Patent Publication Number: US-2021170218-A1

Title: Versatile universal gym

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit of priority under PCT Chapter I, Article 8, and 35 U.S.C. § 119(e) of U.S. Provisional patent Application No. 62/656,126 entitled, “VERSATILE UNIVERSAL GYM,” filed Apr. 11, 2018, and of U.S. Provisional patent Application No. 62/679,828 entitled, “VERSATILE UNIVERSAL GYM,” filed Jun. 3, 2018, which are both incorporated herein by reference in their entirety. 
    
    
     COPYRIGHT NOTICE 
     A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
     FIELD OF INVENTION 
     This invention relates to exercise equipment comprising at least one weight stack. 
     BACKGROUND OF THE INVENTION 
     Universal gyms, which contain stations for several exercises, are known. Also known are exercise machines designed to allow for a single or small number of exercises, such as a bicep curl machine or a rowing machine. A problem arises when an athlete or a weight gym proprietor wants to allow for a wide variety of exercises. That person must deploy numerous machines to occupy a relatively vast floor space in a home or gym to obtain those exercises. 
     Another problem arises with currently-known systems. Exercises must be performed within the design characteristics of the machine. A finite number of positions can accommodate only a certain range of adjustments. If an athlete is larger or smaller than the “average” person contemplated by the machine designer, or has special needs, that athlete may struggle to adjust existing equipment for optimal comfort and performance. A large athlete would need appropriately-sized equipment; but that equipment would be nearly useless for a petite athlete who might barely fit the equipment&#39;s smallest settings. An athlete confined to a wheel chair might not find that equipment useful at all. 
     Yet a further problem can arise with certain known exercise equipment. A single source of resistance such as a weight stack can provide the resistance against which an exercise is performed. However, if the plates of the weight stack have too large of a mass increment between them, an athlete might fail to optimize her repetitions to muscle fatigue because she must use either too light or too heavy a weight from the weight stack. Thus, it could be useful to apply a smaller mass increment than provided by the weight stack in some cases. Similarly, if the weight stack does not have enough mass, particularly strong athletes could not enjoy the maximum benefit from exercising on such a machine. Moreover, it can be desirable to alter the nature of the resistance by adding an elastic band to an exercise. As the exercise progresses through its range of motion, the resistance can change as an elastic band becomes stretched. Many known exercise machines do not accommodate a variety of sources for the resistance. 
     Finally, it is known that the human body can lift different weight with different exercises. A person usually can squat significantly more weight than that person can bench press; and the bench press weight usually dwarfs what that person can curl with their biceps. So far, exercise machine manufacturers have designed different machines for each of those exercises, or inadequately addressed all of those exercises in a single universal gym. As a result, the serious athlete would need multiple purpose-built machines to exercise optimally, requiring a gym with significant floor space. 
     SUMMARY OF THE INVENTION 
     Unexpectedly, and building upon decades of experience as a personal trainer, Applicant has invented a versatile universal gym. In some cases, Applicant&#39;s universal gym can occupy a remarkably-small footprint in a home or a gym, and yet provide for a vast, nearly infinite array of exercises. In further cases, Applicant&#39;s universal gym can further employ attractive and decorative panels that disguise the universal gym when not in use. 
     Accordingly, some embodiments of the present invention relate to an apparatus for exercising against a resistance, comprising:
     a frame, comprising a plurality of vertical members mutually supporting a plurality of horizontal members;   the resistance comprising at least one weight stack contained by the frame;   one or more cables routed about the frame via a plurality of pulleys selectively connecting the at least one weight stack to one or more exercise attachment points;   at least one floating pulley removably and adjustably attached to the frame comprising at least one extension cable having a first end opposite a second end, the first end being attachable to the one or more exercise attachment points, and the second end providing at least one floating exercise attachment point;   wherein at least some of the vertical members of the plurality of vertical members have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction.   

     In some cases, the accessory receiving ports can receive the floating pulley, thereby providing a wide variety of ways to engage the weight stack. Optionally, free weights, elastic bands, and the weight stack alone or in combination can provide the resistance for exercise. 
     Further embodiments relate to a floating pulley for an apparatus for exercising against a resistance, the floating pulley comprising:
     an extension cable having a first end opposite a second end, the first end being attachable to an exercise attachment point on the apparatus, and the second end providing a floating exercise attachment point; and   an accessory engagement structure for removably and adjustably coupling to an accessory receiving port on the apparatus.   

     Still further embodiments relate to an exercise bench adapted for use with an apparatus for exercising against a resistance, the exercise bench comprising:
     a bench frame comprising at least one horizontal bench member mutually supporting at least one vertical bench member;   a seat cushion supported by the bench frame; and   one or more bench accessory receiving ports in the frame, the one or more bench accessory receiving ports being adapted to receive at least one floating pulley to provide at least one bench exercise attachment point.   

     Additional embodiments relate to methods of exercising against a resistance, one such method comprising:
     obtaining an apparatus comprising:   a frame, comprising a plurality of vertical members mutually supporting a plurality of horizontal members;   the resistance comprising at least one weight stack contained by the frame;   one or more cables routed about the frame via a plurality of pulleys selectively connecting the at least one weight stack to one or more exercise attachment points;   at least one floating pulley removably and adjustably attached to the frame comprising at least one extension cable having a first end opposite a second end, the first end being attachable to the one or more exercise attachment points, and the second end providing at least one floating exercise attachment point;   wherein at least some of the vertical members of the plurality of vertical members have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction;   connecting at least one exercise engagement device to one or more exercise attachment points, the at least one floating exercise attachment point, or a combination thereof; and   moving the at least one exercise engagement device against the resistance, thereby exercising against the resistance.   

     Still further embodiments of the present invention relate to methods of making the apparatuses described herein, one such method comprising: routing the one or more cables about the frame via the plurality of pulleys to selectively connect the at least one weight stack to the one or more exercise attachment points. 
     Yet additional embodiments relate to methods of making the floating pulleys as described herein, one such method comprising routing the extension cable through the floating pulley. 
     Other embodiments relate to a gliding extension device for an apparatus for exercising against a resistance, the gliding extension device comprising:
     a roller carriage comprising a plurality of rollers adapted to glidingly engage a guide rod;   an extension frame extending from the roller carriage, the extension frame comprising a proximal end adjacent the roller carriage and a distal end;   an exercise engagement device at or near the distal end; and   an exercise attachment point receiver attached to the roller carriage, the proximal end of the extension frame, or both.   

     Even further embodiments relate to an extension arm for an apparatus for exercising against a resistance, the extension arm comprising:
     an angular selection bracket for attaching the extension arm to a frame of the apparatus, the angular selection bracket comprising a plurality of angle selection ports for establishing a plurality of extension angles;   an extension member extending from the angular selection bracket and comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points;   wherein an extension angle in the plurality of extension angles is determined by a portion of a member of the frame and a portion of the extension member.   

     Still further embodiments provide a sit-up board for an apparatus for exercising against a resistance, the sit-up board comprising:
     a padded board for supporting an athlete;   at least one longitudinal member supporting the padded board; and   at least one lateral member supporting the padded board;   wherein the at least one longitudinal member, the at least one lateral member, or both, comprise a plurality of sit-up board accessory receiving ports.   

     Yet additional embodiments relate to a multivector extension device for an apparatus for exercising against a resistance, the multivector extension device comprising:
     a brace for removably and adjustably attaching to a frame of the apparatus;   a multivector extension arm comprising a plurality of accessory receiving ports;   a ball joint joining the multivector extension arm to the brace while allowing the multivector extension arm significant freedom of movement relative to the brace;   at least one exercise engagement device removably attached to the multivector extension arm via a first accessory receiving port in the plurality of accessory receiving ports; and   at least one exercise attachment point receiver removably attached to the multivector extension arm via a second accessory receiving port in the plurality of accessory receiving ports.   

     Certain embodiments provide multivector extension supports for an apparatus for exercising against a resistance, one such multivector extension support comprising
     a brace for removably and adjustably attaching to a frame of the apparatus; and   a resilient support attached to the brace for receiving and protecting the frame from contact by a multivector extension device.   

     Still further embodiments relate to additional methods of exercising, one such method being a method of exercising against a plurality of resistances having multiple vectors, comprising:
     obtaining a multivector extension device comprising:
       a brace for removably and adjustably attaching to a frame of an apparatus;   a multivector extension arm comprising a first accessory receiving port, a second accessory receiving port, and a third accessory receiving port;   a ball joint joining the multivector extension arm to the brace while allowing the multivector extension arm significant freedom of movement relative to the brace;   a first exercise attachment point receiver removably attached to the multivector extension arm via the first accessory receiving port;   a second exercise attachment point receiver removably attached to the multivector extension arm via the second accessory receiving port; and   an exercise engagement device removably attached to the multivector extension arm via the third accessory receiving port; and   
       attaching a first resistance to the first exercise attachment point receiver;   attaching a second resistance to the second exercise attachment point receiver, wherein the first resistance has a first vector and the second resistance has a second vector, wherein the first vector differs from the second vector, and wherein the first vector and the second vector thereby form the plurality of resistances having multiple vectors; and   moving the exercise engagement device against the plurality of resistances having multiple vectors, thereby exercising against a plurality of resistances having multiple vectors.   

     Still further embodiments provide mobile members for an apparatus for exercising against a resistance, one such mobile member comprising: 
     an elongate section having a first end opposite a second end;
 
a first frame engagement device, at the first end of the elongate section, for securing the mobile member to a first member of a frame of the apparatus; and
 
a second frame engagement device, at the second end of the elongate section, for securing the mobile member to a second member of the frame.
 
     Further embodiments relate to a foot stretching device for an apparatus for exercising against a resistance, the foot stretching device comprising: 
     a brace for removably and adjustably attaching to a frame of the apparatus;
 
an elongate sole portion attached to the brace by a brace hinge; and
 
a heel portion attached to the sole portion by a heel hinge.
 
     Further additional embodiments provide foot exercise attachments for an apparatus for exercising against a resistance, one such attachment comprising: 
     a scaffold for receiving a foot of an athlete;
 
one or more straps for securing the scaffold to the foot; and
 
one or more exercise attachment point receivers for engaging a resistance to the scaffold.
 
     Yet other embodiments relate to leg press accessories for an apparatus for exercising against a resistance, one such leg press accessory comprising: 
     an angular guide having an angular guide brace for removably and adjustably attaching to a horizontal member of a frame of the apparatus;
 
an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide;
 
the extension member receiver being adapted to receive an extension member having a foot pad held in place on the extension member with a foot pad brace comprising a spring-loaded pin for engaging the extension member.
 
     Still other embodiments provide adjustable arcuate bases for an apparatus for exercising against a resistance, one such adjustable arcuate base comprising: 
     a stage comprising one or more retractable pins for engaging one or more accessory receiving ports on one or more vertical members of a frame of the apparatus;
 
an angular guide affixed to the stage;
 
an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide; the extension member receiver further comprising a spring-loaded pin; the extension member receiver being adapted to receive an extension member and secure the extension member with the spring-loaded pin.
 
     Still further embodiments relate to angular telescopic extension devices for an apparatus for exercising against a resistance, one such angular telescopic extension device comprising: 
     an angular selection brace for selectively attaching the angular telescopic extension device to a frame of the apparatus, the angular selection brace comprising a retractable pin for engaging an accessory receiving port in the frame of the apparatus;
 
an angle selector comprising a plurality of angle selection ports attached to the angular selection brace;
 
an angular selection bracket connected to the angular selection brace by a hinge, the hinge defining an axis of rotation, and comprising an angle selecting retractable pin for engaging an angle selection port in the plurality of angle selection ports on the angle selector for establishing a telescopic extension angle;
 
a telescopic extension arm extending from the angular selection bracket and comprising two or more nested extension members each adapted to be secured at a chosen length with a spring-loaded pin, the two or more nested extension members comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points;
 
wherein the telescopic angle is determined by a first imaginary line between the axis of rotation and a first angle selection port in the plurality of angle selection ports, on one hand, and a second imaginary line between the axis of rotation and a chosen angle selection port in the plurality of angle selection ports.
 
     Further additional embodiments relate to portable weight stack assemblies for an apparatus for exercising against a resistance, one such portable weight stack assembly comprising: 
     a portable frame comprising one or more portable vertical members mutually supporting one or more portable horizontal members;
 
a portable weight stack contained by the portable frame;
 
one or more portable cables routed about the portable frame via a plurality of portable pulleys selectively connecting the portable weight stack to a slidably adjustable portable exercise attachment point; and
 
at least one footer for stabilizing the frame.
 
     Yet further additional embodiments provide frames for an apparatus for exercising against a resistance, comprising: 
     a plurality of vertical members mutually supporting a plurality of horizontal members,
 
wherein the plurality of vertical members and the plurality of horizontal members define a rectangular footprint having an aspect ratio of about 1:4, about 2:9, about 1:5, about 3:10, about 1:3, or about 3:10.
 
     While the disclosure provides certain specific embodiments, the invention is not limited to those embodiments. A person of ordinary skill will appreciate from the description herein that modifications can be made to the described embodiments and therefore that the specification is broader in scope than the described embodiments. All examples are therefore non-limiting. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts one embodiment of the invention, apparatus  100 , in a perspective view. 
         FIGS. 2 and 3  depict further embodiments comprising horizontal member  221  and vertical member  311 . 
         FIG. 4  further depicts apparatus  100 . 
         FIG. 5  depicts cable  585  selectively connecting weight stack  541  to exercise attachment point  561 . 
         FIG. 6  depicts cable  685  selectively connecting weight stack  641  to exercise attachment point  661 . 
         FIG. 7  depicts cable  785  selectively connecting weight stack  741  to exercise attachment point  761 . 
         FIG. 8  depicts exercise attachment point  861 . 
         FIG. 9  depicts exercise attachment point  961 . 
         FIG. 10  depicts floating pulley  1081 . 
         FIG. 11  depicts floating pulley  1181 . 
         FIG. 12  provides a front elevation view of apparatus  1200 . 
         FIG. 13  depicts a right side elevation view of extension arm  1300 . 
         FIG. 14  provides a perspective view of apparatus  1400 . 
         FIG. 15  provides a perspective view of a Smith machine  1500  comprising frame members  1561 ,  1562 . 
         FIG. 16  provides a perspective view of weight stack  1641  with free weight  1665 . 
         FIG. 17  provides a perspective view of weight stack  1741  with elastic band  1766 . 
         FIG. 18  provides a perspective view of exercise bench  1800 . 
         FIGS. 19, 20, and 21  depict apparatus  1900  having doors  1901 ,  1902 . 
         FIG. 22  depicts hollow-headed bolt  2220  mounting panel  2208  to vertical member  2214  via rivet  2231 . 
         FIGS. 23 and 24  depict apparatus  2300  comprising dip bar  2350 . 
         FIG. 25  depicts apparatus  2500  comprising angle selector  2531 . 
         FIGS. 26 and 27  depict apparatus  2600  comprising multi-use exerciser  2601 . 
         FIG. 28  depicts apparatus  2800  comprising sit-up board  2801 . 
         FIG. 29  depicts apparatus  2900  comprising flat-screen TV  2901 . 
         FIG. 30  provides a perspective view of apparatus  3000 . 
         FIG. 31  depicts a right-side elevation view of extension arm  3100 . 
         FIG. 32  depicts floating pulley  3200 . 
         FIG. 33  depicts floating pulley  3300 . 
         FIG. 34  depicts apparatus  3400  comprising sit-up board  3401 . 
         FIG. 35  provides a right-side elevation view of gliding extension device  3501 . 
         FIG. 36  provides a perspective view of multivector extension device  3600 . 
         FIG. 37  depicts eye bolt  3662 . 
         FIG. 38  depicts hand grip  3621 . 
         FIGS. 39 and 44  provide a right-side view of multivector extension device  3900 . 
         FIG. 40  provides a partial perspective view demonstrating how support cone  3981  of multivector extension device  3900  protects frame member  4012  from contact by multivector extension arm  3951 . 
         FIG. 41  shows a right-side view, and  FIG. 42  shows a front view, of multivector extension support  4100 . 
         FIG. 43  shows a right-side view of multivector extension device  3600  in operation with multivector extension support  4100 . 
         FIGS. 45 and 46  provide a right-side view of multivector extension device  4500 . 
         FIG. 47  shows a front view, and  FIG. 48  shows a perspective view, of mobile member  4700 . 
         FIG. 49  shows mobile member  4700  engaged between frame members  4911  and  4912 . 
         FIG. 50  shows a front view of mobile member  5000 . 
         FIG. 51  shows a left-side view of foot stretching device  5100 . 
         FIG. 52  shows a left-side view of foot exercise attachment  5200 . 
         FIG. 53  shows a left-side view of leg press accessory  5300 . 
         FIGS. 54 and 55  show adjustable arcuate base  5400 . 
         FIGS. 56, 57, and 58  show angular telescopic extension member  5600 . 
         FIGS. 59 and 60  depict portable weight stack assembly  5900 . 
         FIGS. 61, 62, 63, 64, 65, 66, and 67  provide several views of frame  6100 , which has square tubing. 
         FIG. 68  provides a front perspective view of frame  6800 , which has round tubing. 
         FIG. 69  provides a front perspective view of frame  6900 , which has hexagonal tubing. 
     
    
    
     DETAILED DESCRIPTION 
     As required, detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various forms. The figures are not necessarily to scale, and some features may be exaggerated to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention. 
     Unless defined otherwise, all technical and scientific terms used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this disclosure belongs. In the event that there is a plurality of definitions for a term herein, those in this section prevail unless stated otherwise. 
     Where ever the phrase “for example,” “such as,” “including” and the like are used herein, the phrase “and without limitation” is understood to follow unless explicitly stated otherwise. Similarly “an example,” “exemplary” and the like are understood to be non-limiting. 
     The term “substantially” allows for deviations from the descriptor that don&#39;t negatively impact the intended purpose. Descriptive terms are understood to be modified by the term “substantially” even if the word “substantially” is not explicitly recited. 
     The term “about” when used in connection with a numerical value refers to the actual given value, and to the approximation to such given value that would reasonably be inferred by one of ordinary skill in the art, including approximations due to the experimental and or measurement conditions for such given value. 
     The terms “comprising” and “including” and “having” and “involving” (and similarly “comprises”, “includes,” “has,” and “involves”) and the like are used interchangeably and have the same meaning. Specifically, each of the terms is defined consistent with the common United States patent law definition of “comprising” and is therefore interpreted to be an open term meaning “at least the following,” and is also interpreted not to exclude additional features, limitations, aspects, etc. Thus, for example, “a device having components a, b, and c” means that the device includes at least components a, b and c. Similarly, the phrase: “a method involving steps a, b, and c” means that the method includes at least steps a, b, and c. 
     Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”. 
     Any discussion of the prior art throughout the specification should in no way be considered as an admission that such prior art is widely known or forms part of common general knowledge in the field. 
     It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative. 
     As stated above, some embodiments of the present invention relate to an apparatus for exercising against a resistance. As used herein, “exercising against a resistance” indicates movement of the human body or a part thereof against a force such as provided by gravity acting on a mass, friction, elastic deformation, or the like. The mass can be provided by the body of the athlete or a part thereof; or it can be provided by a selected portion of a weight stack or a free weight device such as a barbell, dumbbell, weight plate, kettle ball, or the like. Elastic bands provide resistance as the material of the band responds to, and opposes, an athlete&#39;s effort to elastically deform the band. Friction can provide resistance such as, for example, by applying a brake against a reciprocating or rotating device such as a flywheel. 
     At least one weight stack contained by the frame appears in several embodiments. In some cases, the resistance comprises two independent weight stacks contained by the frame. A weight stack has a number of plates, each of similar or different masses, and a device such as a rod with appropriately-placed holes so that a desired number of plates in the weight stack can be selected for a particular exercise. A pin or key, optionally tipped with a spring-loaded ball bearing, can connect the desired number of plates in the weight stack to the rod. At one end of the rod, a pulley can connect the rod and thereby the desired number of plates in the weight stack to a cable that when pulled, lifts the desired number of plates from the weight stack. 
     A cable routed about the frame selectively connects the weight stack to an exercise attachment point via one or more pulleys. Generally, the plates of the weight stack will move up and down when an exercise is performed; perfect verticality, however, is not required. The cable with the one or more pulleys translates the up and down motion of the plates from the weight stack into a suitable direction at the exercise attachment point. An exercise attachment point is a place where the cable terminates and allows for the attachment of an exercise engagement device. Any suitable exercise engagement device can be used, such as, for example, a hand grip, an ankle strap, a torso strap, a head strap, a barbell, a dumbbell, or the like, or a multivector extension device as described herein. As used herein, a barbell means a device generally intended for a two-handed grip; a dumbbell is a device generally intended for a one-handed grip. Optionally, a barbell or a dumbbell can receive additional mass in the form of weight plates, and optionally may have one or more elastic band attachment points. Thus, in some cases, a barbell or a dumbbell can engage the weight stack through an exercise attachment point, a floating exercise attachment point (see below), optionally receive one or more weight plates, and optionally engage one or more elastic bands, thereby providing a highly-selective and variable resistance to the athlete. As can be appreciated, weights such as provided by the weight stack or free weight plates, impart a steady resistance, while an elastic band generally provides less resistance when the band is slightly stretched, yet increases resistance as the stretching increases. 
     At least one floating pulley is removably and adjustably attached to the frame. In some cases, a floating pulley can be removably and adjustably attached to the frame by coupling to one or more of the first vertical accessory receiving ports, one or more of the second vertical accessory receiving ports, or a combination thereof. In other cases, a floating pulley can be removably and adjustably attached to the frame by coupling to one or more of the first horizontal accessory receiving ports, one or more of the second horizontal accessory receiving ports, or a combination thereof. The floating pulley is removable, as it can be completely detached from the apparatus, usually without the need for any special tool. The floating pulley is adjustable, in that it can be securely attached to the frame via any of the several accessory receiving ports. The floating pulley has an extension cable having a first end opposite a second end. One of the two ends can be attached to an exercise attachment point, and the other end provides a floating exercise attachment point, to which any suitable exercise engagement device can attach. Accordingly, the floating pulley can be placed in any suitable accessory receiving port in the frame, and then one end of the extension cable is attached to the cable of the frame connected to the weight stack. Then the exercise attachment point on the frame can be moved so that there is no slack in the several cables. A floating pulley can have any suitable number of pulley wheels. For example, a floating pulley can have a single pulley wheel. For another example, the floating pulley can have two pulley wheels, and the extension cable passes between the two pulley wheels. 
     The cable connecting the weight stack can be routed about the frame in any suitable manner. The cable can run along the outside of the frame, in some cases. In other cases, the cable can be routed inside the frame for at least a portion of its course. The cables, including extension cables, useful according to the present invention can be any suitable cable. In some cases, a multi-wire woven or twisted steel cable coated with a suitable flexible polymer can be used. Often, the ends of such cables terminate in a loop optionally reinforced with a metal eyelet. In further instances, just before the end of the terminus of a cable can appear a pulley stop such as a small spherical rubber stopper. The pulley stop is designed to prevent the terminus of the cable from unintentionally exiting the exercise attachment point or the floating pulley, as the case may be. 
     The apparatus comprises a frame having vertical members and horizontal members. Any suitable numbers of vertical members and horizontal members can be used. The vertical members and horizontal members can be made out of any suitable material, such as, for example, steel, aluminum, structural polymers, and combinations thereof. In some instances, the frame comprises tubes. The tubes can have any suitable cross section, such as, for example, round, oval, polygonal, rectangular, or square. At least some of the vertical members of the frame have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction. Having an axis in a certain direction means that an accessory receiving port can receive and secure a rod-like structure. This is useful for securing an exercise attachment point, for example. For another example, a bar can enter an accessory receiving port and thereby support an exercise against the bar: an athlete can execute a pull-up or a dip using the bar, or an elastic band can be secured by the bar. The accessory receiving port can have any suitable shape, such as, for example, circular, oval, square, or polygonal. In some cases, an accessory receiving port comprises two openings in a tube that makes up the frame. The rod-like structure enters a first opening in a facing surface of the tube, and proceeds through the tube to exit the second opening in the opposite surface of the tube. In this way, the two openings provide ample support to the rod like structure. 
     It can be noticed by one of ordinary skill in the art that vertical members need not be strictly vertical, and that horizontal members need not be strictly horizontal. Any suitable member can be included, such as, for example, a member that curves, a member that adheres to an angle other than strictly vertical or strictly horizontal, and combinations thereof. A vertical member is a member that has a vertical aspect; a horizontal member is a member that has a horizontal aspect. Discerning between vertical members and horizontal members can be accomplished by any suitable method. For example, members having a greater angle with respect to the horizontal can be considered vertical members, when there are members having a lesser angle with respect to the horizontal. A frame constructed of members all positioned at 45 degrees relative to the horizontal can be said to comprise vertical members. 
     In certain embodiments, at least some of the horizontal members of the plurality of horizontal members have first horizontal accessory receiving ports having axes in the first direction, and second horizontal accessory receiving ports having axes in a third direction. In some cases, the first direction is “front-to-back,” and the second direction is “left-to-right.” Both of those directions can be parallel to the horizontal. In further cases, the third direction can be “up-and-down.” Thus, the first direction, second direction, and third direction can all be perpendicular to each other; this need not be the case in every situation. The several directions can orient in any suitable manner relative to each other, and relative to the horizontal and the vertical. 
     The apparatus of several embodiments of the present invention comprises one or more exercise attachment points. In some cases, an exercise attachment point comprises one or two pulleys and the terminus of a cable. Pulling on the terminus of the cable moves the desired number of plates on the weight stack. The exercise attachment point can be slidably adjustable along one of the vertical members or one of the horizontal members of the frame. Slidably adjustable means that exercise attachment point can be moved along the member, and then secured at a specific point on the member. Securing the exercise attachment point can be achieved through any suitable means. For example, a spring-loaded pin or rod-like structure on the exercise attachment point can engage an accessory receiving port, thereby securing the exercise attachment point at that accessory receiving port. Optionally, the exercise attachment point can be removed from the frame and re-attached to a different member; in other cases, the exercise attachment point can only slide along a single member without the use of tools to reconfigure the apparatus. In some cases, a vertical member has a vertical length, and comprises first vertical accessory receiving ports and second vertical accessory receiving ports for substantially the entire vertical length. In further cases, a horizontal member has a horizontal length, and comprises first horizontal accessory receiving ports and second horizontal accessory receiving ports for substantially the entire horizontal length. Having accessory receiving ports substantially the entire length means at least more than 50%, more than 60%, more than 70%, more than 80%, or more than 90% of the length. 
     In some instances of the present invention, one or more doors can be attached to the frame. Optionally, at least one door pivotally mounted on at least one vertical member in the plurality of vertical members of the frame. Certain instances provide two doors, each attached to the outside vertical members and closing at the middle of the apparatus. A door can have any suitable structure. For example, a door may comprise at least one door vertical member mutually supporting at least one door horizontal member; and the at least one door vertical member may comprise first door vertical accessory receiving ports having axes in a fourth direction, and second door vertical accessory receiving ports in a fifth direction. Similarly, for example, a door may comprise at least one door horizontal member having first door horizontal accessory receiving ports having axes in the fourth direction, and second door horizontal accessory receiving ports having axes in a sixth direction. The fourth, fifth, and sixth directions can be any suitable directions. For example, any of them can align with any one or more of the first, second, and third directions. In some cases, the fourth direction is substantially perpendicular to the fifth direction. In other cases, the fourth direction and the fifth direction are substantially parallel to the horizontal. In still further cases, the sixth direction is substantially normal to the horizontal. The door members can have any suitable cross section. In some examples, the at least one door vertical member comprises square tubing. In further examples, the at least one door horizontal member comprises square tubing. 
     Certain additional embodiments of the present invention provide one or more decorative panels to disguise the apparatus when it is not in use or for other purposes. Some of those embodiments relate to at least one decorative panel mounted to the frame. Further of those embodiments provide at least one decorative panel mounted to a door. Any suitable means can be used to mount the panel to the apparatus. For example, a decorative panel can be mounted using at least one hollow-headed bolt, the hollow-headed bolt comprising a head and a threaded shaft, the head comprising an axial recess for receiving and retaining a panel-mounting rivet. The bolt attaches to the frame, for example, and the axial recess secures the rivet which holds the panel in place. 
     Further embodiments of the present invention relate to a door having an exercise attachment point, a floating exercise attachment point, or a combination thereof. This can be achieved by any suitable method. An exercise attachment point or a floating exercise attachment point comprising a pulley can be relocated to one or more of the door members, for example, by engaging any of the door accessory receiving ports. Accordingly, in some instances, a floating pulley can be removably and adjustably attached to the frame by coupling to one or more of the first door vertical accessory receiving ports, one or more of the second door vertical accessory receiving ports, or a combination thereof. In other instances, the floating pulley can be removably and adjustably attached to the frame by coupling to one or more of the first door horizontal accessory receiving ports, one or more of the second door horizontal accessory receiving ports, or a combination thereof. 
     Any suitable exercise equipment or accommodations therefor can be used in accordance with the present invention. To assist in the use of free weights and in particular barbells, additional embodiments include at least one power rack for receiving at least one barbell and allowing the performance of at least one exercise with the at least one barbell. Certain instances provide a Smith machine for receiving the barbell and allowing the performance of at least one exercise with the barbell using the Smith machine. Further instances allow for a dip bar, optionally installed to a door of the frame. Additional instances allow for a sit-up board, optionally installed to a door of the frame. Still further instances allow for a multi-use support pad that can be positioned at various angles and heights. Such a multi-use support pad can be used for back extensions and supported bicep curls at a relatively high height and high angle relative to the horizontal, and for sit-ups and crunches at a relatively low height and angle relative to the horizontal. As used herein, a multi-use support pad is mounted on a multi-use exerciser, which comprises a longitudinal member that has ankle braces that can be adjusted as to position along the longitudinal member. The multi-use exerciser can attach to an angle selector at the frame, which angle selector positions the longitudinal member at various angles, and places the multi-use pad at various heights for different exercises. The multi-use pad itself can adopt various tilt angles relative to the longitudinal member. Appropriately-positioned exercise attachment points and floating pulleys can, in some cases, allow access to the weight stack for such exercises, or free weights can be used. Optionally, any attachment can be constructed for convenient stowage within the apparatus when either the attachment or the apparatus are not in use. 
     Still further embodiments allow for the installation of a flat panel television, sound system, media player, and the like. Such components can be used for instructional videos or audio programs, exercise-motivating programs such as music playlists, or purely entertaining programing such as sports broadcasts and movies to be enjoyed during a workout. A media player can be any suitable device, such as, for example, a personal computer, a smart phone, a DVD video player, a BlueRay® video player, an MP3 player, an MP4 player, or a combination thereof. 
     As stated above, the resistance can be provided by any suitable means. Accordingly, some instances of the present invention provide an apparatus having at least one elastic band attachment point to provide or augment the resistance. The elastic band can loop around any suitable appendage of the frame, for example, and then loop around any suitable object moved by the athlete during exercise. Suitable objects includes barbells, dumbbells, and parts of the athlete&#39;s body such as wrists, waist, and ankles. Similarly, the resistance can be provided by free weights, for example. A barbell or a dumbbell having a suitable connectors such as, for example, a hook or carabiner, can attach to an exercise attachment point or a floating exercise attachment point. Thus, in further instances of the present invention, the resistance can be selectively provided by the at least one weight stack, at least one free weight device, at least one elastic band, the weight of the person exercising with the apparatus, or a combination thereof. 
     Yet additional embodiments relate to methods of exercising against a resistance. The athlete obtains any of the apparatuses disclosed herein, in some such methods, and connects at least one exercise engagement device to one or more exercise attachment points, the at least one floating exercise attachment point, or a combination thereof; and moves the at least one exercise engagement device against the resistance, thereby exercising against the resistance. 
     Still other embodiments relate to methods of making any of the apparatuses disclosed herein. Some of those embodiments include routing the one or more cables about the frame via the plurality of pulleys to selectively connect the at least one weight stack to the one or more exercise attachment points. Similarly, further embodiments relate to any of the floating pulleys disclosed herein, comprising routing the extension cable through the floating pulley. Optionally, once the cable or extension cable is properly routed, a pulley stop can be added to an end of the cable, which is then secured in a loop formation optionally with a metal eyelet. 
     Still further embodiments relate to an exercise bench that can be used with any of the apparatuses disclosed herein. An advantage arises in some cases from attaching a floating pulley to the bench, thereby allowing an athlete to exercise using the weight stack(s) of the apparatus. The floating pulley can attach to one or more bench accessory receiving ports in the frame. Certain examples of the exercise bench include a back cushion supported by the frame and capable of adopting an incline angle. Any suitable incline angle, including a negative incline angle relative to the horizontal, can be made available by the back cushion. In some cases, the incline angle ranges from −80 degrees to 120 degrees, relative to the horizontal. Such a broad range of possible incline angles allows for a wide variety of body positions for the athlete. In other cases, the incline angle ranges from zero degrees to 60 degrees relative to the horizontal. 
     It can be a problem in certain exercise benches that the device supporting the back cushion can pop out, causing the back cushion to come crashing down and potentially injuring the athlete. Accordingly, further embodiments of the present invention provide an exercise bench comprising an incline angle selection device comprising: 
     a back cushion brace engaging the back cushion;
 
a plurality of incline angle selection slots for receiving the back cushion brace and establishing the incline angle with the back cushion brace; and
 
a brace guard for preventing the back cushion brace from departing from the incline angle selection device.
 
     The apparatuses, frames, devices, and components thereof of the present invention can be made from any suitable material. For example, steel, aluminum, structural polymers such as high-density polyalkanes, polyurethanes, nylons, perfluorinated polyalkanes such as Teflon®, and combinations thereof can be mentioned. 
     Further instances of the present invention relate to a gliding extension device for an apparatus for exercising against a resistance, the gliding extension device comprising: a roller carriage comprising a plurality of rollers adapted to glidingly engage a guide rod; an extension frame extending from the roller carriage, the extension frame comprising a proximal end adjacent the roller carriage and a distal end; an exercise engagement device at or near the distal end; and an exercise attachment point receiver attached to the roller carriage, the proximal end of the extension frame, or both. As used herein, a gliding extension device is intended to provide smooth and guided movement along a guide rod; that guided movement is against a resistance in the manner of a Smith machine. A gliding extension device of the present invention can be operated with one hand, for example with a single hand grip. Or, a two-handed bar can be used. Optionally, the two-handed bar can connect two gliding extension devices, allowing for example, two separate weight stacks to be engaged. 
     Optionally, a gliding extension device can comprise a brake mechanism for the safety and convenience of the athlete. A brake mechanism allows the gliding extension device to maintain its position relative to the guide rod in spite of any resistance on the gliding extension device. Any suitable brake mechanism can be used. In some instances, the brake mechanism comprises a brake lever at the exercise engagement device, and a braking clamp at the roller carriage for arresting at least one roller among the plurality of rollers, the guide rod, or both, the brake lever adapted to disengage the braking clamp when the brake lever is manipulated. 
     Any suitable resistance can be used with a gliding extension device. The device can have one or more exercise attachment point receivers, which can receive a carabiner or other mechanism for connecting resistance to the gliding extension device. An exercise attachment point receiver can be an eye bolt for selectively connecting a weight stack via a cable, or it can be a J-hook for receiving an elastic band. In some cases, an extension frame further comprises a plurality of extension receiving ports for providing one or more extension exercise attachment points. 
     A guide rod can have any suitable orientation. For example, a guide rod can be vertical, and the gliding extension device can provide a Smith machine-like experience for squat exercises. For another example, a guide rod can be horizontal, and the gliding extension device can function as a rowing exercise device. In addition, a guide rod can be straight, curved, or a combination thereof. 
     Further instances of the present invention relate to an extension arm for an apparatus for exercising against a resistance, the extension arm comprising: an angular selection bracket for attaching the extension arm to a frame of the apparatus, the angular selection bracket comprising a plurality of angle selection ports for establishing a plurality of extension angles; an extension member extending from the angular selection bracket and comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points; wherein an extension angle in the plurality of extension angles is determined by a portion of a member of the frame and a portion of the extension member. So, for example, a vertical member indicates one side of the angle, and the extension member establishes another side of the angle. The extension arm can be adapted to receive one or more floating pulleys capable of selectively connecting at least one weight stack to establish one or more extension exercise attachment points. 
     Certain instances provide an innovative sit up board that can receive a floating pulley for a great variety of exercise options. In one instance, a sit-up board comprises a padded board for supporting an athlete; at least one longitudinal member supporting the padded board; and at least one lateral member supporting the padded board; wherein the at least one longitudinal member, the at least one lateral member, or both, comprise a plurality of sit-up board accessory receiving ports. The sit-up board accessory receiving ports can receive a floating pulley as described herein. Optionally, the sit-up board also comprises two foot braces that the athlete can use to stabilize while using the sit-up board. One or more handgrips also can appear. 
     A sit-up board can attach to the frame of an apparatus by any suitable means. For example, one or more pins on the sit-up board can engage accessory receiving ports of a frame of the apparatus. Optionally, one or more footers can stabilize the sit-up board. 
     Unexpectedly, applicant has invented devices and methods for exercising against a plurality of resistances that have different vectors or directions. For example, gravity can pull a free weight in a downward direction, and an athlete can lift that weight upward against gravity. Now suppose an elastic band under tension is applied to the motion of the athlete, and the elastic band is oriented in a direction other than downward, that is, parallel to or in concert with gravity. An elastic band pulling horizontally, or in any direction other than vertically, would force the athlete lifting the weight vertically to use a larger variety of muscles that might not be engaged if the athlete were only lifting the weight. This multivector resistance exercise can be extraordinarily beneficial. For example, joints such as the shoulders, knees, ankles, elbows, and wrists can be strengthened by having the athlete exercise against two or more resistances having different vectors. Significantly, the apparatuses of the present invention provide the opportunity for a wide variety of vectoral combinations for resistance exercise. 
     Accordingly, in some cases, a multivector extension device for an apparatus for exercising against a resistance comprises a brace for removably and adjustably attaching to a frame of the apparatus; a multivector extension arm comprising a plurality of accessory receiving ports; a ball joint joining the multivector extension arm to the brace while allowing the multivector extension arm significant freedom of movement relative to the brace; at least one exercise engagement device removably attached to the multivector extension arm via a first accessory receiving port in the plurality of accessory receiving ports; and at least one exercise attachment point receiver removably attached to the multivector extension arm via a second accessory receiving port in the plurality of accessory receiving ports. 
     Any suitable brace can be used. For example, the brace may comprise a spring-loaded pin manipulated by a knob for engaging the frame of the apparatus. Further, the materials of the multivector extension device are not limited. For example, the multivector extension arm can comprise square tubing made from any suitable material such as, for example, steel, aluminum, polymer, and combinations thereof. Any suitable exercise engagement device can be used with a multivector extension device, such as, for example a single hand grip, a two-handed bar, an ankle strap, a torso strap, a head strap, or the like. 
     Similarly, any suitable exercise attachment point receivers can be used, such as, for example, a J-hook for receiving elastic band, an eye bolt for receiving a carabiner for selectively connecting to a weight stack, and combinations thereof. Exercise attachment point receivers and exercise engagement devices can attach to the multivector extension device in any suitable manner. In some cases, an exercise attachment point receiver or an exercise engagement device can include a spring-loaded pin that selectively secures the receiver or the device to the multivector extension device. 
     Sometimes, the multivector extension arm comprises at least two telescoping members, and the plurality of accessory receiving ports comprises a plurality of telescoping member accessory receiving ports. The telescoping members can be nested, that is, wherein one member fits inside the other. In such a case, it is possible that one of the at least two telescoping members is selectively secured to the multivector extension arm with at least one spring-loaded pin. When telescoping members are present, an exercise engagement device such as a single hand grip can be removably attached to the multivector extension arm via a third accessory receiving port in the plurality of telescoping member accessory receiving ports. Similarly, an exercise attachment point receiver such as a J-hook or an eye bolt can be removably attached to the multivector extension arm via a fourth accessory receiving port in the plurality of telescoping member accessory receiving ports. 
     Further instances of the present invention provide structure so that the multivector extension device or some part of it does not bang against the frame of the apparatus. For example, in some cases, the brace of the multivector extension device comprises a support cone positioned about the ball joint to protect the frame from contact by the multivector extension arm. The support cone can be made of any suitable material, such as, for example, natural rubber, synthetic rubber, polyurethane, silicone, or a combination thereof. 
     In a similar manner, a multivector extension support can also prevent a multi-vector extension device or another piece of equipment from contacting the frame of the apparatus. A multivector extension support can include a brace for removably and adjustably attaching to a frame of the apparatus; and a resilient support attached to the brace for receiving and protecting the frame from contact by a multivector extension device. In some cases, the brace comprises a spring-loaded pin for engaging the frame of the apparatus. In further cases, the resilient support defines a recess for receiving the multivector extension device. Such a recess can receive a multi-vector extension device or similar piece of equipment when it is not in motion. Any suitable material can be used for the resilient support. Certain instances provide a resilient support comprising natural rubber, synthetic rubber, polyurethane, silicone, or a combination thereof. 
     Methods of exercising against a plurality of resistances having multiple vectors also appear in some embodiments of the present invention. Employing the multivector extension devices as described herein, one such method includes attaching a first resistance to the first exercise attachment point receiver; attaching a second resistance to the second exercise attachment point receiver, wherein the first resistance has a first vector and the second resistance has a second vector, wherein the first vector differs from the second vector, and wherein the first vector and the second vector thereby form the plurality of resistances having multiple vectors; and moving the exercise engagement device against the plurality of resistances having multiple vectors, thereby exercising against a plurality of resistances having multiple vectors. 
     Resistances can be arranged so that the directions of the several vectors orient in any suitable combination. In some cases, vectors or components thereof align or oppose each other. Also, it should be noted that the relative orientations of vectors may change as an exercise motion is performed. Two vectors initially at right angles to each other will not necessarily form a right angle throughout the entire motion of the exercise. This change in relative orientation can be advantageous, increasing or decreasing the overall resistance at different places in the exercise motion. The direction of an exercise motion, moreover, can align with or against one or more vectors of the plurality of resistances applied; or the direction of an exercise motion need not align with any vector of resistance. Of course, care should be taken so that the multiple resistances do not unduly stress or injure the athlete. Initially, small resistances are recommended. 
     Greater versatility is afforded by the use of various mobile members to add structure to the frame in a facile manner. Some instances of the present invention provide a mobile member for an apparatus for exercising against a resistance, the mobile member comprising: an elongate section having a first end opposite a second end; a first frame engagement device, at the first end of the elongate section, for securing the mobile member to a first member of a frame of the apparatus; and a second frame engagement device, at the second end of the elongate section, for securing the mobile member to a second member of the frame. If it is desired that the mobile member provides exercise attachment points, then in certain instances the elongate section comprises square tubing. In certain of those cases, the mobile member comprises between the first end and the second end, first mobile accessory receiving ports having axes in a first mobile direction, and second mobile accessory receiving ports having axes in a second mobile direction. 
     Alternatively, a mobile member can be designed to support contact with part of the human body. For example, the elongate section may comprise a foamed polymer, a cushion, or a combination thereof. Any suitable foamed polymer can be used. In certain instances, the foamed polymer is chosen from latex foam rubber, polyurethane foam, styrene-butadiene foam, or a combination thereof. 
     A mobile member can be secured to the frame of an apparatus by any suitable structure. In one example, the first frame engagement device comprises a first rod having a first port for receiving a first retention key, the first rod being adapted to enter a first accessory receiving port of the first member of the frame. In another example, the second frame engagement device comprises a second rod optionally having a second port for receiving a second retention key, the second rod being adapted to enter a second accessory receiving port of the second member of the frame. The idea behind such structure is to allow the first rod to be inserted into a first accessory receiving port on one member, and then aligning the second rod with a second accessory receiving port on another member. When the second rod is inserted into the second accessory receiving port, the first retention key is inserted into the first port to secure the mobile member in the installed position. This is aided in some cases in which the first rod is longer than the second rod. In other cases, the second rod is longer than the first rod. 
     Still further embodiments relate to a foot stretching device comprising: a brace for removably and adjustably attaching to a frame of the apparatus; an elongate sole portion attached to the brace by a brace hinge; and a heel portion attached to the sole portion by a heel hinge. The foot stretching device can be secured to the frame of the apparatus by any suitable structure. For example, the brace may comprise a spring-loaded pin for engaging the frame of the apparatus. 
     A foot stretching device can include any suitable materials. For example, in some cases the heel portion comprises a non-stick surface. Broadly, in certain cases the foot stretching device comprises steel or aluminum or a combination thereof. 
     Further embodiments provide for a foot exercise attachment comprising: a scaffold for receiving a foot of an athlete; one or more straps for securing the scaffold to the foot; and one or more exercise attachment point receivers for engaging a resistance to the scaffold. Any suitable materials can be used. For example, in some cases, the scaffold comprises steel, aluminum, or a combination thereof. Similarly, the straps may comprise hook-and-loop fabric (Velcro®), snaps, buttons, buckles, or a combination thereof. The scaffold may comprise a toe portion for engaging the top of the toes of the foot, optionally when the foot is wearing a shoe. 
     Still further embodiments relate to a leg press accessory for an apparatus for exercising against a resistance, the leg press accessory comprising: an angular guide having an angular guide brace for removably and adjustably attaching to a horizontal member of a frame of the apparatus; an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide; the extension member receiver being adapted to receive an extension member having a foot pad held in place on the extension member with a foot pad brace comprising a spring-loaded pin for engaging the extension member. To accommodate the foot pad brace, in some cases, the extension member comprises a plurality of extension receiving ports for providing one or more extension exercise attachment points. To accommodate the athlete, further cases allow the horizontal member of the frame to receive a bench having one or more bench braces for engaging the horizontal member, the one or more bench braces comprising one or more spring-loaded pins for engaging the horizontal member. 
     Shoulder presses and calf raises can be accommodated in certain embodiments of the present invention by an adjustable arcuate base comprising: a stage comprising one or more retractable pins for engaging one or more accessory receiving ports on one or more vertical members of a frame of the apparatus; an angular guide affixed to the stage; an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide; the extension member receiver further comprising a spring-loaded pin; the extension member receiver being adapted to receive an extension member and secure the extension member with the spring-loaded pin. In some cases, the one or more retractable pins comprises two spring-loaded pins. In further cases, the extension member comprises a plurality of extension receiving ports for providing one or more exercise engagement devices and/or one or more exercise attachment point receivers. 
     Even more versatility can be obtained from an apparatus according to the present invention with the use of an angular telescopic extension device. In some cases, the angular telescopic extension device comprises: an angular selection brace for selectively attaching the angular telescopic extension device to a frame of the apparatus, the angular selection brace comprising a retractable pin for engaging an accessory receiving port in the frame of the apparatus; an angle selector comprising a plurality of angle selection ports attached to the angular selection brace; an angular selection bracket connected to the angular selection brace by a hinge, the hinge defining an axis of rotation, and comprising an angle selecting retractable pin for engaging an angle selection port in the plurality of angle selection ports on the angle selector for establishing a telescopic extension angle; a telescopic extension arm extending from the angular selection bracket and comprising two or more nested extension members each adapted to be secured at a chosen length with a spring-loaded pin, the two or more nested extension members comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points; wherein the telescopic angle is determined by a first imaginary line between the axis of rotation and a first angle selection port in the plurality of angle selection ports, on one hand, and a second imaginary line between the axis of rotation and a chosen angle selection port in the plurality of angle selection ports. 
     Certain instances provide that the angular telescopic extension device fits onto a vertical member of the frame of the apparatus. In further instances, the angle selecting retractable pin comprises a spring-loaded pin. Any suitable number of nested extension members can be used, such as, for example, two nested extension members, three nested extension members, or four nested extension members. 
     It can be helpful in many cases to have a relatively light weight portable weight stack assembly to use with the apparatuses of the present invention. A portable weight stack assembly can add additional weight and optionally an additional vector to an exercise. In certain instances, a portable weight stack assembly comprises: a portable frame comprising one or more portable vertical members mutually supporting one or more portable horizontal members; a portable weight stack contained by the portable frame; one or more portable cables routed about the portable frame via a plurality of portable pulleys selectively connecting the portable weight stack to a slidably adjustable portable exercise attachment point; and at least one footer for stabilizing the frame. 
     If an athlete or two are to maneuver a portable weight stack assembly, the total weight cannot be excessive in some cases. Accordingly, in some instances, the portable weight stack assembly weighs no more than about 200 lbs, no more than about 150 lbs., no more than about 100 lbs., no more than about 75 lbs., or no more than about 50 lbs. In further instances, the portable weight stack assembly weighs at least about 50 lbs., at least about 75 lbs., at least about 100 lbs., at least about 150 lbs., or at least about 200 lbs. 
     To accommodate different configurations for a variety of exercises, additional instances provide that at least one of the one or more portable vertical members comprises first portable vertical accessory receiving ports having an axis in a first portable direction, and second portable vertical accessory receiving ports having an axis in a second portable direction. Similarly, further instances provide that at least one of the one or more portable horizontal members comprises first portable horizontal accessory receiving ports having an axis in the first portable direction, and second portable horizontal accessory receiving ports having an axis in a third portable direction. 
     Unexpectedly, certain apparatuses of the present invention provide for an exceptionally high density of exercises. This high density potentially obviates the need for numerous space-consuming pieces of equipment in a gym. In several cases, the high density is provided by certain unique properties of some of the frames of the present invention. Accordingly, some embodiments provide a frame comprising: a plurality of vertical members mutually supporting a plurality of horizontal members, wherein the plurality of vertical members and the plurality of horizontal members define a rectangular footprint having an aspect ratio of about 1:4, about 2:9, about 1:5, about 3:10, about 1:3, or about 3:10. As used herein, “aspect ratio” refers to the depth of the apparatus versus the width. Other embodiments provide that the aspect ratio is at least about 1:4, at least about 2:9, at least about 1:5, at least about 3:10, at least about 1:3, or at least about 3:10. Still further embodiments provide that the aspect ratio is no more than about 1:4, no more than about 2:9, no more than about 1:5, no more than about 3:10, no more than about 1:3, or no more than about 3:10. 
     A frame can have any suitable dimensions. For example, in some cases, the frame has a depth of at least about 1 foot, at least about 2 feet, at least about 3 feet, at least about 4 feet, at least about 5 feet, or at least about 6 feet. In further cases, the frame has a depth of no more than about 1 foot, no more than about 2 feet, no more than about 3 feet, no more than about 4 feet, no more than about 5 feet, or no more than about 6 feet. Similarly, further instances provide the frame with a width at least about 3 feet, at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, at least about 12 feet, at least about 13 feet, at least about 14 feet, or at least about 15 feet. In additional instances, the frame has a width of no more than about 3 feet, no more than about 4 feet, no more than about 5 feet, at least about 6 feet, no more than about 7 feet, no more than about 8 feet, no more than about 9 feet, no more than about 10 feet, no more than about 11 feet, no more than about 12 feet, no more than about 13 feet, no more than about 14 feet, or no more than about 15 feet. 
     Yet additional instances provide the frame having a height of at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, or at least about 12 feet. Still further instances relate to the frame having a height of at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, or at least about 12 feet. 
     To accommodate additional configurations, in some cases, at least some of the vertical members of the plurality of vertical members of the frame have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction. In further cases, at least some of the horizontal members of the plurality of horizontal members have first horizontal accessory receiving ports having axes in the first direction, and second horizontal accessory receiving ports having axes in a third direction. 
     Any suitable tubes or rods can be used to construct the frame of an apparatus. In some cases, the frame comprises square tubing, circular tubing, hexagonal tubing, or a combination thereof. 
     DETAILED DESCRIPTION OF THE DRAWINGS 
     Further embodiments of the present invention can be described by reference to the accompanying drawings. 
       FIG. 1  depicts one embodiment of the invention, apparatus  100 . Apparatus  100  has a frame comprising a plurality of vertical members  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117 , and  118  mutually supporting a plurality of horizontal members  121 ,  122 ,  123 ,  124 ,  125 ,  126 ,  127 ,  128 ,  129 ,  131 ,  132 ,  136 , and  137 . Additional vertical members and/or horizontal members can be added as desired. The frame of apparatus  100  contains weight stack  141 , and weight stack  142 . Cable  185  is routed about the frame via a plurality of pulleys  151 ,  154 ,  155 ,  156  (and others not labeled) to selectively connect weight stack  141  to exercise attachment point  161 . Cable  186  is routed about the frame via a plurality of pulleys  171 ,  172 ,  173 ,  174 ,  175 ,  176 ,  177 ,  178 , (and another not labeled) to selectively connect weight stack  142  to exercise attachment point  162 . Exercise attachment point  161  is slidably adjustable along vertical member  111 . Exercise attachment point  162  is slidably adjustable along vertical member  117 . Floating pulley  181  is removably and adjustably attached to the frame at horizontal member  125 . Extension cable  183  attaches at a first end to exercise point  161  via carabiner  163 , and at a second end to hand grip  191  to provide a floating exercise attachment point. Floating pulley  182  is removably and adjustably attached to the frame at horizontal member  125 . Extension cable  184  attaches at a first end to exercise point  162  via carabiner  164 , and at a second end to hand grip  192  to provide a floating exercise attachment point. Apparatus  100  has numerous accessory receiving ports (unlabeled) further explained in the following figures. Decorative panels (not shown) can be mounted in any suitable configuration, including but not limited to: between vertical members  111  and  112 ; between vertical members  117  and  118 , and between vertical members  112  and  118 . 
       FIGS. 2 and 3  depict further embodiments comprising horizontal member  221  and vertical member  311 . Horizontal member  221 , which is a piece of square tubing made from a suitable steel alloy, comprises first horizontal accessory receiving ports  291 ,  292 ,  293 , and  294 . Horizontal accessory receiving port  291  can be considered to include hole  271 , as a suitably-shaped accessory can enter port  291  and hole  271  (or vice versa), and receive stabilization thereby. Vertical member  311 , which is a piece of square tubing made from a suitable steel alloy, comprises first vertical accessory receiving ports  371 ,  372 , and  373 . First vertical accessory receiving port  371  can be considered to include hole  381 . Vertical member  311  also has second vertical accessory receiving ports  361 ,  362 , and  363 . Vertical accessory receiving port  371  has an axis  301  in a first direction. Vertical accessory receiving port  362  has access  302  in a second direction. As shown, horizontal accessory receiving port  291  has an axis  201  in the first direction. Horizontal member  221  also has second horizontal accessory receiving ports  281 ,  282 ,  283  and  284 . Second horizontal accessory receiving port  284  has an axis  203  in a third direction. 
       FIG. 4  further depicts apparatus  100 , with some features already shown in  FIG. 1  omitted for clarity. Vertical member  113  has first vertical accessory receiving ports  187 , which have axes in a first direction that can be described as “front-to-back.” Vertical member  113  also has second vertical accessory receiving ports  188 , which have axes in a second direction that can be described as “left-to-right.” Horizontal member  123  has first horizontal accessory receiving ports  197 , which have axes in the first direction. Horizontal member  123  also has second horizontal accessory receiving ports  198 , which have axes in a third direction, which can be described as “up-and-down.” Horizontal member  136  has horizontal accessory receiving ports  193  and  194  in the second direction and the third direction, respectively. The first direction and the second direction are substantially parallel to the horizontal; and the third direction is substantially normal to the horizontal. Each vertical member and each horizontal member shown in  FIG. 4  has accessory receiving ports substantially along the entire length of each member. Any matter of exercise accessories can engage any of the accessory receiving ports found anywhere on apparatus  100 , to allow for exercise against a resistance provided by either or both weight stacks  141 ,  142 , free weights, elastic bands, the weight of the athlete&#39;s own body, or a combination thereof. The versatility of apparatus  100  can be further expanded by placing similar apparatuses together, with or without mechanical connection between them, and allowing floating exercise attachment points to connect to any suitable exercise attachment points on the several apparatuses. Multiple weight stacks can be brought together in a wide variety of possible exercises. 
     In certain instances of the present invention, apparatus  100  can have remarkably-small dimensions, such as, for example, 9 feet wide (from the vertical member  111  to vertical member  117 ) and 3 feet deep (from vertical member  117  to vertical member  118 ). It is believed that containing such a wide variety of exercises in such a small footprint is unprecedented. This small footprint may offer a dramatic improvement to the home-gym market and to the commercial-gym market alike. 
       FIG. 5  depicts cable  585  selectively connecting weight stack  541  to exercise attachment point  561 . Exercise attachment point  561  is slidably adjustable along a vertical member of the frame of an apparatus (not shown) by manipulating knob  564 , which operates a spring-loaded pin suitable for engaging an accessory receiving port (not shown). Exercise attachment point  561  also comprises two pulleys  565 ,  567  to allow cable  585  significant versatile freedom of movement when carabiner  562  is moved during an exercise. Pulley stop  568 , which is a rubber sphere, prevents cable  585  from exiting exercise attachment point  561 . The other end of cable  585  attaches at connector  563  to exercise attachment point  561 . Pulleys  557 ,  556 ,  555 ,  554 ,  551 ,  552 , and  553  route cable  585  between its two ends through a frame (not shown). When exercise attachment point  561  is slidably adjusted between pulley  553  and pulley  557 , the length of cable  585  between connector  563  and pulleys  565 ,  567  does not change. However, when carabiner  562  is pulled, the length of cable  585  between connector  563  and pulleys  565 ,  567  shortens, causing pulley  551  to raise a selected portion of weight stack  541  to provide resistance to the exercise. 
       FIG. 6  depicts cable  685  selectively connecting weight stack  641  to exercise attachment point  661 . The routing of cable  685  in  FIG. 6  is analogous to the routings of cables  185 ,  186  in  FIG. 1 . Exercise attachment point  661  is slidably adjustable along a vertical member of the frame of an apparatus (not shown) by manipulating knob  664 , which operates a spring-loaded pin suitable for engaging an accessory receiving port (not shown). Exercise attachment point  661  also comprises two pulleys  665 ,  667  to allow cable  685  significant versatile freedom of movement when carabiner  662  is moved during an exercise. Pulley stop  668 , which is a rubber sphere, prevents cable  685  from exiting exercise attachment point  661 . The other end of cable  685  attaches at connector  663  to exercise attachment point  661 . Pulleys  659 ,  656 ,  652 ,  651 ,  653 ,  657 ,  658 ,  654 , and  655  route cable  685  between its two ends. When exercise attachment point  661  is slidably adjusted between pulley  655  and pulley  659 , the length of cable  685  between connector  663  and pulleys  665 ,  667  does not change. However, when carabiner  662  is pulled, the length of cable  685  between connector  663  and pulleys  665 ,  667  shortens, causing pulley  651  to raise a selected portion of weight stack  641  to provide resistance to the exercise. 
       FIG. 7  depicts cable  785  selectively connecting weight stack  741  to exercise attachment point  761 . Exercise attachment point  761  is slidably adjustable along a horizontal member of the frame of an apparatus (not shown) by manipulating knob  764 , which operates a spring-loaded pin suitable for engaging an accessory receiving port (not shown). Exercise attachment point  761  also comprises two pulleys  765 ,  767  to allow cable  785  significant versatile freedom of movement when carabiner  762  is moved during an exercise. Pulley stop  768 , which is a rubber sphere, prevents cable  785  from exiting exercise attachment point  761 . The other end of cable  785  attaches at connector  763  to exercise attachment point  761 . Pulleys  755 ,  752 ,  751 ,  753 ,  754 ,  756 , and  757  route cable  785  between its two ends. When exercise attachment point  761  is slidably adjusted between pulley  755  and pulley  757 , the length of cable  785  between connector  763  and pulleys  765 ,  767  does not change. However, when carabiner  762  is pulled, the length of cable  785  between connector  763  and pulleys  765 ,  767  shortens, causing pulley  751  to raise a selected portion of weight stack  741  to provide resistance to the exercise. 
       FIG. 8  depicts exercise attachment point  861 . Exercise attachment point  861  comprises a brace  871  having knob  864  which operates a spring-loaded pin suitable for engaging an accessory receiving port along a vertical or horizontal member of the frame of an apparatus (not shown). Pulleys  865 ,  867  route cable  885  to carabiner  862 . Pulley stop  868  prevents cable  885  from exiting exercise attachment point  861 . The other end of cable  885  (not shown) is routed through the frame of the apparatus and is selectively connected to a weight stack therein, in some embodiments of the present invention. Hinge  873  allows pulleys  865 ,  867  to swing back and forth (in this case, into and out of the plane of the page), to accommodate a wide variety of exercises performed by pulling carabiner  862  away from pulleys  865 ,  867 . Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  862 . Sometimes, if desirable, an extension cable and a floating pulley can be attached to carabiner  862  for maximum flexibility in designing further exercises. 
       FIG. 9  depicts exercise attachment point  961 . Exercise attachment point  961  comprises a brace  971  having knob  964  which operates a spring-loaded pin suitable for engaging an accessory receiving port along a vertical or horizontal member of the frame of an apparatus (not shown). Pulleys  965 ,  967  route cable  985  to carabiner  962 . Pulley stop  968  prevents cable  985  from exiting exercise attachment point  961 . The other end of cable  985  (not shown) is routed through the frame of the apparatus and is selectively connected to a weight stack therein, in some embodiments of the present invention. Pivot  973  allows pulleys  965 ,  967  to rotate up to 360 degrees (in this case, into and out of the plane of the page), to accommodate a wide variety of exercises performed by pulling carabiner  962  away from pulleys  965 ,  967 . Rotation at pivot  973  is limited of course by cable  985 . Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  962 . Sometimes, if desirable, an extension cable and a floating pulley can be attached to carabiner  962  for maximum flexibility in designing further exercises. 
       FIG. 10  depicts floating pulley  1081 . Floating pulley  1081  comprises brace  1075 , which houses knob  1042 , which in turn operates spring-loaded pin  1041 . Spring-loaded pin  1041  can engage an accessory receiving port. It can be said that floating pulley  1081  has an accessory engagement structure comprising brace  1075 , knob  1042 , and spring-loaded pin  1041  for removably and adjustably coupling to an accessory receiving port on an apparatus. It also can be said that floating pulley  1081  has only a single pulley wheel. Floating pulley  1081  further comprises extension cable  1084  terminating at a second end with carabiner  1062 . Pulley stop  1068  prevents extension cable  1084  from exiting floating pulley  1081 . Hinge  1073  allows floating pulley  1081  to swing back and forth (in this case, into and out of the plane of the page). Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  1062 . Sometimes, if desirable, a further extension cable and a further floating pulley can be attached to carabiner  1062  for maximum flexibility in designing further exercises. 
       FIG. 11  depicts floating pulley  1181 . Floating pulley  1181  comprises brace  1175 , which houses knob  1142 , which in turn operates spring-loaded pin  1141 . Spring-loaded pin  1141  can engage an accessory receiving port. It can be said that floating pulley  1181  has an accessory engagement structure comprising brace  1175 , knob  1142 , and spring-loaded pin  1141  for removably and adjustably coupling to an accessory receiving port on an apparatus. It also can be said that floating pulley  1181  has only a single pulley wheel. Floating pulley  1181  further comprises extension cable  1184  terminating at a second end with carabiner  1162 . Pulley stop  1168  prevents extension cable  1184  from exiting floating pulley  1181 . Pivot  1173  allows floating pulley  1181  to rotate up to 360 degrees (in this case, into and out of the plane of the page). Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  1162 . Sometimes, if desirable, a further extension cable and a further floating pulley can be attached to carabiner  1162  for maximum flexibility in designing further exercises. 
       FIG. 12  provides a front elevation view of apparatus  1200 . A plurality of vertical members  1211 ,  1212 ,  1213 , and  1214  mutually support a plurality of horizontal members  1221 ,  1222 ,  1223 , at  1224 . Each of those vertical members and horizontal members have accessory receiving ports; only accessory receiving ports in the first direction are shown in  FIG. 12 . Exercise attachment point  1261  is slidably adjustable along vertical member  1221  by manipulating knob  1264 . Floating pulley  1281  comprises brace  1275  and is removably and adjustably attached to the frame at horizontal member  1221 . Knob  1242  can be manipulated to allow floating pulley  1281  to move along the horizontal member  1221 , or to be removed therefrom entirely. Floating pulley  1281  further comprises an extension cable  1284  having a first end  1285  attached at exercise attachment point  1261 , and a second end at carabiner  1262  providing a floating exercise attachment point. Extension cable  1284  further comprises pulley stops  1268 ,  1269 .  FIG. 12  illustrates the versatility of certain embodiments of the present invention: virtually any accessory receiving port anywhere on the frame can anchor an exercise attachment point or a floating exercise attachment point. Any slack in extension cable  1284 , such as for example when floating pulley  1281  is brought closer to vertical member  1211 , can be taken up by moving exercise attachment point  1261  lower on vertical member  1211 . Similarly, the further from vertical member  1211  floating pulley  1281  moves, exercise attachment point  1261  can be moved higher on vertical member  1211  to provide more of extension cable  1284  to span the distance between exercise attachment point  1261  and floating pulley  1281 . Apparatus  1200  can further comprise weight stacks and cables, among other things, as described herein. 
       FIG. 13  depicts a right-side elevation view of extension arm  1300 . Extension arm  1300  comprises brace  1375 , which houses spring-loaded pin  1341 , which is manipulated by knob  1342 . Together, brace  1375 , pin  1341 , and knob  1342  allow extension arm  1300  to be removably and adjustably attached to a frame of an apparatus (not shown). Extension arm  1300  further comprises extension member  1351  extending from brace  1375  and comprising a plurality of extension receiving ports  1387 . Floating pulley  1381 , comprising extension cable  1384  ending at carabiner  1362 , is removably attached to extension arm  1351  by manipulating knob  1382 , which operates another spring-loaded pin (not shown). It can be said that carabiner  1362  represents both a floating exercise attachment point and an extension exercise attachment point in this embodiment. 
       FIG. 14  provides a perspective view of apparatus  1400 . Apparatus  1400  illustrates a power rack for receiving at least one barbell  1431  for the performance of at least one exercise with the barbell  1431 . Vertical members  1413 ,  1414 ,  1415 , and  1416  (and others) mutually support horizontal members  1423 ,  1425 ,  1433 , and  1435  (and others) to form a frame for apparatus  1400 . Each vertical member and each horizontal member of apparatus  1400  is depicted with accessory receiving ports (unlabeled) substantially along the entire length of each member. Rack accessories  1451 ,  1452  are removably attached to vertical members  1414  and  1416 , respectively, and hold barbell  1431 . Rod  1461  is positioned between vertical members  1413  and  1414  to protect an athlete exercising with barbell  1431 ; similarly, rod  1462  is positioned between vertical members  1415  and  1416  for the same purpose. Apparatus  1400  can further comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 15  provides a perspective view of a Smith machine  1500  comprising frame members  1561 ,  1562 . Vertical members  1514  and  1516  mutually support horizontal members  1521 ,  1522 , and  1523 . Any of members  1514 ,  1516 ,  1521 ,  5022 , and  1523  can represent members of a frame of an apparatus as described herein; or they can represent a distinct device that can be attached to the frame of such an apparatus. Here, Smith machine  1500  is depicted with numerous accessory receiving ports to maximize the versatility and interoperability with apparatuses as described herein. For example, any of horizontal members  1521 ,  1522 , and  1523  can receive one or more floating pulleys, augmenting the resistance provided by barbell  1531 . Smith machine  1500  can be part of an apparatus that further comprises weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 16  provides a perspective view of weight stack  1641  with free weight  1665 . As illustrated previously for other embodiments, cable  1685  can operate to lift pulley  1651  when an exercise is performed. Pulley  1651  in this case is connected to rod  1631 , which engages weight stack  1641 . Rod  1631  has a series of holes (not seen) aligned with holes  1671 ,  1672 ,  1673 ,  1674 ,  1675 ,  1676 , and  1677  in weight plates  1621 ,  1622 ,  1623 ,  1624 ,  1625 ,  1626 , and  1627 , respectively, of weight stack  1641 . Weight selection key  1615  is placed by an athlete into desired hole  1673 , so that when cable  1685  lifts pulley  1651  and thereby rod  1631 , weight plates  1621 ,  1622  and  1623  will be lifted also. This illustrates one way of selectively connecting weight stack  1641  to one or more exercise attachment points (not shown) via cable  1685 . Here, device  1660  allows the addition of free weight plate  1665 . Device  1660  comprises hollow shaft  1661  which fits over rod  1631 , and comprises a pulley-protecting collar  1663 . Hollow shaft  1661  further comprises rod  1662 , to which free weight  1665  has been added. Rod  1662  represents a free weight attachment point. In this way, greater versatility in the increment and the amount of weight provided by weight stack  1641  can be obtained. 
       FIG. 17  provides a perspective view of weight stack  1741  with elastic band  1766 . As illustrated previously for other embodiments, cable  1785  can operate to lift pulley  1751  when an exercise is performed. Pulley  1751  in this case is connected to rod  1731 , which engages weight stack  1741 . Here, device  1760  allows the addition of free weight plate  1765  and elastic band  1766 . Device  1760  comprises hollow shaft  1761  which fits over rod  1731 , and comprises a pulley-protecting collar  1763 . Shaft  1761  further comprises rod  1762 , to which free weight  1765  has been added. In addition, elastic band  1766  has been added to rod  1762 . Elastic band anchor  1772  also engages elastic band  1766 , so that when cable  1785  lifts pulley  1751  and thereby rod  1731 , resistance is provided by weight stack  1741 , free weight  1765 , and elastic band  1766 . Rod  1762  provides both a free weight attachment point and an elastic band attachment point. Elastic band anchor  1772  provides an elastic band attachment point. In this way, greater versatility in the increment, the amount of weight, and the nature of the resistance provided by weight stack  1741  can be obtained. 
       FIG. 18  provides a perspective view of exercise bench  1800 . Exercise bench  1800  comprises horizontal member  1811  mutually supporting vertical member  1821 , which together constitute part of a bench frame supporting seat cushion  1831 . Back cushion  1832  is further supported by the frame at member  1812 , and is capable of adopting an incline angle. Exercise bench  1800  comprises numerous bench accessory receiving ports  1887 , and a plurality of incline angle selection slots  1842 . Back cushion brace  1841  engages a chosen incline angle selection slot  1842  and establishes a chosen incline angle for back cushion  1832  relative to the horizontal. Brace guard  1845  prevents back cushion brace  1841  from escaping incline angle selection slots  1842 . Together, back cushion brace  1841 , the plurality of incline angle selection slots  1842 , and brace guard  1845  can be said to constitute an incline angle selection device. 
     Here, exercise bench  1800  is shown with floating pulleys  1881  and  1882 . Floating pulley  1881  allows extension cable  1883  to attach a hand grip at carabiner  1891 . The other end of extension cable  1883  (not shown) can connect to an exercise attachment point on the apparatus (not shown). Floating pulley  1882  allows extension cable  1884  to attach to hand grip at carabiner  1892 . The other end of extension cable  1884  (not shown) can connect to an exercise attachment point on the apparatus (not shown). Carabiners  1891  and  1892  can be said to provide bench exercise attachment points. 
       FIGS. 19, 20, and 21  depict apparatus  1900  having doors  1901 ,  1902 . In  FIG. 19 , doors  1901 ,  1902  are closed, and panels  1907 ,  1908  conceal or disguise apparatus  1900 . In  FIG. 20 , doors  1901 ,  1902  are open. Apparatus  1900  comprises vertical members  1911 ,  1912 ,  1913 , and  1914  mutually supporting horizontal member  1921  (among others). Each vertical member and each horizontal member have accessory receiving ports substantially along the entire length. A cable (not shown) selectively connects weight stack  1941  to exercise attachment point  1961 . Another cable (not shown) selectively connects weight stack  1942  to exercise attachment point  1962 . Floating pulley  1981  is removably and adjustably attached to vertical member  1913 . Floating pulley  1982  is removably and adjustably attached to vertical member  1914 . The frame of apparatus  1900  further comprises door  1901  pivotally mounted on vertical member  1911 , at least by door brace  2031 , and door  1902  pivotally mounted on vertical member  1912 , at least by door brace  2032  and hinge  2052 . 
     Door  1901  comprises door vertical members  2011  and  2012  mutually supporting door horizontal members  2021 ,  2022 ,  2023 , and  2024 . Door vertical members  2011 ,  2012  comprise first door vertical accessory receiving ports (e.g.,  2081 ) having axes in a fourth direction and second door vertical accessory receiving ports in a fifth direction (not shown). Door horizontal members  2021 ,  2022 ,  2023 , and  2024  have first door horizontal accessory receiving ports (e.g.,  2082 ) having axes in the fourth direction and second door horizontal accessory receiving ports having axes in a sixth direction (not shown). Panel  1907  is mounted to door  1901 . 
     Door  1902  comprises door vertical members  2013  and  2014  mutually supporting door horizontal members  2025 ,  2026 ,  2027 , and  2028 . Door vertical members  2013 ,  2014  comprise first door vertical accessory receiving ports (e.g.,  2083 ) having axes in a fourth direction and second door vertical accessory receiving ports in a fifth direction (not shown). Door horizontal members  2025 ,  2026 ,  2027 , and  2028  have first door horizontal accessory receiving ports (e.g.,  2084 ) having axes in the fourth direction and second door horizontal accessory receiving ports having axes in a sixth direction (not shown). Panel  1908  is mounted to door  1902 . 
     Door brace  2032  operates by engaging pin  2065  in door horizontal member  2028 , on one end, and on the other end, spring-loaded pin  2043  is operated with knob  2042 . In this way, door  1902  can be secured at a number of desired positions simply by pulling knob  2042  and rotating door  1902 , followed by releasing knob  2042  when door  1902  has reached a desirable position, and allowing pin  2043  to engage an accessory receiving port along horizontal member  1921 . Doors  1901 ,  1902  can provide considerable additional versatility: door  1902 , for example, can receive floating pulley  1982  in any of its accessory receiving ports, and floating pulley  1981  for that matter. In addition, doors  1901 ,  1902  can receive additional accessories such as Smith machine  1500 , rack accessories  1451 ,  1452 , chin up bar attachments, dip bar attachments, or the like. Indeed, any matter of exercise accessories can engage any of the accessory receiving ports found anywhere on apparatus  1900 , to allow for exercise against a resistance provided by either or both weight stacks  1941 ,  1942 , free weights, elastic bands, the weight of the athlete&#39;s own body, or a combination thereof. 
       FIG. 22  depicts hollow-headed bolt  2220  mounting panel  2208  to vertical member  2214  via rivet  2231 . Hollow-headed bolt  2220  comprises threaded shaft  2221  and head  2222 . Axial recess  2223  in head  2222  further comprises an annulus  2224  adapted to receive and retain a corresponding annular structure  2232  on rivet  2231 . Nut  2225  secures hollow-headed bolt to vertical member  2214 . Nut  2225  and hollow-headed bolt  2220  can be made of any suitable material, such as, for example, steel. Rivet  2231  can be made of any suitable material, such as, for example, structural polymers such as high-density polyethylene, or metal or metal alloys such as aluminum or steel. 
       FIGS. 23 and 24  depict apparatus  2300  comprising dip bar  2350 . Apparatus  2300  comprises vertical members  2314 ,  2316  mutually supporting horizontal members  2321 ,  2324 , which could be part of a door of the frame of apparatus  2300 . Dip bar  2350  comprises arm supports  2341 ,  2342 , and is attached to vertical members  2314 ,  2316  at hinges  2351  and  2352 , respectively. Back pad  2361  allows an athlete to use dip bar  2350  to perform leg extension exercises, for example, while facing away from apparatus  2300 .  FIG. 23  shows dip bar  2350  in the stowed position;  FIG. 24  shows dip bar  2350  deployed and ready for exercise. Apparatus  2300  can further comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 25  depicts apparatus  2500  comprising angle selector  2531 . Apparatus  2500  comprises vertical members  2511 ,  2512 , which mutually support horizontal member  2521 . Angle selector  2531  is mounted on horizontal member  2521 , and comprises a plurality of holes  2541  that can select and secure an angle for receiver  2533  using key  2532 . Receiver  2533  is adapted to receive any suitable device, such as, for example, a floating pulley or a longitudinal member of a multi-use exerciser. Apparatus  2500  can further comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIGS. 26 and 27  depict apparatus  2600  comprising multi-use exerciser  2601 . Apparatus  2600  comprises vertical members  2611 ,  2612 , mutually supporting horizontal member  2621 , which could form part of the door of the frame of apparatus  2600 . Multi-use exerciser  2601  comprises an angle selector  2631  supporting a longitudinal member  2671 , wherein longitudinal member  2671  anchors opposing ankle braces  2651 ,  2652  proximal to angle selector  2631 , and further supporting a multi-use pad  2661  distal from the angle selector  2631 . Angle selector  2631  comprises a plurality of holes  2641  that can select and secure an angle for multi-use exerciser  2601  using key  2632 . Multi-use pad  2661  can adopt any suitable angle; in these figures, it is shown in a substantially-horizontal position to receive an athlete who would engage ankle braces  2651 ,  2652  to perform crunches while facing apparatus  2600 , or back extensions while facing away from apparatus  2600 . Alternatively, multi-use pad  2661  can be secured in an angle differing from the horizontal to support a bicep curl exercise, for example. When not in use, multi-use exerciser  2601  can be stowed so that longitudinal member  2671  is substantially parallel with vertical member  2611 , for example, or longitudinal member  2671  can be removed from angle selector  2631 , and stowed elsewhere, such as at another convenient location within apparatus  2600 . Apparatus  2600  can comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 28  depicts apparatus  2800  comprising sit-up board  2801 . Apparatus  2800  comprises vertical members  2811 ,  2812 ,  2813 ,  2814  mutually supporting horizontal members  2821 ,  2822 ,  2823 . Optionally, vertical members  2811 ,  2812 ,  2813 ,  2814  and horizontal members  2821 ,  2822 , and  2823  could form a door of the frame of apparatus  2800 . Sit-up board  2801  comprises padded board  2861  mounting foot braces  2851 ,  2852 , and pins  2831 ,  2832 , which engage the accessory receiving ports  2875 ,  2876  of vertical members  2813 ,  2814 , respectively. Pins  2831 ,  2832  comprise hinges  2841 ,  2842 , respectively, to facilitate incline angle selection of sit-up board  2801 . Sit-up board  2801  can allow for a variety of exercises beyond sit ups. For example, floating pulleys removably and adjustably attached to any of vertical members  2811 ,  2812 ,  2813 , and  2814  and horizontal members  2821 ,  2822 , and  2823  can allow an athlete lying on sit-up board  2801  to engage the weight stacks of apparatus  2800  and perform various exercises against a resistance while executing a crunch motion or while holding crunch posture. For example, one foot can engage one of foot braces  2851 ,  2852 , while the other foot can pull a weight from the weight stack via a floating pulley and ankle strap (not shown), all while the athlete touches an opposing elbow to the knee of the foot pulling the weight. Apparatus  2800  can comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 29  depicts apparatus  2900  comprising flat-screen television  2901 . Apparatus  2900  can comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 30  provides a perspective view of apparatus  3000 . Apparatus  3000  illustrates a power rack for receiving at least one barbell  3031  for the performance of at least one exercise with the barbell  3031 . Vertical members  3013 ,  3014 ,  3015 , and  3016  (and others) mutually support horizontal members  3021 ,  3022 ,  3023 ,  3024 ,  3025 ,  3033 ,  3035 ,  3036 , and  3037  (and others) to form a frame for apparatus  3000 . Each vertical member and each horizontal member of apparatus  3000  is depicted with accessory receiving ports (unlabeled) substantially along the entire length of each member. Rack accessories  3051 ,  3052  are removably attached to vertical members  3014  and  3016 , respectively, and hold barbell  3031 . Rod  3061  is positioned between vertical members  3013  and  3014  to protect an athlete exercising with barbell  3031 ; similarly, rod  3062  is positioned between vertical members  3015  and  3016  for the same purpose. Bench  3081  appears in one possible position that supports exercises using barbell  3031 . Apparatus  3000  can further comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 31  depicts a right-side elevation view of extension arm  3100 . Extension arm  3100  comprises angular selection bracket  3141 , which appears in  FIG. 31  to be bolted to horizontal member  3121 , vertical member  3122 , and diagonal member  3123  of apparatus  3101 . Angular selection bracket  3141  further comprises a plurality of angle selection ports  3145 . Angular selection bracket  3141  attaches extension arm  3100  to apparatus  3101 . Knob  3142  operates a spring-loaded pin (not shown) that secures extension member  3151  at any one of a plurality of extension angles. Each extension angle, defined between vertical member  3122  and extension member  3151  can be selected by manipulating knob  3142  relative to the several angle selection ports  3145 . Extension member  3151  extending from angular selection bracket  3141  comprises a plurality of extension receiving ports  3187 . Floating pulley  3181 , comprising extension cable  3184  ending at carabiner  3162 , is removably and adjustably attached to extension arm  3151  by manipulating knob  3182 , which operates another spring-loaded pin (not shown). It can be said that carabiner  1362  represents both a floating exercise attachment point and an extension exercise attachment point in this embodiment. 
       FIG. 32  depicts floating pulley  3200 . Floating pulley  3200  comprises two pulley wheels  3281 ,  3282 . Floating pulley  3200  further comprises brace  3275 , which houses knob  3242 , which in turn operates spring-loaded pin  3241 . Spring-loaded pin  3241  can engage an accessory receiving port. It can be said that floating pulley  3200  has an accessory engagement structure comprising brace  3275 , knob  3242 , and spring-loaded pin  3241  for removably and adjustably coupling to an accessory receiving port on an apparatus. Floating pulley  3200  further comprises extension cable  3284  passing between pulley wheels  3281 ,  3282 , and terminating at a second end with carabiner  3262 . Pulley stop  3268  prevents extension cable  3284  from exiting floating pulley  3200 . Hinge  3273  allows floating pulley wheels  3281 ,  3282  to swing back and forth (in this case, into and out of the plane of the page). Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  3262 . Sometimes, if desirable, a further extension cable and a further floating pulley can be attached to carabiner  3262  for maximum flexibility in designing further exercises. 
       FIG. 33  depicts floating pulley  3300 . Floating pulley  3300  comprises two pulley wheels  3381 ,  3382 . Floating pulley  3300  further comprises brace  3375 , which houses knob  3342 , which in turn operates spring-loaded pin  3341 . Spring-loaded pin  3341  can engage an accessory receiving port. It can be said that floating pulley  3300  has an accessory engagement structure comprising brace  3375 , knob  3342 , and spring-loaded pin  3341  for removably and adjustably coupling to an accessory receiving port on an apparatus. Floating pulley  3300  further comprises extension cable  3384  passing between pulley wheels  3381 ,  3382  and terminating at a second end with carabiner  3362 . Pulley stop  3368  prevents extension cable  3384  from exiting floating pulley  3300 . Pivot  3373  allows floating pulley wheels  3381 ,  3382  to rotate up to 360 degrees (in this case, into and out of the plane of the page). Any suitable exercise equipment, such as, for example, a hand grip, ankle strap, torso strap, head strap, barbell, dumbbell, or the like, or a multivector extension device as described herein, can be attached to carabiner  3362 . Sometimes, if desirable, a further extension cable and a further floating pulley can be attached to carabiner  3362  for maximum flexibility in designing further exercises. 
       FIG. 34  depicts apparatus  3400  comprising sit-up board  3401 . Apparatus  3400  comprises vertical members  3421  and  3422  mutually supporting horizontal member  3423 . Optionally, vertical members  3421 ,  3422  and horizontal member  3423  could form a door of the frame of apparatus  3400 . Sit-up board  3401  comprises padded board  3461  mounting foot braces  3451 ,  3452 , hand grips  3453 ,  3454 , and pins (not seen) that engage the accessory receiving ports of vertical members  3421 ,  3422 , respectively. Sit-up board  3401  further comprises a longitudinal member  3471  and lateral member  3472  supporting padded board  3461 . Longitudinal member  3471  comprises a plurality of sit-up board accessory receiving ports  3475 . Lateral member  3472  comprises a plurality of sit-up board accessory receiving ports  3476 . Sit-up board  3401  further comprises footers  3481 ,  3482  for stabilizing sit-up board  3401 . Sit-up board  3401  can allow for a variety of exercises beyond sit ups. For example, floating pulleys removably and adjustably attached to any of longitudinal member  3471  and lateral member  3472  via sit-up board accessory receiving ports  3475 ,  3476 , respectively can allow an athlete lying on sit-up board  3401  to engage the weight stacks of apparatus  3400  and perform various exercises against a resistance while executing a crunch motion or while holding crunch posture. For example, the feet can engage foot braces  3451 ,  3452 , while one or both hands can pull a weight from the weight stack via a floating pulley and ankle strap (not shown), all while the athlete performs a sit up or crunch exercise. Apparatus  3400  can comprise weight stacks, cables, exercise attachment points, and floating pulleys, among other things, as described herein. 
       FIG. 35  provides a right-side elevation view of gliding extension device  3501 . The gliding extension device  3501  comprises a roller carriage  3531  that houses rollers  3532 ,  3533 ,  3536 ,  3537 , which glidingly engage guide rod  3523 . Extension frame  3551  of gliding extension device  3501  extends from roller carriage  3531  at its proximal end to the distal end having exercise engagement device  3561 , which is a single hand grip, and brake lever  3562 . Extension frame  3551  further comprises a plurality of extension receiving ports  3571  for providing one or more extension exercise attachment points with the deployment of a floating pulley (not shown). Roller carriage  3531  further comprises exercise attachment point receiver  3581 , which is an eye bolt suitable for receiving a carabiner from an exercise attachment point or a floating exercise attachment point, for example. Roller carriage  3531  further comprises elastic band receiver  3582 , which is a J-hook for receiving an elastic band (not shown). Such an elastic band can further engage elastic band anchor  3583 , which attaches to horizontal member  3522 . Guide rod  3523  is supported by horizontal members  3521 ,  3522  of apparatus  3500 . Optionally, a vertical member parallel to guide rod  3523  can support or assist the use of gliding extension device  3501 , for example, by providing anchor points for a break mechanism. In gliding extension device  3501 , brake lever  3562  releases a braking clamp (not shown) at the roller carriage to allow the gliding extension device  3501  to move. In general, a braking clamp can arrest the movement of a roller, more than one roller, the guide rod, or combinations thereof. In addition, a break mechanism can insert a spring-loaded pin into one of a series of slots, optionally along the guide rod, or one of a series of accessory receiving ports along a member of the frame of apparatus  3500  that runs parallel to guide rod  3523 . The several possible brake mechanisms can be designed to immobilize the gliding extension device  3501  for the safety and convenience of an athlete using it. 
       FIG. 36  provides a perspective view of multivector extension device  3600 . Multivector extension device  3600  comprises brace  3675  for removably and adjustably attaching device  3600  to a frame of an apparatus (not shown). Brace  3675  comprises knob  3642 , which manipulates spring-loaded pin  3641 . Multivector extension arm  3651  comprises a plurality of accessory receiving ports  3687 , and attaches to brace  3675  via a ball joint  3631 . Ball joint  3631  allows multivector extension arm  3651  significant freedom of movement relative to brace  3675 . Ball joints  3631  can be made of any suitable materials. For example, multivector extension arm can terminate at ball joint  3631  with a steel core surrounded by a spherical polytetrafluoroethylene or Teflon® ball. Alternatively, ball joint  3631  can comprise steel lubricated with a suitable grease chosen from, for example, high molecular weight alkanes or silicone greases. Single hand grip  3621 , which is an exercise engagement device, attaches to the multivector extension arm  3651  via an accessory receiving port (not seen). J-hook  3661  for receiving an elastic band (not shown) is an exercise attachment point receiver, and is attached to multivector extension arm  3651  via an accessory receiving port  3687 . Eye bolt  3662  for receiving a carabiner that selectively connects ultimately to a weight stack of an apparatus (not shown), and is an exercise attachment point receiver attached to multivector extension arm  3651  via an accessory receiving port  3687 . 
     To illustrate multivector exercise,  FIG. 36  shows first vector  3691 , which depicts the direction of resistance of an elastic band attached to exercise attachment point receiver (J-hook)  3661 . Second vector  3692  depicts the direction of resistance provided by a weight stack connected via carabiner through an exercise attachment point or a floating exercise attachment point (not shown). Exercise direction  3695  depicts the up-and-down motion of the desired exercise. An athlete, in this example, would grasp single hand grip  3621  and pull down against the resistance provided by the elastic band at J-hook  3661 . However, the resistance provided by the weight stack at eye bolt  3662  would force the athlete to use additional effort to stabilize the multivector extension device  3600  against the resistance along vector  3692 . This additional effort can help the athlete strengthen the shoulder, elbow, and hand joints in a manner not possible if the only resistance was provided by the elastic band along vector  3691 . Any number of resistances can be applied, and the athlete is limited only by imagination. Of course, opposing resistances will cancel each other; but it should be noted that the relative orientation of the vectors likely will change as the exercise motion continues. In other words, the relative orientation (and magnitude, in the case of an elastic band) of the vectors  3691 ,  3692  will change as single hand grip  3621  is moved through exercise motion  3695 . 
       FIG. 37  depicts eye bolt  3662 . Eye bolt  3662  comprises ring  3731  anchored to shaft  3721  which is inserted into an accessory receiving port (not shown). To secure shaft  3721  in an accessory receiving port, shaft  3721  comprises spring-loaded pin  3722 , which is activated (withdrawn into shaft  3721 ) by lever  3724 . Collar  3723  protects lever  3724  from inadvertent engagement by the accessory receiving port during an exercise. 
       FIG. 38  depicts hand grip  3621 . Hand grip  3621  comprises foam gripping portion  3841  anchored to shaft  3821  which is inserted into an accessory receiving port (not shown). To secure shaft  3821  in an accessory receiving port, shaft  3821  comprises spring-loaded pin  3822 , which is activated (withdrawn into shaft  3821 ) by lever  3824 . Collar  3823  protects lever  3824  from inadvertent engagement by the accessory receiving port during an exercise. 
       FIGS. 39 and 44  provide a right-side view of multivector extension device  3900  further comprising a support cone  3981 . Multivector extension device  3900  comprises brace  3975  for removably and adjustably attaching device  3900  to a frame of an apparatus (not shown). Brace  3975  comprises knob  3942 , which manipulates spring-loaded pin  3941 . Multivector extension arm  3951  comprises a plurality of accessory receiving ports  3987 , and attaches to brace  3975  via a ball joint (not seen). Single hand grip  3921 , which is an exercise engagement device, attaches to the multivector extension arm  3951  via an accessory receiving port (not seen). J-hook  3961  for receiving an elastic band (not shown) is an exercise attachment point receiver, and is attached to multivector extension arm  3951  via an accessory receiving port  3987 . Eye bolt  3962  for receiving a carabiner that selectively connects ultimately to a weight stack of an apparatus (not shown), is an exercise attachment point receiver attached to multivector extension arm  3951  via an accessory receiving port  3987 . Support cone  3981  is positioned about the ball joint (not seen) to protect the frame (not shown) from contact by multivector extension arm  3951 . Operating multivector extension device  3900  is similar to the operation of multivector extension device  3600 , as shown in  FIG. 36 . 
       FIG. 40  provides a partial perspective view demonstrating how support cone  3981  of multivector extension device  3900  protects frame member  4012  from contact by multivector extension arm  3951 . Ball joint  3931 , which joins multivector extension arm  3951  to brace  3975  (seen in  FIG. 39 ), appears in  FIG. 40 . When multivector extension device is attached to frame member  4012 , support cone  3981  is positioned about ball joint  3931  to keep multivector extension arm  3951  from contacting frame  4012 . 
       FIG. 41  shows a right-side view, and  FIG. 42  shows a front view, of multivector extension support  4100 . Multivector extension support  4100  comprises brace  4175  for removably and adjustably attaching to frame member  4112  of an apparatus for exercising against a resistance. Brace  4175  comprises a spring-loaded pin manipulated by knob  4142  for engaging frame member  4112 . Multivector extension support  4100  also comprises resilient support  4182  attached to brace  4175  for receiving and protecting frame number  4112  from contact by a multivector extension device (not shown). Resilient support  4182  defines recess  4125  for receiving the multivector extension device. 
       FIG. 43  shows a right-side view of multivector extension device  3600  in operation with multivector extension support  4100 . Multivector extension arm  3651  fits into recess  4125  defined by resilient support  4182  of multivector extension support  4100 . Also seen in  FIG. 43 , elastic band  4166  engages J-hook  3661  of multivector extension device  3600 . Carabiner  4184  connects cable  4185  and a weight stack (not shown) to eye bolt  3662 . Elastic band  4166  and cable  4185  apply different vectors of resistance to multivector extension arm  3651  (see vectors  3691  and  3692  in  FIG. 36 ). Multivector extension support  4100  can help locate multivector extension device  3600  in between sets, and prevent contact between multivector extension arm  3651  and frame member  4112 . 
       FIGS. 45 and 46  provide a right-side view of multivector extension device  4500 . Multivector extension device  4500  comprises brace  4575  for removably and adjustably attaching device  4500  to a frame of an apparatus (not shown). Brace  4575  comprises knob  4542 , which manipulates spring-loaded pin  4541 . Multivector extension arm  4551  comprises a plurality of accessory receiving ports  4587 , and attaches to brace  4575  via a ball joint (not seen). Multivector extension arm  4551  comprises first telescoping member  4567 , second telescoping member  4568 , and third telescoping member  4569 . Second telescoping member  4568  and third telescoping member  4569  are selectively secured to the multivector extension arm  4551  with spring-loaded pins  4578  and  4579 . Second telescoping member  4568  has outer dimensions that are smaller than the inner dimensions of first telescoping member  4567 , allowing second telescoping member  4568  to slide inside of first telescoping member  4567 . Spring-loaded pin  4578  selectively secures second telescoping member  4568  at a chosen position or length relative to the first telescoping number  4567 . Similarly, third telescoping member  4569  has outer dimensions that are smaller than the inner dimensions of second telescoping member  4568 , allowing third telescoping member  4569  to slide inside of second telescoping member  4568 . Spring-loaded pin  4579  selectively secures third telescoping member  4569  at a chosen position or length relative to second telescoping member  4568 . It can be said that first telescoping member  4567 , second telescoping member  4568 , and third telescoping member  4569  are nested. 
     Single hand grip  4521 , which is an exercise engagement device, attaches to the multivector extension arm  4551  via an accessory receiving port (not seen) on third telescoping member  4569 . J-hook  4561  for receiving an elastic band (not shown) is an exercise attachment point receiver, and is attached to multivector extension arm  4551  via an accessory receiving port  4587 , which can also be referred to as a telescoping member accessory receiving port  4588 , on third telescoping member  4569 . Eye bolt  4562  for receiving a carabiner that selectively connects ultimately to a weight stack of an apparatus (not shown), is an exercise attachment point receiver attached to multivector extension arm  4551  via an accessory receiving port  4587 , which can also be referred to as a telescoping member accessory receiving port  4588 , on second telescoping member  4568 . Support cone  4581  is positioned about the ball joint (not seen) to protect the frame (not shown) from contact by multivector extension arm  4551 . Operating multivector extension device  4500  is similar to the operation of multivector extension device  3600 , as shown in  FIG. 36 , with the added advantage of lengthening the device as allowed by telescoping members  4568  and  4569 . 
       FIG. 47  shows a front view, and  FIG. 48  shows a perspective view, of mobile member  4700 .  FIG. 49  shows mobile member  4700  engaged between frame members  4911  and  4912 . Mobile member  4700  comprises elongate section  4710  which has a first end  4711  opposite second end  4712 . First end  4711  has first frame engagement device  4720 , which comprises first rod  4721  and port  4722  for receiving retention key  4723 , for securing mobile member  4700  to frame member  4911 . Second end  4712  contains second frame engagement device  4730 , which comprises second rod  4731 , for securing mobile member  4700  to frame member  4912 . Elongate section  4710  comprises a foamed polymer. In this embodiment, first rod  4721  is longer than second rod  4731 . In operation, first rod  4721  is entered in a first accessory receiving port of frame member  4911 . Second rod  4731  is aligned with and enters a second accessory receiving port of frame member  4912 . When the mobile member  4700  is positioned correctly, with both first rod  4721  and second rod  4731  engaging frame members  4911  and  4912 , first key  4723  is placed in first port  4722  to secure mobile member  4700  between frame members  4911  and  4912 . To disengage mobile member  4700 , first key  4723  is removed from first port  4722 , mobile member  4700  is slated toward frame member  4911  until second rod  4731  disengages frame member  4912 , and then first rod  4721  can be slid from frame member  4911 . Mobile member  4700  can enable a variety of exercises, such as, for example, those that require robust support for a portion of an athlete&#39;s body, like arm curls, floating crunches, back extensions, and the like. 
       FIG. 50  shows a front view of mobile member  5000 . Mobile member  5000  comprises elongate section  5010  which has a first end  5011  opposite second end  5012 . First end  5011  has first frame engagement device  5020 , which comprises first rod  5021  and port  5022  for receiving retention key  5023 , for securing mobile member  5000  to a first frame member (not shown). Second end  5012  contains second frame engagement device  5030 , which comprises second rod  5031 , for securing mobile member  5000  to a second frame member (not shown). In this embodiment, first rod  5021  is longer than second rod  5031 . Elongate section  5010  comprises square tubing, which allows for the selective attachment of any desired accessories such as, for example, a floating pulley (not shown). Accordingly, mobile member  5000  affords greater flexibility to an apparatus already capable of unprecedented arrangements for exercise. Elongate section  5010  comprises first mobile accessory receiving ports  5045  having axes in a first mobile direction (normal to the page), and second mobile accessory receiving ports (not seen) having axes in a second mobile direction (in the plane of the page). 
       FIG. 51  shows a left-side view of foot stretching device  5100 . Foot stretching device  5100  comprises brace  5175  for removably and adjustably attaching to a frame, such as, for example frame member  5113 , by engaging a spring-loaded pin manipulated by knob  5142  into an accessory receiving port  5193 . Foot stretching device  5100  also comprises an elongate sole portion  5110  attached to brace  5175  by brace hinge  5114 . Heel portion  5121  attaches to the elongate sole portion  5110  by heel hinge  5112 . The angle of stretch that an athlete&#39;s foot  5190  experiences can be adjusted by moving brace  5175  up or down frame member  5113 . 
       FIG. 52  shows a left-side view of foot exercise attachment  5200 . Foot exercise attachment  5200  comprises scaffold  5210  for receiving a foot  5290  of an athlete. Scaffold  5210  also comprises toe portion  5212  for engaging the top of the toes of the foot  5290 , or a shoe in some cases. Scaffold  5210  anchors straps  5221 ,  5222 ,  5223 , and  5224  for securing the scaffold  5210  to the foot  5290 . Straps  5221  and  5222  are adapted to engage each other with, for example, hook-and-loop fabric, and straps  5223  and  5224  are adapted to engage each other with, for example, hook-and-loop fabric. Scaffold  5210  also comprises one or more exercise attachment point receivers in the form of eyebolts  5231 ,  5232 , and  5233  for engaging a resistance to the scaffold  5210 . 
       FIG. 53  shows a left-side view of leg press accessory  5300 . Leg press accessory  5300  comprises angular guide  5310  having an angular guide brace  5321  for removably and adjustably attaching the leg press accessory  5300  to horizontal member  5311 . Extension member receiver  5331  is anchored to angular guide  5310  so that extension member receiver  5331  can move an arcuate manner within angular guide  5310 , in this case, in the plane of the page. Extension member receiver  5331  has received extension member  5341  having foot pad  5351  held in place on extension member  5341  with a footpad brace  5352  comprising spring-loaded pin  5354  for engaging the extension member  5341  at one of extension receiving ports  5345 . Another of extension receiving ports  5345  has received exercise attachment point receiver  5381 , which is an eye bolt to which carabiner  5383  and cable  5385  have attached. Cable  5385  ultimately joins to a weight stack (not shown) to provide resistance against athlete  5390  straightening his legs. Leg press accessory  5300  is accompanied by bench  5361 , which engages horizontal member  5311  with bench braces  5362 ,  5363 . Knobs  5322 ,  5372 , and  5373  manipulate spring-loaded pins that secure their respective bases  5321 ,  5362 , and  5363  to horizontal member  5311 . 
       FIGS. 54 and 55  show adjustable arcuate base  5400 . Adjustable arcuate base  5400  comprises stage  5410 , which itself comprises retractable pins  5411 ,  5412  for engaging accessory receiving ports on vertical members  5417 ,  5418 , respectively. In operation, an athlete can pull retractable pins  5411 ,  5412  laterally to disengage vertical members  5417 ,  5418 . Adjustable arcuate base  5400  then can be moved up or down to a new position relative to vertical members  5417 ,  5418 . At the new position, retractable pins  5411 ,  5412  are released to engage new accessory receiving ports on vertical members  5417 ,  5418 , respectively, thereby securing adjustable arcuate base  5400  in the new position. In this embodiment, retractable pins  5411 ,  5412  are spring loaded. 
     Angular guide  5421  is affixed to stage  5410 , and anchors extension member receiver  5431  at axle  5432 . Extension member receiver  5431  can move in an arcuate manner within angular guide  5421 , for example, during exercise. Extension member receiver  5431  further comprises spring-loaded pin  5441 , so that extension member receiver  5431  is adapted to receive an extension member (not shown) and secure the extension member with spring-loaded pin  5441 . Any suitable extension member can engage extension member receiver  5431 . In one case, an extension member can comprise square tubing with extension receiving ports for receiving exercise engagement devices (e.g., single hand grip  3621  in  FIG. 36 ) and exercise attachment point receivers (e.g., J-hook  3661  and eye bolt  3662  in  FIG. 36 ). 
       FIGS. 56, 57, and 58  show angular telescopic extension device  5600 .  FIG. 56  provides a right-side view of the device with nested extension members  5632 ,  5633  contracted into the shortest configuration.  FIG. 57  provides the same view, but with nested extension members  5632 ,  5633  fully extended, and with floating pulley  5691  providing an extension exercise attachment point.  FIG. 58  provides a partial top plan view of angular telescopic extension device  5600 . 
     Angular telescopic extension device  5600  comprises angular selection brace  5610  for selectively attaching angular telescopic extension device  5600  to frame member  5612  of an apparatus for exercising against a resistance. Angular selection brace  5610  comprises retractable pin  5641  for engaging an accessory receiving port in the frame member  5612 . Angle selector  5620  comprises a plurality of angle selection ports  5621 ,  5622 ,  5624 , for example, and is attached to the angular selection brace  5610 . Angular selection bracket  5651  is connected to angular selection brace  5610  by a hinge  5655  having hinge axle  5629 . Hinge  5655  defines an axis of rotation at hinge axle  5629 . Angle selecting retractable pin  5642  engages angle selection port  5624  in  FIG. 58 , thereby establishing a telescopic extension angle. That angle is determined by an imaginary line from hinge axle  5629  to angle selection port  5621 , on one hand, and another imaginary line from hinge axle  5629  to angle selection port  5624 , on the other hand. 
     Telescopic extension arm  5630  extends from angular selection bracket  5651  and comprises first nested extension member  5631 , second nested extension member  5632 , and third nested extension member  5633 . Nested extension members  5631 ,  5632 , and  5633  comprise a plurality of extension receiving ports  5638 . Spring-loaded pins  5643  and  5644  allow nested extension members  5632 ,  5633  to be independently secured at chosen lengths. 
       FIGS. 59 and 60  depict portable weight stack assembly  5900 . Portable weight stack assembly  5900  comprises portable frame  5910 , which comprises portable vertical members  5911 ,  5912  mutually supporting horizontal members  5913 ,  5914 . Portable weight stack  5921  contained by portable frame  5910  is selectively connected by portable cable  5985  routed about portable frame  5910  via a plurality of portable pulleys  5941 ,  5942 ,  5943 ,  5944 ,  5945 ,  5946 , and  5947  to slidably adjustable portable exercise attachment point  5961 . Footers  5991 ,  5992  stabilize frame  5910 . Portable exercise attachment point  5961  comprises two pulleys  5965 ,  5967  that allow cable  5985  significant versatile freedom of movement when carabiner  5962  is moved during an exercise. Pulley stop  5968 , which is a rubber sphere, prevents cable  5985  from exiting portable exercise attachment point  5961 . Portable exercise attachment point  5961  is slidably adjustable along vertical member  5912  by manipulating knob  5964 . Vertical member  5912  comprises first portable vertical accessory receiving ports  5987  having axes in a first portable direction, i.e., normal to the page in  FIG. 59 . Vertical member  5912  comprises second portable vertical accessory receiving ports  5988  having axes in a second portable direction, i.e., normal to the page in  FIG. 60 . 
       FIGS. 61, 62, 63, 64, 65, 66, and 67  provide several views of frame  6100 , which has square tubing.  FIG. 61  provides a front perspective view;  FIG. 62  provides a right-side view;  FIG. 63  provides a left-side view;  FIG. 64  provides a top plan view;  FIG. 65  provides a bottom plan view;  FIG. 66  provides a front elevation view; and  FIG. 67  provides a back elevation view. A plurality of vertical members  6111 ,  6112 ,  6113 ,  6114 ,  6115 ,  6116 ,  6117 , and  6118  mutually support a plurality of horizontal members  6121 ,  6122 ,  6123 ,  6124 ,  6125 ,  6126 ,  6127 ,  6128 ,  6129 ,  6131 ,  6132 , and  6133 . The rectangular footprint defined by horizontal members  6121 ,  6122 ,  6123 ,  6124  and  6125  has an aspect ratio of about 2:9. In other words, the distance from vertical member  6111  to vertical member  6112 , the depth, is about 2 feet; the distance from vertical member  6111  to vertical member  6117 , the width, is about 9 feet, in one embodiment. Frame  6100  is about 9 feet in height, i.e., the longest dimension of vertical member  6111 . Vertical member  6114  has first vertical accessory receiving ports  6187  having axes in a first direction, and second vertical accessory receiving ports  6188  having axes in a second direction. Horizontal member  6123  has first horizontal accessory receiving ports  6197  in the first direction, and second horizontal accessory receiving ports  6198  in a third direction. 
       FIG. 68  provides a front perspective view of frame  6800 , which has round tubing. A plurality of vertical members  6811 ,  6812 ,  6813 ,  6814 ,  6815 ,  6816 ,  6817 , and  6818  mutually support a plurality of horizontal members  6821 ,  6822 ,  6823 ,  6824 ,  6825 ,  6826 ,  6827 ,  6828 ,  6829 ,  6831 ,  6832 , and  6833 . 
       FIG. 69  provides a front perspective view of frame  6900 , which has hexagonal tubing. A plurality of vertical members  6911 ,  6912 ,  6913 ,  6914 ,  6915 ,  6916 ,  6917 , and  6918  mutually support a plurality of horizontal members  6921 ,  6922 ,  6923 ,  6924 ,  6925 ,  6926 ,  6927 ,  6928 ,  6929 ,  6931 ,  6932 , and  6933 . 
     EMBODIMENTS 
     Embodiment 1. An apparatus for exercising against a resistance, comprising:
     a frame, comprising a plurality of vertical members mutually supporting a plurality of horizontal members;   the resistance comprising at least one weight stack contained by the frame; one or more cables routed about the frame via a plurality of pulleys selectively connecting the at least one weight stack to one or more exercise attachment points;   at least one floating pulley removably and adjustably attached to the frame comprising at least one extension cable having a first end opposite a second end, the first end being attachable to the one or more exercise attachment points, and the second end providing at least one floating exercise attachment point;   wherein at least some of the vertical members of the plurality of vertical members have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction.   

     Embodiment 2. The apparatus of embodiment 1, wherein at least some of the horizontal members of the plurality of horizontal members have first horizontal accessory receiving ports having axes in the first direction, and second horizontal accessory receiving ports having axes in a third direction. 
     Embodiment 3. The apparatus of any one of embodiments 1-2, wherein the frame comprises square tubing. 
     Embodiment 4. The apparatus of any one of embodiments 1-3, wherein the first direction is substantially perpendicular to the second direction. 
     Embodiment 5. The apparatus of any one of embodiments 1-4, wherein the resistance comprises two independent weight stacks contained by the frame. 
     Embodiment 6. The apparatus of any one of embodiments 1-5, wherein at least one of the one or more exercise attachment points is slidably adjustable along one of the vertical members of the plurality of vertical members. 
     Embodiment 7. The apparatus of any one of embodiments 1-6, wherein at least one of the one or more exercise attachment points is slidably adjustable along one of the horizontal members of the plurality of horizontal members. 
     Embodiment 8. The apparatus of any one of embodiments 1-7, wherein at least one vertical member of the plurality of vertical members has a vertical length, and comprises first vertical accessory receiving ports and second vertical accessory receiving ports for substantially the entire vertical length. 
     Embodiment 9. The apparatus of any one of embodiments 1-8, wherein at least one horizontal member of the plurality of horizontal members has a horizontal length, and comprises first horizontal accessory receiving ports and second horizontal accessory receiving ports for substantially the entire horizontal length. 
     Embodiment 10. The apparatus of any one of embodiments 1-9, wherein the first direction and the second direction are substantially parallel to the horizontal. 
     Embodiment 11. The apparatus of any one of embodiments 2-10, wherein the third direction is substantially normal to the horizontal. 
     Embodiment 12. The apparatus of any one of embodiments 1-11, wherein the frame further comprises at least one door pivotally mounted on at least one vertical member in the plurality of vertical members. 
     Embodiment 13. The apparatus of embodiment 12, wherein the at least one door comprises two doors. 
     Embodiment 14. The apparatus of any one of embodiments 12-13, wherein the at least one door comprises
     at least one door vertical member mutually supporting at least one door horizontal member; and   wherein the at least one door vertical member comprises first door vertical accessory receiving ports having axes in a fourth direction, and second door vertical accessory receiving ports in a fifth direction.   

     Embodiment 15. The apparatus of embodiment 14, wherein the at least one door horizontal member comprises first door horizontal accessory receiving ports having axes in the fourth direction, and second door horizontal accessory receiving ports having axes in a sixth direction. 
     Embodiment 16. The apparatus of any one of embodiments 14-15, wherein the fourth direction is substantially perpendicular to the fifth direction. 
     Embodiment 17. The apparatus of any one of embodiments 14-16, wherein the fourth direction and the fifth direction are substantially parallel to the horizontal. 
     Embodiment 18. The apparatus of any one of embodiments 15-17, wherein the sixth direction is substantially normal to the horizontal. 
     Embodiment 19. The apparatus of any one of embodiments 14-18, wherein the at least one door vertical member comprises square tubing. 
     Embodiment 20. The apparatus of any one of embodiments 14-19, wherein the at least one door horizontal member comprises square tubing. 
     Embodiment 21. The apparatus of any one of embodiments 1-20, comprising at least one decorative panel mounted to the frame. 
     Embodiment 22. The apparatus of any one of embodiments 12-21, comprising at least one decorative panel mounted to the at least one door. 
     Embodiment 23. The apparatus of any one of embodiments 21-22, wherein the at least one decorative panel is mounted using at least one hollow-headed bolt, the hollow-headed bolt comprising a head and a threaded shaft, the head comprising an axial recess for receiving and retaining a panel-mounting rivet. 
     Embodiment 24. The apparatus of embodiment 12, wherein the at least one door comprises at least one of the one or more exercise attachment points, the at least one floating exercise attachment point, or a combination thereof. 
     Embodiment 25. The apparatus of embodiment 13, wherein each of the two doors comprises at least one of the one or more exercise attachment points, the at least one floating exercise attachment point, or a combination thereof. 
     Embodiment 26. The apparatus of any one of embodiments 1-25, wherein the at least one floating pulley is removably and adjustably attached to the frame by coupling to one or more of the first vertical accessory receiving ports, one or more of the second vertical accessory receiving ports, or a combination thereof. 
     Embodiment 27. The apparatus of any one of embodiments 2-25, wherein the at least one floating pulley is removably and adjustably attached to the frame by coupling to one or more of the first horizontal accessory receiving ports, one or more of the second horizontal accessory receiving ports, or a combination thereof. 
     Embodiment 28. The apparatus of any one of embodiments 14-27, wherein the at least one floating pulley is removably and adjustably attached to the frame by coupling to one or more of the first door vertical accessory receiving ports, one or more of the second door vertical accessory receiving ports, or a combination thereof. 
     Embodiment 29. The apparatus of any one of embodiments 15-28, wherein the at least one floating pulley is removably and adjustably attached to the frame by coupling to one or more of the first door horizontal accessory receiving ports, one or more of the second door horizontal accessory receiving ports, or a combination thereof. 
     Embodiment 30. The apparatus of any one of embodiments 1-29, comprising at least one power rack for receiving at least one barbell and allowing the performance of at least one exercise with the at least one barbell. 
     Embodiment 31. The apparatus of any one of embodiments 1-30, comprising at least one Smith machine for receiving at least one barbell and allowing the performance of at least one exercise with the at least one barbell. 
     Embodiment 32. The apparatus of any one of embodiments 1-31, comprising at least one elastic band attachment point to provide or augment the resistance. 
     Embodiment 33. The apparatus of any one of embodiments 1-32, comprising at least one free weight attachment point to provide or augment the resistance. 
     Embodiment 34. The apparatus of any one of embodiments 1-33, wherein the resistance is selectively provided by the at least one weight stack, at least one free weight device, at least one elastic band, the weight of a person exercising with the apparatus, or a combination thereof. 
     Embodiment 35. A floating pulley for an apparatus for exercising against a resistance, the floating pulley comprising:
     an extension cable having a first end opposite a second end, the first end being attachable to an exercise attachment point on the apparatus, and the second end providing a floating exercise attachment point; and   an accessory engagement structure for removably and adjustably coupling to an accessory receiving port on the apparatus.   

     Embodiment 36. The floating pulley of embodiment 35, further comprising:
     a first pulley stop proximal to the first end of the extension cable; and   a second pulley stop proximal to the second end of the extension cable.   

     Embodiment 37. The floating pulley of any one of embodiments 35-36, wherein the floating pulley comprises a single pulley wheel. 
     Embodiment 38. The floating pulley of any one of embodiments 35-36, wherein the floating pulley comprises two pulley wheels, and the extension cable passes between the two pulley wheels. 
     Embodiment 39. The floating pulley of any one of embodiments 35-38, wherein the accessory engagement structure comprises a hinge for attaching the floating pulley to the accessory engagement structure. 
     Embodiment 40. The floating pulley of any one of embodiments 35-39, wherein the accessory engagement structure comprises a pivot for attaching the floating pulley to the accessory engagement structure. 
     Embodiment 41. The floating pulley of any one of embodiments 35-40, wherein the apparatus for exercising against a resistance is the apparatus of any one of embodiments 1-34. 
     Embodiment 42. A method of exercising against a resistance, comprising:
     obtaining an apparatus comprising:   a frame, comprising a plurality of vertical members mutually supporting a plurality of horizontal members;   the resistance comprising at least one weight stack contained by the frame;   one or more cables routed about the frame via a plurality of pulleys selectively connecting the at least one weight stack to one or more exercise attachment points;   at least one floating pulley removably and adjustably attached to the frame comprising at least one extension cable having a first end opposite a second end, the first end being attachable to the one or more exercise attachment points, and the second end providing at least one floating exercise attachment point;   wherein at least some of the vertical members of the plurality of vertical members have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction;   connecting at least one exercise engagement device to one or more exercise attachment points, the at least one floating exercise attachment point, or a combination thereof; and   moving the at least one exercise engagement device against the resistance, thereby exercising against the resistance.   

     Embodiment 43. The method of embodiment 42, wherein the apparatus is the apparatus of any one of embodiments 1-34. 
     Embodiment 44. The method of any one of embodiments 42-43, wherein the at least one floating pulley comprises the floating pulley of any one of embodiments 35-41. 
     Embodiment 45. A method of making the apparatus of any one of embodiments 1-34, comprising:
     routing the one or more cables about the frame via the plurality of pulleys to selectively connect the at least one weight stack to the one or more exercise attachment points.   

     Embodiment 46. A method of making the floating pulley of any one of embodiments 35-41, comprising routing the extension cable through the floating pulley. 
     Embodiment 47. An exercise bench adapted for use with an apparatus for exercising against a resistance, the exercise bench comprising:
     a bench frame comprising at least one horizontal bench member mutually supporting at least one vertical bench member;   a seat cushion supported by the bench frame; and   one or more bench accessory receiving ports in the frame, the one or more bench accessory receiving ports being adapted to receive at least one floating pulley to provide at least one bench exercise attachment point.   

     Embodiment 48. The exercise bench of embodiment 47, further comprising:
     a back cushion supported by the frame and capable of adopting an incline angle.   

     Embodiment 49. The exercise bench of embodiment 48, wherein the incline angle ranges from −80 degrees to 120 degrees, relative to the horizontal. 
     Embodiment 50. The exercise bench of embodiment 49, wherein the incline angle ranges from zero degrees to 60 degrees relative to the horizontal. 
     Embodiment 51. The exercise bench of any one of embodiments 47-50, further comprising an incline angle selection device comprising:
     a back cushion brace engaging the back cushion;   a plurality of incline angle selection slots for receiving the back cushion brace and establishing the incline angle with the back cushion brace; and   a brace guard for preventing the back cushion brace from departing from the incline angle selection device.   

     Embodiment 52. An extension arm for an apparatus for exercising against a resistance, the extension arm comprising:
     a brace for removably and adjustably attaching to a frame of the apparatus;   an extension member extending from the base and comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points.   

     Embodiment 53. The extension arm of embodiment 52, wherein the extension arm is adapted to receive at least one floating pulley capable of selectively connecting at least one weight stack of the apparatus to establish the one or more extension exercise attachment points. 
     Embodiment 54. The extension arm of any one of embodiments 52-53, wherein the apparatus is the apparatus of any one of embodiments 1-34. 
     Embodiment 55. The extension arm of any one of embodiments 52-54, wherein the floating pulley is the floating pulley of any one of embodiments 35-41. 
     Embodiment 56. The apparatus of any one of embodiments 1-34, further comprising a dip bar, a multi-use exerciser, a sit-up board, a television, a sound system, a media player, or a combination thereof. 
     Embodiment 57. The apparatus of embodiment 56, wherein the multi-use exerciser comprises an angle selector supporting a longitudinal member, the longitudinal member anchoring opposing ankle braces proximal to the angle selector, and supporting a multi-use pad distal from the angle selector. 
     Embodiment 58. A gliding extension device for an apparatus for exercising against a resistance, the gliding extension device comprising:
     a roller carriage comprising a plurality of rollers adapted to glidingly engage a guide rod;   an extension frame extending from the roller carriage, the extension frame comprising a proximal end adjacent the roller carriage and a distal end;   an exercise engagement device at or near the distal end; and   an exercise attachment point receiver attached to the roller carriage, the proximal end of the extension frame, or both.   

     Embodiment 59. The gliding extension device of embodiment 58, wherein the exercise engagement device is a single hand grip. 
     Embodiment 60. The gliding extension device of embodiment 58, wherein the exercise engagement device is a two-handed bar. 
     Embodiment 61. The gliding extension device of any one of embodiments 58-60, further comprising a brake mechanism, the brake mechanism comprising a brake lever at the exercise engagement device, and a braking clamp at the roller carriage for arresting at least one roller among the plurality of rollers, the guide rod, or both, the brake lever adapted to disengage the braking clamp when the brake lever is manipulated. 
     Embodiment 62. The gliding extension device of any one of embodiments 58-61, further comprising an elastic band receiver attached to the roller carriage, the proximal end of the extension frame, or both. 
     Embodiment 63. The gliding extension device of any one of embodiments 58-62, wherein the extension frame further comprises a plurality of extension receiving ports for providing one or more extension exercise attachment points. 
     Embodiment 64. An extension arm for an apparatus for exercising against a resistance, the extension arm comprising:
     an angular selection bracket for attaching the extension arm to a frame of the apparatus, the angular selection bracket comprising a plurality of angle selection ports for establishing a plurality of extension angles;   an extension member extending from the angular selection bracket and comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points;   wherein an extension angle in the plurality of extension angles is determined by a portion of a member of the frame and a portion of the extension member.   

     Embodiment 65. The extension arm of embodiment 64, wherein the extension arm is adapted to receive at least one floating pulley capable of selectively connecting at least one weight stack of the apparatus to establish the one or more extension exercise attachment points. 
     Embodiment 66. The extension arm of any one of embodiments 64-65, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 67. The extension arm of any one of embodiments 64-66, wherein the floating pulley is the floating pulley of any one of embodiments 35-41. 
     Embodiment 68. A sit-up board for an apparatus for exercising against a resistance, the sit-up board comprising:
     a padded board for supporting an athlete;   at least one longitudinal member supporting the padded board; and   at least one lateral member supporting the padded board;   wherein the at least one longitudinal member, the at least one lateral member, or both, comprise a plurality of sit-up board accessory receiving ports.   

     Embodiment 69. The sit-up board of embodiment 68, further comprising two foot braces for receiving the feet of the athlete. 
     Embodiment 70. The sit-up board of embodiment 69, further comprising two handgrips for receiving the hands of the athlete. 
     Embodiment 71. The sit-up board of any one of embodiments 68-70, further comprising one or more pins for engaging accessory receiving ports of a frame of the apparatus for exercising against a resistance. 
     Embodiment 72. The sit-up board of any one of embodiments 68-71, further comprising one or more footers for stabilizing the sit-up board. 
     Embodiment 73. A multivector extension device for an apparatus for exercising against a resistance, the multivector extension device comprising:
     a brace for removably and adjustably attaching to a frame of the apparatus;   a multivector extension arm comprising a plurality of accessory receiving ports;   a ball joint joining the multivector extension arm to the brace while allowing the multivector extension arm significant freedom of movement relative to the brace;   at least one exercise engagement device removably attached to the multivector extension arm via a first accessory receiving port in the plurality of accessory receiving ports; and   at least one exercise attachment point receiver removably attached to the multivector extension arm via a second accessory receiving port in the plurality of accessory receiving ports.   

     Embodiment 74. The multivector extension device of embodiment 73, wherein the brace comprises a spring-loaded pin manipulated by a knob for engaging the frame of the apparatus. 
     Embodiment 75. The multivector extension device of any one of embodiments 73-74, wherein the multivector extension arm comprises square tubing. 
     Embodiment 76. The multivector extension device of any one of embodiments 73-75, wherein the at least one exercise engagement device comprises a single hand grip. 
     Embodiment 77. The multivector extension device of any one of embodiments 73-75, wherein the at least one exercise engagement device comprises a two-handed bar. 
     Embodiment 78. The multivector extension device of any one of embodiments 73-77, wherein the at least one exercise attachment point receiver comprises a J-hook for receiving an elastic band. 
     Embodiment 79. The multivector extension device of any one of embodiments 73-78, wherein the at least one exercise attachment point receiver comprises an eye bolt for receiving a carabiner. 
     Embodiment 80. The multivector extension device of any one of embodiments 73-79, wherein the at least one exercise attachment point receiver comprises a spring-loaded pin for securing the exercise attachment point receiver in an accessory receiving port. 
     Embodiment 81. The multivector extension device of any one of embodiments 73-80, wherein the at least one exercise engagement device comprises a spring-loaded pin for securing the exercise engagement device in an accessory receiving port. 
     Embodiment 82. The multivector extension device of any one of embodiments 73-81, wherein the multivector extension arm comprises at least two telescoping members, and the plurality of accessory receiving ports comprises a plurality of telescoping member accessory receiving ports. 
     Embodiment 83. The multivector extension device of embodiment 82, wherein at least one of the at least two telescoping members is selectively secured to the multivector extension arm with at least one spring-loaded pin. 
     Embodiment 84. The multivector extension device of any one of embodiments 82-83, wherein the at least one exercise engagement device is removably attached to the multivector extension arm via a third accessory receiving port in the plurality of telescoping member accessory receiving ports. 
     Embodiment 85. The multivector extension device of any one of embodiments 82-84, wherein the at least one exercise attachment point receiver is removably attached to the multivector extension arm via a fourth accessory receiving port in the plurality of telescoping member accessory receiving ports. 
     Embodiment 86. The multivector extension device of any one of embodiments 73-85, wherein the brace further comprises a support cone positioned about the ball joint to protect the frame from contact by the multivector extension arm. 
     Embodiment 87. The multivector extension device of embodiment 86, wherein the support cone comprises natural rubber, synthetic rubber, polyurethane, silicone, or a combination thereof. 
     Embodiment 88. The multivector extension device of any one of embodiments 73-87, wherein the apparatus for exercising against a resistance is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 89. A multivector extension support for an apparatus for exercising against a resistance, the multivector extension support comprising: a brace for removably and adjustably attaching to a frame of the apparatus; and a resilient support attached to the brace for receiving and protecting the frame from contact by a multivector extension device. 
     Embodiment 90. The multivector extension support of embodiment 89, wherein the brace comprises a spring-loaded pin for engaging the frame of the apparatus. 
     Embodiment 91. The multivector extension support of any one of embodiments 89-90, wherein the resilient support defines a recess for receiving the multivector extension device. 
     Embodiment 92. The multivector extension support of any one of embodiments 89-91, wherein the resilient support comprises natural rubber, synthetic rubber, polyurethane, silicone, or a combination thereof. 
     Embodiment 93. The multivector extension support of any one of embodiments 89-92, wherein the multivector extension device is the multivector extension device of any one of embodiments 73-88. 
     Embodiment 94. The multivector extension support of any one of embodiments 89-93, wherein the apparatus for exercising against a resistance is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 95. A method of exercising against a plurality of resistances having multiple vectors, comprising: 
     obtaining a multivector extension device comprising:
         a brace for removably and adjustably attaching to a frame of an apparatus;   a multivector extension arm comprising a first accessory receiving port, a second accessory receiving port, and a third accessory receiving port;   a ball joint joining the multivector extension arm to the brace while allowing the multivector extension arm significant freedom of movement relative to the brace;   a first exercise attachment point receiver removably attached to the multivector extension arm via the first accessory receiving port;   a second exercise attachment point receiver removably attached to the multivector extension arm via the second accessory receiving port; and   an exercise engagement device removably attached to the multivector extension arm via the third accessory receiving port; and
 
attaching a first resistance to the first exercise attachment point receiver;
 
attaching a second resistance to the second exercise attachment point receiver,
 
wherein the first resistance has a first vector and the second resistance has a second vector, wherein the first vector differs from the second vector, and wherein the first vector and the second vector thereby form the plurality of resistances having multiple vectors; and
 
moving the exercise engagement device against the plurality of resistances having multiple vectors, thereby exercising against a plurality of resistances having multiple vectors.
       

     Embodiment 96. The method of embodiment 95, wherein the multivector extension device is the multivector extension device of any one of embodiments 73-88. 
     Embodiment 97. The method of any one of embodiments 95-96, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 98. A mobile member for an apparatus for exercising against a resistance, the mobile member comprising: 
     an elongate section having a first end opposite a second end;
 
a first frame engagement device, at the first end of the elongate section, for securing the mobile member to a first member of a frame of the apparatus; and
 
a second frame engagement device, at the second end of the elongate section, for securing the mobile member to a second member of the frame.
 
     Embodiment 99. The mobile member of embodiment 98, wherein the elongate section comprises square tubing. 
     Embodiment 100. The mobile member of any one of embodiments 98-99, comprising between the first end and the second end, first mobile accessory receiving ports having axes in a first mobile direction, and second mobile accessory receiving ports having axes in a second mobile direction. 
     Embodiment 101. The mobile member of any one of embodiments 98-99, wherein the elongate section comprises a foamed polymer, a cushion, or a combination thereof. 
     Embodiment 102. The mobile member of embodiment 101, wherein the foamed polymer is chosen from latex foam rubber, polyurethane foam, styrene-butadiene foam, or a combination thereof. 
     Embodiment 103. The mobile member of any one of embodiments 98-102, wherein the first frame engagement device comprises a first rod having a first port for receiving a first retention key, the first rod being adapted to enter a first accessory receiving port of the first member of the frame. 
     Embodiment 104. The mobile member of any one of embodiments 98-103, wherein the second frame engagement device comprises a second rod optionally having a second port for receiving a second retention key, the second rod being adapted to enter a second accessory receiving port of the second member of the frame. 
     Embodiment 105. The mobile member of embodiment 104, wherein the first rod is longer than the second rod. 
     Embodiment 106. The mobile member of embodiment 104, wherein the second rod is longer than the first rod. 
     Embodiment 107. A foot stretching device for an apparatus for exercising against a resistance, the foot stretching device comprising: a brace for removably and adjustably attaching to a frame of the apparatus; an elongate sole portion attached to the brace by a brace hinge; and a heel portion attached to the sole portion by a heel hinge. 
     Embodiment 108. The foot stretching device of embodiment 107, wherein the brace comprises a spring-loaded pin for engaging the frame of the apparatus. 
     Embodiment 109. The foot stretching device of any one of embodiments 107-108, wherein the heel portion comprises a non-stick surface. 
     Embodiment 110. The foot stretching device of any one of embodiments 107-109, comprising steel, aluminum, or a combination thereof. 
     Embodiment 111. The foot stretching device of any one of embodiments 107-110, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-67. 
     Embodiment 112. A foot exercise attachment for an apparatus for exercising against a resistance, the attachment comprising: 
     a scaffold for receiving a foot of an athlete;
 
one or more straps for securing the scaffold to the foot; and
 
one or more exercise attachment point receivers for engaging a resistance to the scaffold.
 
     Embodiment 113. The foot exercise attachment of embodiment 112, wherein the scaffold comprises steel, aluminum, or a combination thereof. 
     Embodiment 114. The foot exercise attachment of any one of embodiments 112-113, wherein the one or more straps comprise hook-and-loop fabric, snaps, buttons, buckles, or a combination thereof. 
     Embodiment 115. The foot exercise attachment of any one of embodiments 112-114, wherein the scaffold comprises a toe portion for engaging the top of the toes of the foot. 
     Embodiment 116. The foot exercise attachment of any one of embodiments 112-115, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 117. A leg press accessory for an apparatus for exercising against a resistance, the leg press accessory comprising: 
     an angular guide having an angular guide brace for removably and adjustably attaching to a horizontal member of a frame of the apparatus;
 
an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide;
 
the extension member receiver being adapted to receive an extension member having a foot pad held in place on the extension member with a foot pad brace comprising a spring-loaded pin for engaging the extension member.
 
     Embodiment 118. The leg press accessory of embodiment 117, wherein the extension member comprises a plurality of extension receiving ports for providing one or more extension exercise attachment points. 
     Embodiment 119. The leg press accessory of any one of embodiments 117-118, wherein the horizontal member of the frame is adapted to receive a bench having one or more bench braces for engaging the horizontal member, the one or more bench braces comprising one or more spring-loaded pins for engaging the horizontal member. 
     Embodiment 120. The leg press accessory of any one of embodiments 117-118, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 121. An adjustable arcuate base for an apparatus for exercising against a resistance, the adjustable arcuate base comprising: 
     a stage comprising one or more retractable pins for engaging one or more accessory receiving ports on one or more vertical members of a frame of the apparatus;
 
an angular guide affixed to the stage;
 
an extension member receiver anchored to the angular guide so that the extension member receiver can move in an arcuate manner within the angular guide; the extension member receiver further comprising a spring-loaded pin; the extension member receiver being adapted to receive an extension member and secure the extension member with the spring-loaded pin.
 
     Embodiment 122. The adjustable arcuate base of embodiment 121, wherein the one or more retractable pins comprises two spring-loaded pins. 
     Embodiment 123. The adjustable arcuate base of any one of embodiments 121-122, wherein the extension member comprises a plurality of extension receiving ports for providing one or more exercise engagement devices and/or one or more exercise attachment point receivers. 
     Embodiment 124. The adjustable arcuate base of any one of embodiments 121-123, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 125. An angular telescopic extension device for an apparatus for exercising against a resistance, the angular telescopic extension device comprising: 
     an angular selection brace for selectively attaching the angular telescopic extension device to a frame of the apparatus, the angular selection brace comprising a retractable pin for engaging an accessory receiving port in the frame of the apparatus;
 
an angle selector comprising a plurality of angle selection ports attached to the angular selection brace;
 
an angular selection bracket connected to the angular selection brace by a hinge,
 
the hinge defining an axis of rotation, and comprising an angle selecting retractable pin for engaging an angle selection port in the plurality of angle selection ports on the angle selector for establishing a telescopic extension angle;
 
a telescopic extension arm extending from the angular selection bracket and comprising two or more nested extension members each adapted to be secured at a chosen length with a spring-loaded pin, the two or more nested extension members comprising a plurality of extension receiving ports for providing one or more extension exercise attachment points;
 
wherein the telescopic angle is determined by a first imaginary line between the axis of rotation and a first angle selection port in the plurality of angle selection ports, on one hand, and a second imaginary line between the axis of rotation and a chosen angle selection port in the plurality of angle selection ports.
 
     Embodiment 126. The angular telescopic extension device of embodiment 125, adapted to fit onto a vertical member of the frame of the apparatus. 
     Embodiment 127. The angular telescopic extension device of any one of embodiments 125-126, wherein the angle selecting retractable pin comprises a spring-loaded pin. 
     Embodiment 128. The angular telescopic extension device of any one of embodiments 125-127, wherein the telescopic extension arm comprises two nested extension members. 
     Embodiment 129. The angular telescopic extension device of any one of embodiments 125-128, wherein the telescopic extension arm comprises three nested extension members. 
     Embodiment 130. The angular telescopic extension device of any one of embodiments 125-129, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 131. A portable weight stack assembly for an apparatus for exercising against a resistance, the portable weight stack assembly comprising: 
     a portable frame comprising one or more portable vertical members mutually supporting one or more portable horizontal members;
 
a portable weight stack contained by the portable frame;
 
one or more portable cables routed about the portable frame via a plurality of portable pulleys selectively connecting the portable weight stack to a slidably adjustable portable exercise attachment point; and
 
at least one footer for stabilizing the frame.
 
     Embodiment 132. The portable weight stack assembly of embodiment 131, wherein the portable weight stack assembly weighs no more than about 200 lbs, no more than about 150 lbs., no more than about 100 lbs., no more than about 75 lbs., or no more than about 50 lbs. 
     Embodiment 133. The portable weight stack assembly of any one of embodiments 131-132, wherein the portable weight stack assembly weighs at least about 50 lbs., at least about 75 lbs., at least about 100 lbs., at least about 150 lbs., or at least about 200 lbs. 
     Embodiment 134. The portable weight stack assembly of any one of embodiments 131-133, wherein at least one of the one or more portable vertical members comprises first portable vertical accessory receiving ports having an axis in a first portable direction, and second portable vertical accessory receiving ports having an axis in a second portable direction. 
     Embodiment 135. The portable weight stack assembly of any one of embodiments 131-134, wherein at least one of the one or more portable horizontal members comprises first portable horizontal accessory receiving ports having an axis in the first portable direction, and second portable horizontal accessory receiving ports having an axis in a third portable direction. 
     Embodiment 136. The portable weight stack assembly of any one of embodiments 131-135, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     Embodiment 137. A frame for an apparatus for exercising against a resistance, comprising: 
     a plurality of vertical members mutually supporting a plurality of horizontal members,
 
wherein the plurality of vertical members and the plurality of horizontal members define a rectangular footprint having an aspect ratio of about 1:4, about 2:9, about 1:5, about 3:10, about 1:3, or about 3:10.
 
     Embodiment 138. The frame of embodiment 137, wherein the aspect ratio is at least about 1:4, at least about 2:9, at least about 1:5, at least about 3:10, at least about 1:3, or at least about 3:10. 
     Embodiment 139. The frame of any one of embodiments 137-138, wherein the aspect ratio is no more than about 1:4, no more than about 2:9, no more than about 1:5, no more than about 3:10, no more than about 1:3, or no more than about 3:10. 
     Embodiment 140. The frame of any one of embodiments 137-139, wherein at least some of the vertical members of the plurality of vertical members have first vertical accessory receiving ports having axes in a first direction, and second vertical accessory receiving ports having axes in a second direction. 
     Embodiment 141. The frame of any one of embodiments 137-140, wherein at least some of the horizontal members of the plurality of horizontal members have first horizontal accessory receiving ports having axes in the first direction, and second horizontal accessory receiving ports having axes in a third direction. 
     Embodiment 142. The frame of any one of embodiments 137-141, wherein the frame comprises square tubing, circular tubing, hexagonal tubing, or a combination thereof. 
     Embodiment 143. The frame of any one of embodiments 137-142, wherein the frame has a depth of at least about 1 foot, at least about 2 feet, at least about 3 feet, at least about 4 feet, at least about 5 feet, or at least about 6 feet. 
     Embodiment 144. The frame of any one of embodiments 137-143, wherein the frame has a depth of no more than about 1 foot, no more than about 2 feet, no more than about 3 feet, no more than about 4 feet, no more than about 5 feet, or no more than about 6 feet. 
     Embodiment 145. The frame of any one of embodiments 137-144, wherein the frame has a width at least about 3 feet, at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, at least about 12 feet, at least about 13 feet, at least about 14 feet, or at least about 15 feet. 
     Embodiment 146. The frame of any one of embodiments 137-145, wherein the frame has a width of no more than about 3 feet, no more than about 4 feet, no more than about 5 feet, at least about 6 feet, no more than about 7 feet, no more than about 8 feet, no more than about 9 feet, no more than about 10 feet, no more than about 11 feet, no more than about 12 feet, no more than about 13 feet, no more than about 14 feet, or no more than about 15 feet. 
     Embodiment 147. The frame of any one of embodiments 137-146, wherein the frame has a height of at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, or at least about 12 feet. 
     Embodiment 148. The frame of any one of embodiments 137-147, wherein the frame has a height of at least about 4 feet, at least about 5 feet, at least about 6 feet, at least about 7 feet, at least about 8 feet, at least about 9 feet, at least about 10 feet, at least about 11 feet, or at least about 12 feet. 
     Embodiment 149. The frame of any one of embodiments 137-148, wherein the apparatus is the apparatus of any one of embodiments 1-34 and 56-57. 
     As previously stated, detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention that may be embodied in various forms. It will be appreciated that many modifications and other variations stand within the intended scope of this invention as claimed below. Furthermore, the foregoing description of various embodiments does not necessarily imply exclusion. For example, “some” embodiments may include all or part of “other” and “further” embodiments within the scope of this invention. In addition, “a” does not mean “one and only one;” “a” can mean “one and more than one.”