Patent Publication Number: US-2022233908-A1

Title: Exercise Apparatus with Linear Positioning System

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of and priority to U.S. Provisional Patent Application No. 63/142,783, filed 28 Jan. 2021, the entire disclosure of which is incorporated by reference herein. 
    
    
     BACKGROUND 
     Aspects of the present application relate to linear positioning systems, for example motorized or actuated positioning systems and user interaction with such systems. Additional aspects of the present application relate to exercise and rehabilitation equipment, and in particular to stands, racks, supports, etc. for use with barbells, weights, and other resistance-training, weight-training, and strength-training equipment. 
     For example, squat racks typically include cradles that can support a barbell. In some conventional squat racks, a pair of cradles can be manually repositioned to adjust a height at which a barbell is held when not in use. However, manually repositioning of the cradles is typically cumbersome and physically difficult (e.g., due to the weight of the cradle structure, friction, non-user-friendly design) and generally cannot be done without removing the barbell from the cradles. It may also be challenging for users of such racks to place the cradles at equal heights to avoid creating an uneven support for the barbell. In addition, the manual height adjustment of the cradles is typically limited to a limited number of discrete positions, which often do not align exactly with the ideal or preferred position for a given user and exercise. Accordingly, improved systems for position adjustment of cradles or supports for a barbell or other resistance-training equipment are desirable. 
     SUMMARY 
     One implementation of the present disclosure is a strength training assembly. The strength training assembly includes a stand and a frame movable along the stand in a vertical direction. The frame includes a cradle configured to receive a barbell. The strength training also includes a drive system coupled to the frame and controllable to affect a velocity of the frame relative to the stand, a force sensor coupled to the frame such that the force sensor moves with the frame, the force sensor configured to provide a signal indicative of an amount of force exerted on the force sensor by a user, and a controller configured to receive the signal from the force sensor and control the drive system such that the velocity of the frame varies as a function of the amount of force exerted on the force sensor. 
     Another implementation of the present disclosure is a linear positioning system. The linear positioning system includes a load mounted on a rail, an actuator controllable to cause movement of the load along the rail, and a force sensor rigidly coupled to the load such that the force sensor moves with the load. The force sensor is configured to measure an amount of force exerted on the force sensor by a user. The linear positioning system also includes a controller configured to control the actuator to provide the load with a velocity that varies as a function of the amount of force measured by the force sensor. 
     Another implementation of the present disclosure is a strength training assembly. The strength training assembly includes a stand and a frame movable along the stand in a vertical direction. the frame includes a pair of cradles configured to receive a barbell. The strength training assembly also includes an electric motor operable to provide motorized adjustment of a vertical position of the frame relative to the stand. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is perspective view of a strength-training apparatus with a linear positioning system, according to an example embodiment. 
         FIG. 2  is another perspective view of the strength-training apparatus of  FIG. 1 , according to an example embodiment. 
         FIG. 3  is a side view of a bar cradle with an input assembly for use with the strength-training apparatus of  FIG. 1 , according to an example embodiment. 
         FIG. 4  is perspective view of the bar cradle and input assembly of  FIG. 3 , according to an example embodiment. 
         FIG. 5  is a block diagram of a linear positioning system, according to an example embodiment. 
         FIG. 6  is another block diagram of a linear positioning system, according to an example embodiment. 
         FIG. 7  is another block diagram of a linear positioning system, according to an example embodiment. 
         FIG. 8  is another block diagram of a linear positioning system, according to an example embodiment. 
         FIG. 9  is a graph of a function mapping a user-applied force to a target velocity or voltage percentage which may be used by a linear positioning system, according to an example embodiment. 
         FIG. 10  is a perspective view of a fitness system including the strength-training apparatus of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Before turning to the figures, which illustrate certain exemplary embodiments in detail, it should be understood that the present disclosure is not limited to the details or methodology set forth in the description or illustrated in the figures. It should also be understood that the terminology used herein is for the purpose of description only and should not be regarded as limiting. 
     Referring generally to the FIGURES, improved systems for position adjustment of cradles or supports for a barbell or other resistance-training (strength training) equipment are shown. Additionally, the linear positioning systems described herein can also be adapted for use with other types of equipment. For example, the linear positioning systems herein can be used in motorized/adjustable standing desks or tables, adjustable beds, adjustable chairs, other position-adjustable furniture. As another example, the linear positioning systems herein could be used in industrial equipment, e.g., manufacturing equipment, construction equipment, warehousing applications, etc. Many variations are within the scope of the present disclosure. 
     Referring now to  FIGS. 1-2 , perspective views of a strength training apparatus  100  are shown, according to example embodiments. The strength training apparatus  100  is adapted for use for strength training, in particular by being adapted for supporting a barbell between exercises performed using the barbell. As described in detail below, the strength training apparatus  100  allows for intuitive and user-friendly motorized repositioning of the height at which the barbell is supported between exercises, in order to enable use of the strength training apparatus for many different exercises and for a wide range of users. 
     As shown in  FIGS. 1-2 , the strength training apparatus  100  includes a stand  102  extending in a vertical direction and providing a support structure for the strength training apparatus. The stand  102  includes vertical beams (posts)  104  connected by a top cross-piece  106  at a top end of the apparatus  100 , and a middle cross-piece  108  part-way along the vertical beams  104  between a bottom of the apparatus  100  and the top cross-piece  106 . The stand also includes bracing legs  110  extending diagonally downwardly from the vertical beams  104  to increase the stability of the stand  102  and prevent or substantially prevent instability of the stand  102 . An anchor  112  is included with the stand  102  at an opposite side from the bracing legs  110  to add stability to the stand  102 . In some embodiments, additional legs  114  extend from the middle cross-piece  108  to a floor or other surface supporting the stand  102  to provide structure support from the middle cross-piece  108 . The additional legs  114  may also extend up to the top cross-piece  106  in some embodiments. The stand  102  is thereby configured as a stable, static structure configured to bear a substantial amount of weight. 
     According to some embodiments, the stand  102  may be made of steel or any other metal and/or any other strong and rigid material. In some embodiments, the stand  102  is formed having a height in a range between six feet and nine feet, however, it should be understood that the stand  102  may be taller or shorter. In some embodiments, the middle cross-piece  108  is positioned at a height between two feet and four feet. 
     The strength training apparatus  100  further comprises a linear positioning system  116 . The linear positioning system  116  includes one or more rails (tracks, beams, etc.)  118  extending between the middle cross-piece  108  and the top cross-piece  106  of the stand  102 . In the embodiment shown, a pair of rails  118  are included and are positioned symmetrically across a centerline of the stand  102  so as to be horizontally spaced from one another. 
     The linear positioning system  116  also includes a frame  120  movably mounted on the rails  118 . The frame  120  has an open rectangular or u-shape such that the frame  120  extends both horizontally across the frame (spanning between the pair of rails  118 ) and forward in a direction normal to a plane defined by the vertical beams  104  of the stand  102 . The frame  120  connects a pair of cradles (hooks, receptacles, etc.)  122 . The cradles  122  are configured to receive a barbell and to support the barbell from beneath the barbell. The cradles have an angled opening to facilitate a user in positioning the barbell in the cradles  122 . The frame  120  is configured to support the cradles  122  and the barbell when the barbell is held by the cradles  122 . The frame  120  is rigidly designed so as to maintain the cradles  122  fixed relative to each other, thereby preventing the cradles  122  from being in uneven or misaligned positions during operation. 
     In the example of  FIGS. 1-2 , bearing assemblies  124  are included to slidably mount the frame  120  on the rails  118 . The bearing assemblies  124  are shown as rigidly and statically mounted to the frame  120 , while extending at least partially around the rails  118 . According to some embodiments, the bearing assemblies  124  include roller bearings, ball bearings, or various other types of bearings to provide low-friction movement of the bearing assemblies  124  (and the frame  120  coupled thereto) along the rails  118 . Linear motion of the frame  120  along a path defined by the rails  118  is thereby enabled. In other embodiments, the rails  118  may be curved, in which case motion of the frame  120  is enabled along a curved path defined by such rails  118 . 
     The linear positioning system of the apparatus  100  is also shown as including a pair of belts  126  and an electric motor  128 . The belts  126  are rigidly coupled to the frame  120  (e.g., using plates mounted on the belt), such that movement of the belts  126  causes corresponding movement of the frame  120 . The belts  126  are formed as loops which extend around pulleys  130  mounted on the top cross-piece  106  of the stand  102  and rotors  132  of the electric motor  128 . In the embodiment illustrated in  FIGS. 1 and 2 , for example, two belts  126  are coupled to the rotors  132 ; however, it should be understood that other configurations are applicable. For example, only a single belt  126  may be utilized. In other embodiments, multiple motors  128  and one or more belts  126  may be utilized on each motor  128 . In still other embodiments, it should be understood that the linear positioning system may be differently configured even further. For example, instead of using a belt and pulley configuration as best illustrated in  FIGS. 1 and 2 , the output from the motor  128  is operable to turn a screw-drive or other gear system to raise and lower the frame  120 . 
     The electric motor  128  is operable to create rotation of the belts  126 . In the example of  FIGS. 1-2 , when the electric motor  128  operates to rotate the belts  126  in a first direction (e.g., clockwise), the frame  120  (and the cradles  122 ) moves in an upward direction along the rails  118 . When the electric motor  128  operates to rotate the belts  126  in a second, opposite direction (E.g., counterclockwise) the frame  120  (and the cradles  122 ) moves in a downward direction along the rails  118 . The electric motor may be a permanent magnetic brush direct current motor. Other types of actuators can be used in other embodiments (e.g., hydraulic or pneumatic actuators). 
     In some embodiments, the electric motor  128  and the belts  126  are configured to prevent movement of the frame  120  except by operation of the electric motor  128 . In such embodiments, the electric motor  128  and the belts  126  are configured to hold the frame  120  in a static, selected position when the electric motor  128  is not being controlled to cause movement of the frame  120 . In some embodiments, the bearing assemblies  124  include brakes or locks that prevent movement of the frame  120  along the rails  118  when movement of the frame  120  is not desired, for example when the electric motor  128  is not actively moving the frame  120  along the rails  118 . 
     The linear positioning system  116  is configured to allow repositioning of the frame  120  to substantially any position along the rails  118 , i.e., such that a user perceives the linear positioning system  116  as providing continuous rather than discrete repositioning of the frame  120 . The position of the cradles  122  is thus highly customizable and modifiable for different users and for different exercises. In some embodiments, the linear positioning system  116  is controlled using force-sensitive input based on a force applied by a user. In other embodiments, a binary approach is used using a pair of buttons, such as, for example, one for up and one for down, to allow user control of the linear positioning system  116 . 
     A range of motion of the frame  120  may also be large enough to enable a large range of exercises using the apparatus  100 . In the example shown, the frame  120  can be driven along substantially a full length of the rails, i.e., from a position proximate the middle cross-piece  108  to a position proximate the top cross-piece  106 . In the embodiments shown, this allows the cradles  122  to be repositioned to highest position suitable for initiation of squat or shoulder-press type exercises using a barbell held by the cradles  122  (e.g., up to approximately seven feet above the floor)), and to a lowest position suitable for a bench press exercise (e.g., down to approximately three feet above the floor). In other embodiments, the apparatus  100  may be configured such that a lower end of a range of motion of the cradles  122  enables initiation of a deadlift-type activity using a barbell held by the cradles (e.g., down to less than one foot above the floor). In various embodiments, the frame  120  has a range of motion in a range between approximately three feet and approximately six feet, although the range of motion may longer or shorter. The strength training apparatus  120  can thereby be used in a wide range of exercise by users of various heights. 
     In the example of  FIGS. 1-2 , the linear positioning system  116  is configured to provide motorized repositioning of the frame  120  relative to the stand  102  while the cradles  122  hold weights, for example a barbell with additional plates positioned on the ends of the barbell. In some embodiments and when used with conventional weights, the electric motor  128  is sufficiently powerful to move up to several hundred points (e.g., three hundred pounds, four hundred pounds, etc.) in either an upward or downward direction. Thus, the strength training apparatus  100  allows for changing the height of the cradles  122  without removing plates from the barbell or removing the barbell from the cradles  122 . This can allow a user to easily make adjustments after weight has been added, for example making it much easier to adjust to different heights for different users (e.g., for users of different heights alternating sets using the same apparatus  100 ). This feature could also enable a user to add weights without needing to lift plates to a higher or highest position of the bar, before raising the weights using the linear positioning system  116 . The strength training apparatus  100  thereby provides an advantageous solution for many of the challenges of existing squat racks. 
     Referring now to  FIGS. 2-3 , close-up views of a cradle  122  having a user input assembly  200  are shown, according to example embodiments. In particular,  FIG. 3  shows a side view of the cradle  122  and user input assembly  200 , while  FIG. 4  shows a perspective view of the cradle  122  and the user input assembly  200  with a barbell  202  received by the cradle  122 . 
     From the side-view shown in  FIG. 3 , the cradle  122  has a hook-shape including a front lip  204 , a back ramp  206 , and a curved bottom  208  joining an inside of the front lip  204  to the back ramp  206 . The back ramp  206  is higher than the front lip  204 . The cradle  122  is thereby configured to allow a user to easily engage a barbell  202  with the back ramp  206  and slide the barbell  202  down the back ramp  206  to the curved bottom  208 , where the barbell  202  will sit in and mate against the curved bottom  208  while the front lip  204  retains the barbell  202  in the cradle  122 . Various designs of the cradle  122  to facilitate easy removal of the barbell  202  from the cradle  122  and return of the barbell  202  to the cradle  122  are possible in various embodiments. 
       FIGS. 3-4  show that apparatus  100  and linear positioning system  116  as including a user input assembly  200 . The user input assembly  200  includes a force sensor  210  and a cap (handle, cover, etc.)  212 . The user input assembly  200  extends from a bottom of the front lip  204  of the cradle  122  in a direction parallel with the cradle  122  (e.g., normal to plane defined by vertical beams  104  of the stand  102 ). In the example shown, one user input assembly  200  is included in the apparatus  100 . In other embodiments, multiple user input assemblies  200  are included (e.g., one on each cradle  122 , on the stand  102  or even remotely). 
     As shown, the cap  212  is connected to the cradle  122  via the force sensor  210 . In the example shown, the force sensor  210  is substantially rigid and coupled to the cradle  122  so as to be static relative to the cradle  122 . A force exerted by a user on the user input assembly  200  thus creates and equal-and-opposite force of the cradle  122  pushing back on the user, without perceptible movement of the cap  212  relative to the cradle  122 . The force sensor  210  is thus arranged to measure external forces exerted on the cap  212  by a user. 
     In the example shown, the force sensor  210  includes a strain gauge or other type of force sensor configured to generate a signal indicative of both a magnitude and sign (indicating direction) of the force exerted by a user on the user input assembly  200 . In various other embodiments, the force sensor  210  can be a pressure sensitive button, a spring with deflection sensor, or some other type of force sensor. The user input assembly  200  is thereby configured to determine whether a user is pushing up or down on the user input assembly  200  and to determine an amount of force applied by the user on the user input assembly  200 . 
     Referring now to  FIG. 5 , a block diagram of an example embodiment of a linear positioning system  500  is shown, according to an example embodiment. The linear positioning system  500  of  FIG. 5  may be an example implementation of the linear positioning system  116  (or a portion thereof) of  FIGS. 1-4 , and reference is made to the strength training apparatus  100  in the description of  FIG. 5  herein. The linear positioning system  500  can also be implemented with other hardware or systems, including in the context of other equipment or furniture in addition to strength training apparatuses, and all such adaptations are within the scope of the present disclosure. For example, a motor or other actuator could be controlled to move other loads as alternatives to the frame  120  as may be advantageous in various implementations. 
     As shown in  FIG. 5 , the linear positioning system  500  includes the force sensor  210 , a controller  502 , and the motor  128 . In other embodiments, the motor  128  is replaced by a different type of actuator. The force sensor  210  is electrically communicable with the controller  502  (e.g., connected thereto by a wire or other conductive path, wirelessly communicable or otherwise) and the controller  502  is electrically communicable with the motor  128  (e.g., connected thereto by a wire or other conductive path, wirelessly communicable or otherwise). 
     In various embodiments, the controller  502  is formed as circuitry mounted on the strength training apparatus  100 , provided inside a housing of the motor  128 , or otherwise provided onboard the strength training apparatus  100 . In some embodiments, the controller  502  is included as part of a computing and processing system that controllers other elements of a strength training system, for example a cable-based force production system as described with reference to  FIG. 10  below. 
     The controller  502  may include one or more processors and non-transitory computer readable media storing program instructions executable by the one or more processors to perform the various operations described herein. For example, the hardware and data processing components used to implement the controller  502 , other computing components and methods described herein may include a general purpose single- or multi-chip processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, conventional processor, or state machine. A processor also may be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some embodiments, particular processes and methods may be performed by circuitry that is specific to a given function. Controllers herein may include computer-readable media (e.g., memory, memory unit, storage device), which may include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, EPROM, EEPROM, other optical disk storage, magnetic disk storage or other magnetic storage devices, any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures, combinations thereof) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present disclosure. The memory may be or include volatile memory or non-volatile memory, and may include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. According to an exemplary embodiment, the memory is communicably connected to the processor via a processing circuit and includes computer code for executing (e.g., by the processing circuit or the processor) the one or more processes described herein. The controller  502  includes an internal clock and/or standard capabilities for measuring passage of time in a computer system. Although  FIG. 5  shows the controller  502  as a discrete computing system, in some embodiments features attributed herein to the controller  502  are performed at a remote server and/or onboard a user&#39;s personal device (e.g., a smartphone or tablet of a user). 
     As shown in  FIG. 5 , the force sensor  210  is configured to generate a force signal indicative of a magnitude and direction of a force exerted on the force sensor  210 . The force signal may be an analog signal, with a magnitude proportional to the magnitude of force measured by the force sensor  210  and sign indicative of the direction of the force (e.g., positive indicating up and negative indicating down or vice versa), or a digital signal. The force sensor  210  may provide a substantially continuous signal to the controller  502 , so that the controller  502  continuously receives a real-time indication of the force exerted on the force sensor  210 . Various signal processing techniques (filtering, smoothing, amplifying) can be used to improve the user experience and performance of the linear positioning system  500 . 
     In the example of  FIG. 5 , the controller  502  is configured to output a motor voltage for the motor  128  based on the force signal from the force sensor  210 . The controller  502  can determine the motor voltage for the motor  128  using a program, algorithm, function, etc. configured to provide a velocity of the frame  120  (or other frame or member moved by the motor  128  in various embodiments) that varies as a function of the magnitude and sign of the force signal. The controller  502  may determine the amount of voltage to provide to the motor  128  (e.g., as a percentage of total capacity) by applying a function to the magnitude of the force signal. The function may be based on a known or predetermined relationship between velocity of the frame and motor voltage. The controller  502  may determine a sign of the motor voltage to be provided to the motor  128  based on the sign of the force signal. 
     In some embodiments, for example, the function is configured such that the absolute value of the motor voltage and of the velocity of the frame increase as a magnitude of the force increases. In such embodiments, the user can apply more force to the force sensor  210  to cause the frame  120  to move faster, and apply less force to the force sensor  210  to cause the frame  120  to move slower. When zero force is applied to the force sensor  210 , the velocity of the frame (and the voltage applied to the frame) is zero. 
     In some embodiments, the function is an exponential function. For example, the controller  502  may use a function |V|=C|f| x , where V is the motor voltage selected from the set −100%≤V≥100, f is the force, C is a constant scaling factor, and x is an exponential factor that varies in different embodiments. As another example, the controller  502  may use a function |v|=C|f| x , where v is velocity of the frame, along with another process mapping velocity to voltage. In such examples, the exponential factor x is preferably greater than one (e.g., 1.5, 2, 3, etc.), such that the velocity of the frame increases non-linearly with increased force. This can allow for fine, highly accurate repositioning of the frame when low amounts of force are provided, while also enabling relatively quick gross repositioning of the frame when large movements are desired. 
     In some embodiments, the controller  502  is configured to provide a deadband around zero force, such that the motor voltage (and the velocity) is kept at zero unless the magnitude of the force exceeds a threshold magnitude, at which point the motor voltage and velocity can start to increase from zero. The deadband may or may not be symmetric around zero, in various embodiments. The deadband can prevent the controller  502  from responding to environmental fluctuations, sensor noise, etc. and can help avoid other undesirable control behaviors. An example function that can be used by the controller  502  is shown in a graphical form in  FIG. 9  and described in detail with reference thereto below. 
       FIG. 5  thus shows that a motor voltage for the motor  128  is varied by the controller as a function of a force signal from the force sensor  210 . This arrangement allows for a highly intuitive interaction between a user and the linear positioning system  116 . Because the force sensor  210  is statically mounted on the frame  120  such that the force sensor  210  moves with the frame  120 , the perceived effect of this input and control modality for the user is that users perceive themselves as pushing the frame  120  in the direction that the user desires the frame  120  to move. A user is able to easily track the user input assembly  200  with the user&#39;s hand, maintaining contact and control with the user input assembly  200  as the frame  120  is moved. 
     Additionally, by mapping force input to velocity output, an intuitive relationship is established between the user input and the movement of the frame  120 . Other embodiments contemplated by the present disclosure include using the controller  502  and motor  128  for force multiplication, i.e., controlling the motor  128  to provide as multiple of the user&#39;s input force (e.g., F=k*f, where F is the force output by the motor, f is the measured input force, and k is a scaling factor greater than one). Although such an approach may be used in some embodiments of the present application, the movement of the frame  120  in such embodiments is dependent upon the weight of the frame  120  (i.e., its own gravitational forces which resist upward motion and increase downward motion) and the variable weight that may be supported by the cradles  122 . The mapping of force to velocity (or proxy for velocity such as voltage) by the controller  502  as described above allows for a user to control the motion of the frame  120  with the same effects in either direction (up or down) and substantially regardless of the weight supported by the frame  120  at any given point in time. Additionally, linking applied force to frame velocity (as compared to force/load) provides a more stable and controllable system and relatively simple implementation in hardware. 
     Although the primary examples herein relate to linear system, the control approaches described herein could also be applied along a curved path or in multiple dimensions. For example, force sensors could be used to measure applied force in multiple degrees of freedom and can be used as input for control of velocity of a load in the corresponding degrees of freedom. For example, movement in a plane could be controlled in this manner. 
     Referring now to  FIG. 6 , another linear positioning system  600  is shown, according to an example embodiment. In the example of  FIG. 6 , the linear positioning system  600  includes the force sensor  210 , controller  502 , and motor  128  as described above with reference to  FIG. 5 . The linear positioning system  600  varies from the linear positioning system  500  by including a switch  602  between the force sensor  210  and the controller  502 . 
     The switch  602  is configured to selectively connect and disrupt the connection between the force sensor  210  and the controller  502 . In the example of the linear positioning system  600  of  FIG. 6 , the controller  502  will receive no (zero) force signal from the force sensor  210  when the switch  602  is open and the connection therebetween is broken. Accordingly, the controller  502  will control the motor  128  to hold the frame  120  in a constant position while the switch  602  is open. When the switch  602  is closed, thereby connecting the force sensor  210  and the controller  502 , the controller can receive the force signal from the force sensor  210  and operate as described above. 
     In some embodiments, the switch  602  is a physical switch, button, sensor, or other input device which can be selected (closing the switch  602 ) when the user wants to use the linear positioning system  600  to reposition the frame  120 , and unselected (opening the switch  602 ) when the user wants the frame  120  to stay in its position. The switch  602  can be positioned somewhere on the stand  102  or the frame  104  to enable user selection of the switch  602 . 
     In other embodiments, the switch  602  is triggered by other software logic or sensors. For example, the switch  602  may be connected to sensors, tracking systems, force-production systems (e.g., as in  FIG. 10 , described below), in order to disable the linear positioning system  600  while an exercise is actively being performed at the apparatus  100 . The switch  602  may thus avoid inadvertent repositioning of the frame  120  during an exercise. As another example, the switch  602  may be communicable with an authentication system which requires a user to verify the user&#39;s identity and/or access privileges before the linear positioning system  600  can be used to operate the motor  128 . Many such variations of the switch  602  are possible. 
     Referring now to  FIG. 7 , a linear positioning system  700  is illustrated according to an exemplary embodiment. The linear positioning system  700  includes the force sensor  210  and the motor  128 , as in the linear positioning system  500  described above.  FIG. 7  shows that the linear positioning system  700  includes a controller  702 , which is a variation on the controller  502  described above. In particular, the controller  702  is enabled or otherwise configured to use feedback control to improve an accuracy of the mapping of the force measured by the force sensor  210  to velocity of the frame  120 . 
     The linear positioning system  700  is also shown as including a velocity sensor  708  to enable the feedback control. The velocity sensor  708  can be included with the motor  128  to measure velocity by counting rotations, for example, or may be positioned on the frame  120  and/or belt  126  to measure velocity in another way, such as, for example, using an inertial sensor. 
     As shown in  FIG. 7 , the controller  702  includes setpoint circuitry  704  which receives the force signal from the force sensor  210  and outputs a target velocity. The setpoint circuitry  704  can use various functions, algorithms, programs, operations, etc. to generate a target velocity. For example, in some embodiments, the target velocity is determined using a function having the form v target =S*C(|f|−f threshold ) x , where v is velocity of the frame, f is the force signal, C is constant scaling factor, x is an exponential factor (preferably greater than one as described above), f threshold  is a threshold value which defines the deadband and s determines the direction based on the sign of the force input and implements a deadband, e.g., s= 
     
       
         
           
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               . 
             
           
         
       
     
     Various other examples are possible in different embodiments. For example, in some embodiments, the controller  702  uses the function graphically represented in  FIG. 10  or a variation thereof. 
     The setpoint circuitry  704  supplies the target velocity to the feedback controller  706 . The feedback controller  706  receives the target velocity and a measured velocity from the velocity sensor  708 , and controls the motor  128  to drive the measured velocity toward the target velocity. For example, proportional-integral-derivative control or some other known feedback control approach can be used by the feedback controller  706 . In some embodiments, the feedback controller  706  uses a stored mapping of target velocity to motor voltage as a starting place, and then refines the motor voltage using the measurements from the velocity sensor  708 , in order to minimize an error between the measured velocity and the target velocity. These features enable the linear positioning system  700  to adjust for different gravitational loads on the frame  120  and/or compensate for any other variations that can affect the relationship between motor voltage and velocity. 
     Referring now to  FIG. 8 , a linear positioning system  800  is shown, according to an example embodiment. The linear positioning system  800  is shown a user identification device  802 , a controller  804 , the motor  128 , and a position sensor  810 . The linear positioning system  800  is an embodiment in which a desired position (target position) is determined and used in order to provide motorized movement of the frame  120  and cradles  122  to the target position. The linear positioning system  800  can be provided as an alternative to the linear positioning systems  500 ,  600 ,  700  of  FIGS. 5-7 , or can be combined therewith to provide an alternative control mode in which a desired position is used instead of force input for control of the motor  128 . 
     The linear positioning system  800  is shown to include a user identification device  802  configured to identify a user to the controller  804 . In some embodiments, the user identification device  802  is integrated into the apparatus  100 , and can be a touchscreen or other interface that allows a user to input a username, identification number, user height, etc. into the system for use by the controller  804 . In other embodiments, the user identification device  802  includes a sensor and processing system configured to automatically identify the user (e.g., using facial recognition) or identify a trait of the user (e.g., measure a user&#39;s height). In yet other embodiments, the user identification device  802  is a personal computing device of a user (e.g., smartphone) running an application associated with the apparatus  100 , and which is communicable with the controller  804  (e.g., via Bluetooth, Wi-Fi, etc.). The user identification device  802  can thereby provide identifying information (e.g., name, identity, height, etc.) relating to the user to the controller  804 . 
     The controller  804  is shown as including a target position determination circuit  806  and a motor controller  808 . The target position determination circuit  806  is configured to receive the identifying information from the user identification device  802  and determine a target position for the frame  120  based on the identifying information. For example, the target position determination circuit  806  may store user preferences for a list of users, and can determined the target position based on the user preferences for a user identified by the user identification device  802 . In some such embodiments, the target position is determined as the last position of the frame  120  used by the identified user. 
     In some embodiments, the target position is determined based on the user&#39;s height or other physical characteristic. For example, the target position may be determined based on the user&#39;s height to move the cradles to a preferred position for initiation of an expected or planned exercise. In some embodiments, the circuit  806  determines the target position as a height suitable for a squat-type exercise based on the user&#39;s height (e.g., to a position slightly below the user&#39;s shoulders). In other embodiment, the target position determination circuit  806  receives a selection of a particular exercise (e.g., from a device mounted on apparatus  100 , from a user&#39;s smartphone, from a processing system of a strength training system for example as shown in  FIG. 10 ) and determines a proper position of the frame  120  for the selected exercise. The target position can be determined by the target position determination circuit  806  in a variety of ways in various embodiments. 
     The motor controller  808  receives the target position from the target position determination circuit  806  and controls a voltage provided to the motor  128  in order to cause the motor to move the frame  120  to the target position. A position sensor  810  is included in the embodiment shown in order to monitor and verify the position to facilitate the motor controller  808  in controlling the motor based on the target position. The position sensor  810  may be included in the motor (e.g., counting rotations at the motor) or positioned elsewhere on the apparatus  100  (e.g., to directly detect the position of the frame  120  relative to the stand  102 ). Once the target position is achieved (as verified using the position sensor  810 ), the motor controller  808  can control the motor  128  to hold the frame  120  at the target position. 
     The target position may be updated by the controller  804  in response to a change in user, a selection of a user (e.g. a selection of different exercise, a request for a different height), or some other change considered by the target position determination circuit  806 . The motor controller  808  can then cause the motor  128  to move the frame  120  to an updated target position. As one advantageous scenario that can be provided by this approach, the linear positioning system  800  can automatically move the frame  120 , cradles  122 , and a barbell held by the cradles  122  to different positions preferred by different users alternating use of the same apparatus  100 , which may be very helpful to exercise partners of different heights. As another advantageous scenario that can be provided by this approach, the linear positioning system  800  can sequentially and automatically move the frame  120 , cradles  122 , and a barbell held by the cradles  122  to different target positions in accordance with a sequence of different exercise in an exercise routine (program, class, workout, etc.). 
     Any combination of the features described with reference to  FIGS. 5-8  should be considered to be within the scope of the present application. Additional functionality can be enabled by the combination of these features as well. For example the position sensor  810  can be used in the embodiments of  FIG. 5-7  to provide for controls around the ends of the range of motion of the frame  120 . The position sensor  810  can be used to reduce the motor voltage supplied to the motor  128  proximate the ends of the range of motion to slow and stop the frame before physical limits are met. 
     Referring now to  FIG. 9 , a graphical representation  900  of a function that can be used by the controller  502  or the controller  702  to determine a target velocity or motor voltage as a function of the measured force from the force sensor  210  is shown, according to an example embodiment.  FIG. 9  shows the user-applied force (measured force from the force sensor) on the horizontal axis and a target velocity or percentage of maximum voltage on the vertical axis. A line  902  represents the target velocity or percentage of maximum voltage as a function of the user-applied force. 
     In the example of  FIG. 9 , the line  902  illustrates that a deadband is provided in a region around zero applied force such that the velocity or voltage is set to substantially zero when the force is within the deadband (region  904 , indicated by vertical dashed lines) and non-zero outside the deadband. For positive values of force outside the deadband (greater than a force threshold), the line  902  curves upwardly from zero such that velocity (or voltage) increases exponentially in a positive direction as force increases (region  906 ). For negative values of force outside the deadband (magnitude greater than a force threshold), the line  902  curves downwardly from zero such that velocity (or voltage) decreases exponentially (increases exponentially in magnitude while having a negative direction) as force decreases (increases in magnitude in a negative direction (region  908 ). In both directions, the velocity or voltage reaches a maximum and plateaus at the maximum value, e.g., at 100% of maximum voltage (regions  910  and  912 ). 
     As shown in  FIG. 9 , the function represented by line  902  provides substantially equivalent behavior of the linear positioning system in both the positive and negative directions. That is, the velocity and/or voltage varies in a negative direction with a force applied in the negative direction in substantially the same way that the velocity and/or voltage varies in a positive direction with a force applied in the positive direction. A user would thus experience consistent response of the linear positioning system in both directions, which may enhance usability. In other embodiments, such symmetry is not provided and the function is different in the positive direction compared to the negative direction. 
     The function shown in  FIG. 9  is included for example purposes, and variations thereof may be included in various embodiments. For example, the size of the deadband and the degree of curvature in regions  906  and  906  may be different in various embodiments. In some cases, the function used in a particular implementation may be user-adjustable or selectable based on user preferences. 
     A function such as that shown in  FIG. 9  provides for inherently stable control. If the conversion from applied force to velocity is too high, the frame  120  or other load (and the input assembly coupled thereto) will quickly move away from the user&#39;s hand, thus reducing the force and reducing the velocity. 
     Referring now to  FIG. 10 , a perspective view of a fitness system  1000  is shown, according to an example embodiment. The fitness system  1000  includes the strength training apparatus  100 , in addition to additional features and systems configured to provide a full fitness experience, especially a resistance training experience. In particular, the fitness system  1000  includes the strength training apparatus  100  described above, a multi-cable force production system  1002 , a pacing lighting system  1004 , a display interface  1006 , an integrated bench  1008 , and adjustable rails  1010 . 
     The multi-cable force production system  1002  can be configured as described in detail in U.S. patent application Ser. No. 16/909,003, filed Jun. 23, 2020, the entire disclosure of which is incorporated by reference herein. The multi-cable force production system  1002  as shown here in  FIG. 10  includes multiple (shown as four) cables  1012  connected to a barbell  1014  that can be supported by the cradles  122 . The cables  1012  are connected to independent electric motors via separate pulleys  1016 . The electric motors can be operated to independently vary the tension in each cable in order to create a desired force profile at the barbell  1014 , as described in detail in the above-cited U.S. patent application Ser. No. 16/909,003. The multi-cable force production system  1002  can also include platform  1018 , which can include sensors as described in the above-cited U.S. patent application Ser. No. 16/909,003. 
     The pacing lighting system  1004  can be configured as described in detail in U.S. patent application Ser. No. 17/010,573, filed Sep. 2, 2020, the entire disclosure of which is incorporated by reference herein. The pacing lighting system  1004  as shown here in  FIG. 10  includes a pair of vertically-arranged rows of lighting element configured to illuminate dots (points, circles, areas) of different colors. The dots illuminated on the pacing lighting system  1004  can indicate to a user a desired/preferred range of motion for an exercise a real-time indication of the preferred position of the user (showing movement intended to be followed by the user), and a current position of the user (or barbell  1014 ) relative to that range of motion. As shown in  FIG. 10 , the pacing lighting system  1004  can be arranged parallel to the linear path along which the frame  120  can move, such that the pacing lighting system  1004  can illuminate points that correspond to heights relative to the frame  120 . In some cases, control of the pacing lighting system  1004  and the linear positioning system for the frame  120  are coordinated so that an illuminated dot intended to guide the user&#39;s motion is aligned with the cradles  122  at the beginning and end of an exercise. 
     The display interface  1006  is configured to show various instructions, exercise data, resistance amounts, exercise routines, and other information to a user. The display interface  1006  may be a touchscreen to enable interaction between the user and the display interface  1006 . For example, the display interface  1006  may be configured to accept user inputs requesting operations and changing settings for the strength training apparatus  100 , force production system  1002 , and/or pacing lighting system  1004 . Various customized exercise programs and content can be provided via the display interface  1006 , including as described in U.S. patent application Ser. No. 16/909,003 cited above and incorporated herein by reference. 
     The fitness system  1000  is also shown as including an integrated bench  1008  which can be selectively included or removed from the fitness system  1000  to enable exercises suitable for performance using a bench (e.g., bench press). The integrated bench  1008  may be configured to be coupled to the platform  1018  in some embodiments. The integrated bench  1008  can be adjustable to different inclinations for various exercises. In some embodiments, the integrated bench  1008  includes sensors or electronics to facilitate use of the integrated bench with other elements of the fitness system  1000 . 
     The fitness system  1000  is also shown as including adjustable rails  1010 . The adjustable rails  1010  are positioned below the cradles  122  and along sides of the platform  1018 , and are configured to stop the bar from moving lower than height defined by the adjustable rails  1010 . The adjustable rails  1010  can thus receive the barbell  1014  when a user is unable to complete an exercise or otherwise wishes to place the barbell  1014  somewhere other than in the cradles  122 . 
     Various hardware and/or software of the various elements of the fitness system  1000  can be integrated and/or interoperable to provide for a comprehensive, unified experience for users of the fitness system  1000 . For example the controller  502  described above can be provided as part of a control system for the fitness system  1000  that also controls the force production system  1002 , the pacing lighting system  1004 , and the display interface  1006 . As one feature enabled by this integration, the force production system  1002  can be controlled in coordinate with the motorized movement of the cradles  122  by the linear positioning systems described above by either allowing the cables  1012  to be extended as the cradles  122  move upwards or by retracting slack in the cables  1012  as the cradles  122  move downwards, in response to user input via the force sensor  210 . Various other integrations are also possible in various embodiments. 
     The foregoing description of embodiments has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from this disclosure. The embodiments were chosen and described in order to explain the principals of the disclosure and its practical application to enable one skilled in the art to utilize the various embodiments and with various modifications as are suited to the particular use contemplated. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the embodiments without departing from the scope of the present disclosure as expressed in the appended claims.