping load on the drive assembly based on the detected angular velocity and the torque on the object. Non-linear damping is provided, for example, by non-linear dampers, such as variable air, fluid or viscous dampers, while linear damping is provided, for example, by linear dampers, such as magnetic dampers. 
     Also disclosed is a method for simulating movement along water. The method includes receiving angular velocity and torque data from at least one simulated oar in a rotation about a rotational axis, and determining a damping load for a drive assembly, that is coupled with the simulated oar, from the received angular velocity and torque data, the damping load including non-linear and linear damping components. The drive assembly is then subjected to determined damping load, to damp the motion of the oar, to simulate the resistance of water. The angular velocity and torque data is, for example, in the form of electrical signals. The non-linear damping component, for example, includes a square law function, while the linear damping component includes, for example, a linear function. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Attention is now directed to the drawings, where like reference numerals or characters indicate corresponding or like components. In the drawings: 
         FIG. 1  is a perspective view of an apparatus in accordance with the disclosed subject matter; 
         FIG. 2  is a perspective view of the drive assembly of the apparatus if  FIG. 1 ; 
         FIG. 3  is a cross sectional view of a drive assembly of the apparatus of  FIG. 1 , taken along line  3 - 3  of  FIG. 2 ; 
         FIG. 4  is a perspective view of the transmission and damper assemblies within the drive assembly; 
         FIG. 5  is a perspective view of the damper assemblies within the drive assembly; 
         FIG. 6  is a cross sectional view of the damper assemblies of  FIG. 5 , as taken along line  5 - 5  of  FIG. 5 ; 
         FIG. 7  is a cross sectional view of the non-linear damper assembly of  FIG. 5 , as taken along line  5 - 5  of  FIG. 5 ; 
         FIG. 8  is a perspective view of the non-linear damper assembly of the apparatus; 
         FIG. 9  is a cross sectional view of the non-linear damper assembly taken along line  9 - 9  of  FIG. 8 ; 
         FIG. 10  is a cross sectional view of the linear damper assembly of  FIG. 5 , as taken along line  5 - 5  of  FIG. 5 ; 
         FIG. 11  is a block diagram of the computer system of the apparatus; 
         FIG. 12  is a flow diagram for the angular velocity and torque sensing; 
         FIG. 13  is a flow diagram of the linear and non-linear damping adjustment and control; 
         FIG. 14  is a schematic block diagram of the torque and velocity load path for the drive assembly and its major components in accordance with the disclosed subject matter; and 
         FIG. 15  is a block diagram of the computer system of the apparatus networked to receive various programs or other data entry. 
     
    
    
     DETAILED DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows the apparatus  100  of the disclosed subject matter. The apparatus  100  is shown, for example, as a sculling or rowing training machine. The apparatus  100  includes a longitudinal support beam  102 , over which a seat  103  rolls. The seat  103  includes wheels  103   a  on both sides of the support beam  102 , that ride on parallel runners  103   b . The runners  103   b  are disposed on opposite sides of the support beam  102 , on a support plate  104 . The runners  103   b  are curved upward at their ends, to define the extent of travel for the wheels  103   a , and accordingly, limit travel of the seat  103 . Foot pedals  106  extend from the sides of the longitudinal support  102 . These foot pedals  106  allow the user to brace his feet during operation. 
     Oars  107  are received by drive assemblies or actuators  200  in gimbal supports  201 . Each oar  107  includes a counterweight  108  that is positioned on the respective oar  107 , for example, in a fixed engagement. The counterweights  108  balance and inertially simulate the mass properties of a true oar. The oars  107  are maintained in a null position by a parallel arrangement of return springs  109 . The drive assemblies  200  are maintained in position by transverse support arms  111  and diagonal support arms  112 , both extending from the longitudinal support  102 . 
     A computer display  114 , such as a monitor, is electronically linked, by wired or wireless links, or combinations thereof, to a computer  600 , with a processor (for example, a conventional microprocessor)  601  and an A/D (analog to digital) converter  602 , shown diagramatically in  FIG. 11 , housed in the longitudinal support  102 . In this document, “electronically linked” means electronic and/or data connections by wired or wireless links or combinations thereof. The computer  600  is also electronically linked to the damping (or damper) assemblies, a non-linear or air damper  300 , and a linear or magnetic damper  500 , as well as a keypad  116 , through which the user inputs data, as shown diagramatically in  FIG. 11 . 
     Attention is now directed also to  FIGS. 2 and 3 , to detail the drive assemblies or actuators  200 . While only one drive assembly  200  is shown, this drive assembly  200  is representative of both drive assemblies, as the other drive assembly  200  is symmetric and otherwise identical. Additionally, the components of the drive assemblies  200  detailed below may be joined, connected or the like by various mechanical adhesive fasteners, such as screws, bolts, seals and the like, that may not be mentioned specifically, but whose use is well known to one of skill in the art. 
     The input end  200   a  of the drive assembly  200  includes the oar gimbal support  201 , that is, for example, cylindrical or of another shape sufficient to receive a correspondingly shaped oar  107 . The oar gimbal support  201  is typically pivotally mounted on a gimbal support post  202 , with bushings  203 , for example, of Teflon®, therebetween. Strain gages (SG)  204  form the variable resistive component of a bridge circuit (detailed below). A set of strain gages  204  are integrated into each gimbal support post  202 . The remainder of the bridge circuitry, along with voltage amplification circuitry (not shown) are located on a circuit board  800 . The torque sensor  802  is the assemblage of components encompassing the support posts  202 , strain gages  204 , bridge and amplifier circuits. 
     The torque sensor  802  is electronically linked to the computer  600 , as shown in  FIG. 11 , via a slip ring  211 /brush block  212  interface. The slip ring  211  is mounted on a clutch housing  215 . The brush block  212  is mounted on the drive assembly housing  216 . The clutch housing  215  terminates in a cog wheel  217 . Angular velocity sensor  218   a , for example, a conventional chip, such as an Allegretto ATS651LSH, is mounted within the angular velocity sensor support post  218   b . The support post  218   b  is in turn mounted on the drive assembly housing  216 . The angular velocity sensor  218   a  is electromagnetically coupled to the cog wheel  217 . 
     The clutch housing  215  supports the gimbal support posts  202 , and encases a clutch  226  that is coaxial with, and surrounds, an input drive shaft  227 . The clutch  226  and input drive shaft  227  rotate about a central axis CX. The clutch  226  is designed to allow actuation in only one (a single) rotational direction. The input drive shaft  227  extends downward through a ball bearing  228 . 
     Within the drive assembly housing  216 , the input drive shaft  227  is rigidly coupled to input  229   a  of the harmonic drive  229  at the flex spline input coupling flange  230 , with associated fastening mechanisms  230   a . Also, within the housing  216 , the proximal end of the splined output drive shaft  234  (that rotates about the central axis CX and is coaxial with the input drive shaft  227 ) is rigidly mounted to the output  229   b  of the harmonic drive  229  at the wave generator output coupling flange  231 , also with associated fastening mechanisms  231   a . The harmonic drive  229  couples to the variable non-linear damper  300  via the splined output drive shaft  234 . 
     The drive assembly housing  216  is coupled to the damper housing  301  by an intermediate flange  235 . The damper housing  301  includes air vents where the damping medium of the non-linear damper is air. However, the damper housing  301  may be sealed if the damping medium for the non-linear damper is a liquid. The damper housing  301  also includes vertical support posts  301   a  and encloses the components that form the non-linear damper  301 . The splined output drive shaft  234  is supported at the flange  235  by a ball bearing  236  and a seal  237 , for example, an elastomeric O-ring, labyrinth seal, or the like. 
     Attention is now also directed to  FIGS. 4-9 , that show the non-linear damper (damping assembly or mechanism)  300  in detail. The splined output drive shaft  234  is torsionally coupled to the torque transfer housing assembly  400  at the proximal support plate  401 , by a female splined coupling interface  401   a . The proximal support plate  401  in turn is rigidly coupled to the distal support plate  403   a /torque transfer cylinder  403   b  by the multiple support struts  402 . The torque transfer cylinder  403   b  encloses a ball screw  304  (that rotates about the central axis CX), ball nut  305 , the internally radiating spokes of a spoked ball nut support ring  307 , and an end support cap  308  that houses a ball bearing  309 . The ball screw  304  is supported at one end (proximal end)  304   a  by the ball bearing  322 , encased in the distal support plate  403   a , and at the other (distal) end  304   b  by the ball bearing  309 , supported within the end support cap  308 . The first (proximal) end  304   a  of the ball screw  314  has a pinion gear  315  mounted on it. The pinion gear  315  meshes with a triad of radial gears  316  (only two radial gears  316  are shown in  FIG. 9 ). Each radial gear  316  is formed of coaxial gears  317   a  (lower or distal),  317   b  (upper or proximal). 
     The lower or distal coaxial gear  317   a  meshes with the pinion gear  315 . This gear  317   a  includes an integrated axle  317   a ′, an upper or proximal portion that extends through the upper or proximal coaxial gear  317   b . The other, lower or distal portion is received in the distal support plate  403   a  and is mounted with ball bearings  317   c.    
     The upper or proximal coaxial gear  317   b  meshes with an internal gear  318   a , that is integrated into a hollow short aspect axle  319  at its internal cylindrical face. An external gear  318   b  is integrated into the short aspect axle  319  at its external cylindrical face. The short aspect axle  319  is supported proximally and distally by low profile ball bearings  320   a  and  320   b  respectively. 
     Low profile ball bearings  320   a  (positioned proximally with respect to the other low profile ball bearings  320   b ) are supported proximally by the support plate  401 , and distally by the short aspect axle  319 . The distal low profile bearing(s)  320   b  is supported proximally by the short aspect axle  319  and distally by the support plate  403   a.    
     The external gear  318   b  meshes with a series of multiple circumferentially positioned sector pinion gears  333 . Each sector pinion gear  333  is mounted centrally within the vane-axle-gear assembly  334 . For example, gearing from the pinion gear  315  to the sector pinion gears is at a ratio of approximately 3:1 reduction. The multiple vane-axle-gear assemblies  334  are supported at the periphery of the non-linear damper  300  by the proximal support plate  401 , distal support plate  403   a , and their respective sets of support bushings  337 . A flywheel  342  is rigidly mounted to the proximal support plate  401 . 
     A spoked ball nut mount ring  307  is supported at its internal cylindrical face by the ball nut  305 , and at its external cylindrical face by a ball bearing  351 . The spoked ball nut mount ring  307  is allowed to translate axially along the slots of the torque transfer cylinder  403   b . Torque transferred to the spoked ball nut mount ring  307  from the torque transfer cylinder  403   b  is due to contact between the ring  346  and cylinder  403   b  at the slot interface. 
     Ball bearing  351  is mounted on an externally threaded ball bearing support cylinder  352 . The externally threaded outer support cylinder  352  is in turn, coupled to the internally threaded cylindrical portion of the linear damper housing cover  501   a  ( FIG. 3 ). The externally threaded ball bearing support cylinder  352  is also coupled to a pinion gear  354  mounted on a stepper motor  359  via integrated spur gear  361 . The stepper motor  359  is also electronically linked to the computer  600 . 
     A magnetic damping wheel  503  of the linear or magnetic damper  500 , for example, a variable linear or magnetic damper, is rigidly supported on the torque transfer cylinder  403   b . The torque transfer cylinder  403   b  is supported by a ball bearing  364  on the non-linear damper housing  301  ( FIGS. 2 and 3 ). 
     Turning also to  FIG. 10 , which illustrates the linear or magnetic damper (damping apparatus or assembly)  500  in detail, there is a series (set) of circumferentially positioned proximal magnets  505  that is supported at the distal external face of the damper housing  301  ( FIG. 2 ). A series (set) of distal magnets  506  is located on the magnet support plate  508 . The distal magnet support plate  508  is such that it rotates about the central axis (CX), while being confined radially and axially by the linear damping housing cover  501  ( FIG. 2 ). 
     A sector spur gear  514  is mounted on the distal magnet support plate  508 . The sector spur gear  514  includes gear teeth at its edge  514   a  that mesh with a pinion gear  516  of a stepper motor  518 . The stepper motor  518  is also electronically linked to the computer  600 . The magnetic damping wheel  503  is positioned in between the set of proximal  505  and distal  506  magnets. The linear damper housing cover  501  has a central opening (not shown) that allows the torque transfer cylinder  403   b  unrestrained access through its center. 
     Attention is now directed to  FIGS. 1-11 , to illustrate an exemplary operation of the apparatus  100 , and in particular, the operation of the drive assemblies or actuators  200 . When force is applied to an oar  107 , a twisting moment or torque is generated and transmitted to the respective input drive shaft  227 . The counterweights  108  on each oar  107  simulate the inertial properties of the suspended mass of an oar. The level of torque applied to the drive assembly  200 , as well as its rotational velocity, is a function of the impedance created by the inertial and damping elements of the drive assembly  200 , and the force that the user provides at the oar  107 . 
     Linear damping is provided by the linear or magnetic dampers  500  that are under computer  600  control ( FIG. 11 ). Non-linear damping, for example, square law damping, is provided by the non-linear dampers  300 , detailed above, that are also known as air, fluid or viscous dampers. The non-linear dampers  300  are also under computer  600  control ( FIG. 11 ). 
     Turning now also to  FIG. 12 , a flow chart detailing a process for obtaining torque and velocity data is illustrated. Initially, at block B 1 , a change in resistance of the strain gage (SG)  204  caused by deflection of the gimbal support posts  202  causes a change in bridge circuit output that is in turn amplified by the analog amplifier mounted on the circuit board  800 , at block B 2 . The circuit boards  800  are mounted on the clutch housings  205  of their respective actuators  200 . The amplifier output voltage is then routed via the slip ring  211 /brush block  212  electrical interface, at block B 3  to the noise filter and analog to digital converter circuits  602  of the computer  600 , at block B 4 . This converted signal will then be used by the data analysis computer programs contained within the storage  603  or non-volatile memory of the processor, for example, a microprocessor  601 , to convert the data into real time input torque data, at block B 5 . 
     At block B 7 , motion of the cog wheel  205  is sensed by the digital angular velocity sensor  218   a . The digital angular velocity sensor  218   a  converts this motion into a digital signal, at block B 8 , and sends it to the computer  600 , at block B 5 . This digital signal will then be used by the data analysis computer programs contained within the storage  603  and the non-volatile memory of the microprocessor  601 , at block B 5 , to convert the data into real time input velocity data. 
     The microprocessor  601  at block B 5  executes the appropriate data conversion and analysis routines and displays the output data in the user selected format on the display monitor  114  (B 6 ). The keypad  116  allows the user to select from a menu the program that will display the data. 
     Turning also to  FIG. 13 , a flow chart detailing a process for varying the non-linear damping and linear damping is illustrated. Changes in linear or non-linear damping are typically performed under computer control, through algorithms, such as those detailed below, or the like, but may also be manual. This automatic or manual control requires interfacing with the computer  600  via the keypad  116 . Specific sculling (rowing) routines can be selected via the keypad  116 . Alternately, if the user wishes to use the machine without executing a preprogrammed routine, changes to the damping levels can be made via the keypad  116 , such that the stepper motors  359  and  516  will be set to predetermined operating conditions (rotations). Still alternately, the stepper motors  359 ,  516  can also be set to default settings (rotations), such that computer  600  interaction is not necessary. 
     Initially, a rowing routine is selected from a menu of preprogrammed routines via the keypad  116 , at block B 9 . During execution of a rowing program, subroutines contained within the program, typically held in the storage  603  ( FIG. 11 ), will dynamically alter the linear and non-linear damping to create a dynamic change in input impedance, as seen from input drive shaft  227 , at block B 11 . This is then realized by the user as a change in load condition at the oar that will require a change in physical output by the user to effect a desired torque output, velocity output or energy expenditure. 
     Linear damping is a linear function of the rotational velocity of the output drive shaft  234 . Linear damping is, for example, in the form of magnetic damping and is varied when the computer  600  sends a signal to the stepper motor  518  to increment its rotation, at block B 10 . Rotation of the stepper motor  518  causes rotation of the pinion gear  516  attached to it. Rotation of the pinion gear  516  rotates the sector spur gear  514  attached to the magnet support plate  508 . This in turn causes rotation of the magnet support plate  508 . Rotation of the magnet support plate  508  causes a rotational shift in the distal set of magnets  506  mounted on the magnetic wheel  503 , with respect to the proximal set of magnets  505 , about the axial center CX of the drive assembly  200 . This is reflected at block B 13  as a change in angular position of the magnet support plate  508 . 
     This in turn alters the magnetic field created between the opposing proximal  505  and distal  506  sets of magnets. Hence, altering the position of one set of magnets or the flux density of the magnets changes magnetic or linear damping by altering the way the induced back voltage in the magnetic damping wheel  503  interacts with the magnetic flux lines. 
     The flux density of the magnets can be fixed with the use of permanent magnets or can be varied with the use of electromagnets. The amount of magnet support plate  508  rotation needed to effect a specific amount of linear damping is pre-programmed and contained within the computer control routines. 
     Non-linear damping is a square law function of the rotational velocity of the output drive shaft  234 . Non-linear damping is in the form of air or fluid viscous drag and is varied when the computer  600  sends a signal to the stepper motor  359  to increment its rotation, at block B 12 . This causes a ball screw  304  phase adjustment, at block B 14 , that causes movements resulting in differential rotations of the fan blades  334 , in block B 15 . The processes of blocks B 12 , B 14  and B 15  occur as follows. 
     Incremental rotation of the stepper motor  359  causes incremental rotation of the pinion gear  354  attached to it. This in turn causes incremental rotation of the sector spur gear  361  attached to the externally threaded ball bearing support cylinder outer support ring  352 . Incremental rotation of the externally threaded ball bearing support cylinder outer support ring  352  causes an incremental axial translation of the ring  352 . This is a result of its screw interface with the internally threaded portion of the linear damper housing cover  501   a . Incremental translation of the outer support ring  352  causes an incremental axial translation of the ball bearing  351  supporting the ball nut spoke ring  346 . Incremental translation of the ball bearing  351  causes an incremental axial translation of the spoke ring  307 . Incremental translation of the spoke ring  305  results in incremental axial translations of the ball nut  305 . 
     Incremental translation of the ball nut  305  causes an incremental rotation of the ball screw  304  beyond that imparted to it by its own rotational velocity. High velocity rotations of the ball screw  304  is a result of the interfacial coupling between the torque transfer cylinder  403   b  of the non-linear damper  300  and the spokes of the ball nut spoke ring  307 . The incremental rotation of the ball screw  304  then causes an incremental rotation of the pinion gear  315 . The incremental rotation of the pinion gear  315  causes an incremental rotation of the triad of radially oriented gears  316 , resulting in a corresponding incremental rotation of the coaxial gears  317   a ,  317   b . The incremental rotation of the coaxial gears  317   a ,  317   b  will cause incremental rotation of internal gear  318   a . This in turn will cause corresponding incremental rotation of the short aspect hollow axle  319 , and accordingly, the external gear  318   b . The incremental rotation of the external gear  318   b  causes an incremental rotation of the planetary sector pinion gear  333  mounted within the vane-axle-gear assembly  334 . In effect, translation of the ball nut  305  creates a phase difference in rotation between the vane-axle-gear assemblies  334  and the torque transfer housing  400 . The epicyclic gear train described above is incorporated to match the ball screw  304  displacement to vane rotation range of motion. The amount of axial translation necessary to effect a specific amount of vane rotation for a specific amount of non-linear damping is pre-programmed and contained within the computer control routines. 
     As a result, the damping load is adjusted in both the non-linear  300  and linear  500  dampers and transferred to the output drive shaft  234  to simulate damping (on an oar) caused by water. This can be further augmented by the computer programs, as detailed herein, that can further account for the velocity of the water, slow moving, fast moving, still, or the like. 
     The mathematical relations describing the basis for the apparatus  100 , with its drive assemblies or actuators  200  (also referred to as transmissions), that incorporate inertial and linear and non-linear damping elements, will now be described. Given a one stage mechanical transmission with defined properties of input and output rotational inertia, output linear and non-linear damping, the equation relating input drive torque to angular velocity and accelerations is expressed by the following equation:
 
 T   i =( J   i   +N   2   •J   o )• w   iaa +( b   i   +N   2 •( b   o   +b   l )• w   i   +b   nl   •N   3   •w   i   2  
 
where:
 
     T i =input torque applied to the transmission 
     J i =rotational inertia at the input side of the transmission 
     J o =rotational inertia at the output side of the transmission 
     N=transmission multiplying factor or gear factor 
     w i =angular velocity at the input side of the transmission 
     w iaa =angular acceleration at the input side of the transmission 
     b i =drag coefficient at the input side of the transmission 
     b o =drag coefficient at the output side of the transmission 
     b l =linear damping coefficient at the output side of the transmission 
     b nl =non-linear damping coefficient at the output side of the transmission. 
     A schematic outline of the load path for the above formulation is shown in  FIG. 14 . Based on the equation above, the input torque level, required to obtain or maintain a given input velocity, is sensitive to variations in output damping levels. By sensitive, it is meant that small changes in linear or non-linear damping will require large changes in input torque to maintain a desired input velocity level. Accordingly, the apparatus  100  is such that fine control of damping parameters forces large changes in energy expenditure by the user in order to maintain a constant rowing velocity. 
     Returning back to the equation previously defined, for example, design parameters may be selected representing the various equation variables, as follows:
         input inertia, J i , is represented by the combined inertia of the oar  107  and its counterweight  109  and all other components that rotate at the same velocity with each stoke of the oar at the input end of the transmission  200 ;   output inertia, J o , is represented by the combined rotational inertias of the harmonic drive  229 , output drive shaft  234 , non-linear viscous damper assembly  300  including ball screw  304  and ball nut  305 , magnetic damping wheel  503 , and all other components that rotate at the same velocity as the output end of the harmonic drive  229 ;   linear, n l , and non-linear, n nl , damping, are represented by the variable linear magnetic  500  and variable non-linear fluid viscous  300  dampers respectively;   transmission multiplying factor, N, is represented by the harmonic drive gear ratio.       

     The apparatus  100  incorporates routines (including algorithms) within its storage  603  and non-volatile memory of the microprocessor  601  that converts information obtained from the angular velocity sensors  218   a , and torque sensors  802 , to a format usable to data manipulation, control, and three dimensional (3D) gaming/simulation routines. The control routines allow the user to adjust damping parameters of the linear damper  500  and the non-linear damper  300  as desired. 
     The routines are also accessed by the simulation and gaming routines to adjust the damping parameters dynamically during program execution. The data collection routines will be used to provide the user and gaming routines information regarding energy expenditure, angular velocity, force or torque input. The gaming routines are included to stimulate participation in scenarios that encourage various levels of participant energy expenditure to accomplish game and/or exercise goals. 
     For example, the user can interact with the computer  600  of the apparatus  100  during an exercise session with the apparatus  100 , in numerous ways. Three exemplary modes of interaction are described, although numerous other interactions are also possible. 
     In a first case, the user defines the level of linear or non-linear damping directly, by sending commands via the keypad  116  to the computer  600 . The level of damping in this case is held constant. This represents an open loop control scheme between the user and the computer  600 . 
     In the second case, the user adjusts his work output to meet exercise demands set by the computer program during various phases of program execution. The amount of linear or non-linear damping for each phase is programmed independent of what the user&#39;s input torque, input velocity or energy expenditure is. The damping levels are quasi-statically maintained during program execution. This is a closed loop control scheme between the user and the computer program but open loop control scheme within the computer program. 
     In the third case, the computer adjusts the linear or non-linear damping levels depending on the user&#39;s work output (as determined by the torque and velocity sensor analysis routines, and what phase of program execution the program is in). The damping levels are dynamically adjusted during program execution. This represents a closed loop type of feedback between the user and the computer program and closed loop feedback control within the computer program. 
     For example, there may be a program on the computer  600 , such that another sculler boater or the like may be shown on the display screen  114 . This would cause the user to attempt to keep up with, and try to pass, this hypothetical competitor. This hypothetical competitor is traveling at a reference velocity, that would be displayed on the screen display  114 . The computer  600  would be programmed such that this reference velocity is used to adjust the damping of the non-linear  300  and linear  500  dampers, and accordingly, control the damping load on the output drive shaft  234 , to simulate the damping of the water, for this user. 
     As shown in  FIG. 15 , the computer  600 , through its network interface  604  ( FIG. 11 ) can also be linked (by wired or wireless links) to a local  980  or wide area network  982  (the direct link shown in broken lines), for example, a public network such as the Internet, and allow multiple users to interact with each other in various simulations on a real time basis (box  984 ) using the apparatus  100  as a user interface. 
     The processes (methods) and systems, including components thereof, herein have been described with exemplary reference to specific hardware and software. The processes (methods) have been described as exemplary, whereby specific steps and their order can be omitted and/or changed by persons of ordinary skill in the art to reduce these embodiments to practice without undue experimentation. The processes (methods) and systems have been described in a manner sufficient to enable persons of ordinary skill in the art to readily adapt other hardware and software as may be needed to reduce any of the embodiments to practice without undue experimentation and using conventional techniques. 
     While preferred embodiments of the disclosed subject matter have been described, so as to enable one of skill in the art to practice the disclosed subject matter, the preceding description is intended to be exemplary only. It should not be used to limit the scope of the disclosure, which should be determined by reference to the following claims.