Patent Grant
11529543
Six degree of freedom exercise devices in the prior art can have issues related to friction and/or inertia of moving parts, as well as high cost, excessive assembly time, reliability, strength, and limited functionality.
The present invention can provide an exercise apparatus that can exercise complex motions with six degrees of freedom, having minimized size, friction and inertia, allowing for an improved exercise experience, increased reliability, more linear force response, and increased precision of resistance output was well as measurement over that in the prior art.
The exercise apparatus can include a linear arm portion having an elongate arm member with proximal and distal ends and an elongate support member having proximal and distal ends. The arm member can be slidably mounted to the support member by a sliding joint positioned at the distal end of the support member. The arm member can be movable along a first axis between retracted and extended positions relative to the support member. The sliding joint can include first and second bearing assemblies which are spaced apart a sufficient distance from each other for constraining portions of the arm member within the sliding joint along the first axis at the distal end of the support member. The proximal end of the arm member that overlaps with the support member outside of the sliding joint when in retracted positions is unconstrained relative to the first axis. A linear arm brake assembly can be coupled to the arm member for resisting linear motion of the arm member. A torso portion can be included to which the linear arm portion is rotatably mounted about a second axis by a rotary shoulder joint located at about half way or midway along the length of the support member of the linear arm portion.
In particular embodiments, the torso portion can include a central support member extending along a third axis. The torso portion can be rotatable about the third axis by a rotary waist joint. Some embodiments may enable rotation over 360 degrees. A shoulder brake assembly can be mounted to the central support member for resisting movement of the rotary shoulder joint. The shoulder brake assembly can include a shoulder brake transmission having components positioned on opposite sides of the central support member and the third axis for minimizing rotational size and rotational inertia of the torso portion. The torso portion can be rotatably mounted about the third axis to a base by the waist joint. The base can include a base support member. A waist brake assembly can be mounted to the base support member for resisting movement of the rotary waist joint. The waist brake assembly can include a waist brake transmission. Transmission components can be positioned on opposite sides of the base support member for minimizing size of the base. The linear arm brake assembly can include a cable or belt secured to the arm member. An arm brake pulley that is engaged by the cable or belt can be rotatably coupled to an arm brake. The shoulder brake assembly can include at least one timing belt transmission stage rotatably coupled to a shoulder brake. The waist brake assembly can include at least one timing belt transmission stage rotatably coupled to a waist brake. The cable or belt of the arm brake assembly can engage a first support member pulley at the proximal end of the support member and a second support member pulley located at the sliding joint inward from the distal end of the support member. The sliding joint can extend from the distal end of the support member overlapping the support member about ⅓ or less of the length of the support member.
The present invention can also provide an exercise apparatus including a linear arm portion having an elongate arm member with proximal and distal ends and an elongate support member having proximal and distal ends. The arm member can be slidably mounted to the support member by a sliding joint positioned at the distal end of the support member. The arm member can be movable along a first axis between retracted and extended positions relative to the support member. The sliding joint can include first and second bearing assemblies which are spaced apart a sufficient distance from each other for constraining portions of the arm member within the sliding joint along the first axis at the distal end of the support member. The proximal end of the arm member that overlaps with the support member outside of the sliding joint when in retracted positions can be capable of some unconstrained lateral movement relative to the first axis. A linear arm brake assembly can be coupled to the arm member for resisting linear motion of the arm member. A torso portion can be included to which the linear arm portion is rotatably mounted about a second axis by rotary shoulder joint. The linear arm portion can be configured, and the rotary shoulder joint can be positioned along the length of the support member at a location that substantially balances the linear arm portion about the rotary shoulder joint at least when the arm member is in the retracted position.
In particular embodiments, the torso portion can include a central support member extending along a third axis. The torso portion can be rotatable about the third axis by a rotary waist joint. A shoulder brake assembly can be mounted to the central support member for resisting movement of the rotary shoulder joint. The shoulder brake assembly can include a shoulder brake transmission having components positioned on opposite sides of the central support member and the third axis for minimizing rotational size and rotational inertia of the torso portion. The torso portion can be rotatably mounted about the third axis to a base by the waist joint. The base can include a base support member. A waist brake assembly can be mounted to the base support member for resisting movement of the waist joint. The waist brake assembly can include a waist brake transmission. The linear arm brake assembly can include a timing belt transmission secured to the arm member. An arm brake can be rotatably coupled to the timing belt transmission. The shoulder brake assembly can include at least one timing belt transmission stage rotatably coupled to a shoulder brake, and the waist brake assembly can include at least one timing belt transmission stage rotatably coupled to a waist brake. The belt of the arm brake assembly can engage a first support member pulley at the proximal end of the support member and a second support member pulley located at the sliding joint inward from the distal end of the support member. A counterweight can be secured to the belt near the second support member pulley when the arm member is in the retracted position. The rotary shoulder joint can be positioned inward about ¼ to ⅓ of a length of the support member from the distal end. The counterweight and the arm brake can be positioned on a side of the rotary shoulder joint that is opposite to the proximal end of the support member to substantially balance the linear arm portion about the rotary shoulder joint when the arm member is in the retracted position. The base can include a pair or two legs extending from the base support member on opposite sides of the torso portion. A third or single leg can extend from the base support member spaced apart from and extending between the pair of legs. The legs can include at least one of retractable rollers for moving the apparatus, leveling mechanisms for leveling the apparatus, and mounting holes. The rotary shoulder joint can include a linear arm mounting bracket rotatably mounted to the shoulder brake transmission. The linear arm portion can be removably securable to the linear arm mounting bracket. The sliding joint can extend from the distal end of the support member overlapping the support member about ⅓ or less of the length of the support member.
The present invention can also provide an exercise apparatus including a linear arm portion having an elongate arm member with proximal and distal ends and an elongate support member having proximal and distal ends. The arm member can be slidably mounted to the support member by a sliding joint positioned at the distal end of the support member. The arm member can be movable along a first axis between retracted and extended positions relative to the support member. The sliding joint can include first and second bearing assemblies which are spaced apart a sufficient distance from each other for constraining portions of the arm member within the sliding joint along the first axis at the distal end of the support member. The proximal end of the arm member that overlaps with the support member outside of the sliding joint when in retracted positions can be capable of some unconstrained lateral movement relative to the first axis. A linear arm brake assembly can be coupled to the arm member for resisting linear motion of the arm member. The linear arm brake assembly can include a timing belt transmission secured to the arm member. An arm brake can be rotatably coupled to the timing belt transmission. The belt of the arm brake assembly can engage a first support member pulley at the proximal end of the support member and a second support member pulley located at the sliding joint inward from the distal end of the support member. A counterweight can be secured to the belt near the second support member pulley when the arm member is in the retracted position. A torso portion can be included to which the linear arm portion is rotatably mounted about a second axis by rotary shoulder joint. The rotary shoulder joint can be positioned inward about ¼ to ⅓ of a length of the support member from the distal end. The counterweight and the arm brake can be positioned on a side of the rotary shoulder joint that is opposite to the proximal end of the support member to substantially balance the linear arm portion about the rotary shoulder joint when the arm member is in the retracted position.
The present invention can also provide a method of exercising with an exercise apparatus including engaging a linear arm portion having an elongate arm member with proximal and distal ends and an elongate support member having proximal and distal ends. The distal end of the arm member can have an interface device or handle for engagement by a user. The arm member can be slidably mounted to the support member by a sliding joint positioned at the distal end of the support member. The arm member can be movable along a first axis between retracted and extended positions relative to the support member. The sliding joint can include first and second bearing assemblies which are spaced apart a sufficient distance from each other for constraining portions of the arm member within the sliding joint along the first axis at the distal end of the support member. The proximal end of the arm member that overlaps with the support member outside of the sliding joint when in retracted positions can be capable of some unconstrained lateral movement relative to the first axis. Linear motion of the arm member can be resisted with a linear arm brake assembly coupled to the arm member. Rotary motion of the linear arm portion can be allowed relative to a torso portion to which the linear arm portion is rotatably mounted about a second axis by a rotary shoulder joint. The linear arm portion can be configured, and the rotary shoulder joint can be positioned along the length of the support member at a location that substantially balances the linear arm portion about the rotary shoulder joint at least when the arm member is in the retracted position.
In particular embodiments, the torso portion can include a central support member extending along a third axis. The torso portion can be rotatable about the third axis by a rotary waist joint allowing rotary motion of the torso portion. A shoulder brake assembly can be mounted to the central support member for resisting movement of the rotary shoulder joint. The shoulder brake assembly can include a shoulder brake transmission having components positioned on opposite sides of the central support member and the third axis for minimizing rotational size and rotational inertia of the torso portion. The torso portion can be rotatably mounted about the third axis to a base by the waist joint. The base can include a base support member. A waist brake assembly can be mounted to the base support member for resisting movement of the waist joint. The waist brake assembly can include a waist brake transmission. The linear arm brake assembly can include a timing belt transmission secured to the arm member. An arm brake can be rotatably coupled to the timing belt transmission. The shoulder brake assembly can include at least one timing belt transmission stage rotatably coupled to a shoulder brake. The waist brake assembly can include at least one timing belt transmission stage rotatably coupled to a waist brake. The belt of the arm brake assembly can engage a first support member pulley at the proximal end of the support member and a second support member pulley located at the sliding joint inward from the distal end of the support member. A counterweight can be secured to the belt near the second support member pulley when the arm member is in the retracted position. The rotary shoulder joint can be positioned inward about ¼ to ⅓ of a length of the support member from the distal end. The counterweight and the arm brake can be positioned on a side of the rotary shoulder joint that is opposite to the proximal end of the support member to substantially balance the linear arm portion about the rotary shoulder joint when the arm member is in the retracted position. The base can support the exercise device with a pair or two legs extending from the base support member on opposite sides of the torso portion. A third or single leg can extend from the base support member spaced apart from and extending between the pair of legs. The legs can include at least one of retractable rollers for moving the apparatus, leveling mechanisms for leveling the apparatus, and mounting holes. The rotary shoulder joint can include a linear arm mounting bracket rotatably mounted to the shoulder brake transmission. The linear arm portion can be removably securable to the linear arm mounting bracket. The sliding joint can extend from the distal end of the support member overlapping the support member about ⅓ or less of the length of the support member.
The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.
Details of some embodiments of the exercise apparatus in the present invention are described below. Referring to
The transmission stages for the torso 2 and base 3 portions can include timing belts and pulleys, which decrease in width and weight for the purpose of increasing strength and decreasing costs, in addition to being on opposite sides of the respective support members. Pulleys on opposite sides of a support member can be rotatably coupled to each other or a brake by a common transmission shaft extending through the support member along respective horizontal or vertical axes. This can minimize size, and in the torso portion, can minimize the distance or rotational radius away from the axis A3 that the weight of the shoulder brake assembly is located to minimize rotational inertia. Using belts for rotating the waist joint 78 can allow unrestricted rotary motion 360 degrees and beyond. The number of the transmission stages, as well as the sizing and gear ratios of the transmission stages, can vary depending upon the amount of force expected to be exerted on the exercise apparatus, as well as the desired safety factor. In some embodiments, the safety factor can be a 6× safety factor, and in other embodiments, it can be less. Alternatively, other transmissions can be used such as V-belt, chain or gear transmissions, including planetary/epicyclic and cycloid configurations. The cable transmission for the arm member can also be replaced with any of these transmissions, while maintaining backlash requirements. A bushing system can provide for variable tensioning which further can allow for adjustable or variable backlash and friction trade-offs for maximum customization. The magnetic particle brakes 13, 31 and 58 can be connected to a controller 74, for example by a line 72 or wirelessly, for controlling the exercise machine as well as generating and storing data.
In some embodiments, shoulder and/or waist transmissions having three transmission stages can be sized to provide an overall ratio of about 32:1, where three stages each having about 3.2:1 ratios can be rotatably connected together in series. The particle brake can have about 10 ft-lbs max torque, and about 1800 RPM max. The handle 70 of the exercise apparatus can be moved during exercise with a max speed of about 10 m/sec and with about 35 lbs max force.
In other embodiments of the present invention, refer to
The linear arm brake assembly 86 can have a timing belt 88 positioned over two timing belt pulleys 90 that are rotatably mounted to the arm support member 75 as shown. Brake 13 can be coupled to the pulley 90 positioned at the proximal end of the arm support member 75. The timing belt 88 can be connected to or attached to or near the proximal end of the arm member 7 with a connecting member 92 such as a clamp, thereby providing linear motion resistance to the arm member 7.
In other embodiments, exercise apparatus 80 can include shoulder and/or waist transmissions having a single transmission stage that can be sized to provide a ratio of about 6.3:1. The particle brake can have about 18 ft-lbs max torque, and about 1000 RPM max. With a slight change in the length of the linear arm portion and/or arm member 7, the handle 70 of the exercise apparatus can be moved during exercise with a max speed of about 20 m/sec and with about 15 lbs max force. The lower rating can allow smaller shafts, pulleys, gears, etc. to be used.
Additional details of embodiments of the exercise apparatus now follows.
Solutions provided.
OTS belt/pulley system:
Reduced cost.
Reduced physical size and weight.
Reduced assembly time.
Increased precision of measurements and resistance.
Improved durability and resistance to wear in the field.
Ease of serviceability—belts can be retensioned and replaced without disassembling the entire system stage. Can be performed by non-expert technician or client/owner of system.
Meets ASTM safety guidelines (6× on structural parts, 4× on all other mechanical parts).
Linear stage: reduced friction throughout by eliminating carriage/wheels and rail and adding a second front stop with rollers.
Range of motion of base stage (left/right) can be unrestricted 360 degrees with belts and pulleys.
Referring to
Referring to
Referring to
Referring to
The polar angular motion stage (2) can be connected to the azimuthal angular motion stage (3) by way of screws (42) connecting their flanges (
Referring to
Removable base (4) can attach to the azimuthal angular motion stage (3) through screws (64), as seen in
This system can meet ASTM safety factor guidelines (6× on structural parts, 4× on other mechanical parts) for commercial fitness placement, when other markets (medical, physical rehab, at-home/consumer fitness) are targeted, the safety factor can be reduced, thereby reducing the size of many large structural and non-structural parts (e.g. the welded steel frame dimensions; the size of the OTS pulleys and belts). This can further reduce the cost, size (visual and physical), and weight of the system.
ID load requirement reduced, the safety factor also can be reduced, and the changes above apply as well.
Other suitable types of sensors.
Brake on the back of the linear stage.
Linear stage flipped upside down.
Reducing stroke/linear length.
Different belt types.
Adding motor.
System can be free standing instead of bolted to the floor—floor stand swaps out for legged system.
Referring to
Referring to
Referring to
Referring to
Referring to
The roller or bearing assemblies 5 and 6 that form the sliding joint 64 along axis A1 can be similar to that in the embodiments of
The longitudinal position of the distal end pulley 90 can be adjusted relative to the upper support portion 75a by a pulley or belt adjustment or tension arrangement, device, apparatus or mechanism 79 (
Referring to
The torso portion 2 can include an upright central support member 130 extending along axis A3 having an upright column portion 130a, a bottom mounting flange 132 for mounting to the rotatable flange 140 of the base, waist or azimuthal motion stage 3 with screws through holes, and an upper mounting fork 134 with spaced apart upright arms 134a to which the bearings 128a/128b are mounted on upper surfaces. As a result, the timing pulley 124a of the first pulley transmission stage 82a of shoulder brake transmission 82 is rotatably supported between the arms 134a of fork 134. The first transmission stage 82a includes a timing belt 124c that engages the large pulley 124a and a small timing pulley 124b rotatably mounted to one side of upright column portion 130a below the fork 134 about horizontal axis H1. The small pulley 124b of the first transmission stage 82a is rotatably coupled to the large timing pulley 126a of the second pulley transmission stage 82b located on the opposite side of column portion 130a by a transmission or driveshaft 136 extending along axis H1 laterally through the column portion 130a. The second transmission stage 82b includes a timing belt 126c that engages the large pulley 126a and a small timing pulley 126b rotatably mounted to the column portion 130a below the large pulley 126a. The small pulley 126b of the second transmission stage 82b is rotatably coupled to the shoulder brake 31 located on the opposite side of column portion 130a by a transmission, drive or brake shaft 138 extending along horizontal axis H2 laterally through the column portion 130a. As a result, the shoulder brake 31 is located on the same side of the support member 130 as the first transmission stage 82a. The shoulder brake 31 and the shoulder brake transmission 82 can provide bi-directional rotary or rotational resistance or force against the rotation or rotary movement of the linear arm portion 1 and/or shoulder joint 76 about axis A2 relative to torso portion 2. Positioning components of the shoulder brake transmission 82 on opposite sides of support member 130 and axis A3 can provide some rotational inertial balancing for rotation of torso portion 2 about axis A3. The pulleys, shafts and brake of the shoulder brake transmission 82 can be rotatably mounted to the column portion 130a in a similar manner as previously described in embodiments above. Column portion 130a can be formed of rectangular tubing.
Referring to
In some embodiments, the upper support portion 75a can weigh about 5-9 lbs. The proximal end of the linear arm portion 1 can extend away from the rotary shoulder joint 76 and axis A2 about ⅔ to ¾ more in length, such as about 5/7 or about 55 inches, than the distal end which can extend about ¼-⅓ in length such as about 2/7 or about 22 inches on the opposite side, while the arm member 7 is in the retracted position R (
Referring to
In some embodiments, the linear arm brake assembly 86 can include two pulleys 90 about 4.2 inches in diameter on which belt 88 is positioned, the distal pulley 90 being rotatably coupled to an arm brake 13 having a rating of about 115 in-lbs. The shoulder brake transmission 82 can have two reduction stages with a ratio of about 13.66:1, and include a first pulley transmission stage 82a having about a 3.29:1 ratio rotatably connected in series to a second pulley transmission stage 82b having a ratio of 4.15:1, rotatably coupled to a shoulder brake 31 having a rating of about 220 in-lbs. The waist brake transmission 84 can also have two reduction stages with a ratio of about 13.66:1, and include a first pulley transmission stage 84a having a ratio of 3.29:1 rotatably connected in series to a second pulley transmission stage 84b having a ratio of 4.15:1, rotatably coupled to a waist brake 58 having a rating of about 220 in-lbs. Controller 74 can be secured to the base 4 and can be connected to a monitor screen 74a by line 74b or wirelessly for controlling operation of the brakes 13, 31 and 58, and the exercises performed on exercise apparatus 100, which can be complex six degree of freedom motions. Further details of embodiments of exercise apparatus 100 can be as follows.
Free-Standing Version
With the addition of extension legs, the exercise apparatus 100 can be used without being bolted to the floor. A freestanding version can increase the amount of facilities that could use exercise apparatus 100 as not every potential client will be able to drill into the floor for mounting.
Belted Linear Sub-Assembly
The linear sub-assembly uses belts, which has significant advantages.
Arm throw length has been optimized (arm throw refers to how far the arm can move from its starting position to its ending position). The start and end bumpers are on the side of the belt mount to allow for near-0 loss of range due to mechanical constraints.
Linear Sub-Assembly Pivot Location
The linear sub-assembly can be configured such that the center of linear sub-assembly is not aligned with the pivot point or shoulder joint 76. This can reduce both the max and min torques on the structure.
Moving the pivot has a cascade of effects including: lowering the overall gear ratio of each sub-assembly (which allows the reduction of the number of pulleys), lowering the stresses on the structure (allowing the use of thinner and smaller tubes), and a more balanced linear sub-assembly system. This in turn yields both cost reductions and improved user experience.
Number of Gear Stages in Each Sub-Assembly
Reducing the torque requirement and upgrading the brakes allows the reduction of the number of gear stages in each sub-assembly from 3 to 2 for the same resistance ratings. This has significant cost, reliability and assembly optimizations.
Electronics Box
The expensive motherboard and touchscreen monitor can be replaced by a single, cheaper Android monitor. The off the shelf components can be replaced by a custom designed electronics board. Software modifications can be made, and the product is cheaper, scalable and more reliable.
Shipping
Exercise apparatus 100 can be taken apart into 4 subassemblies (base, waist, linear, and monitor) and shipped in smaller corrugate boxes. Each subassembly has wiring harnesses to attach all the electronics once fully built on site. Shipping in smaller boxes allows easy logistics and lower shipping costs. It also allows easy storage management at distribution centers.
Exercise apparatus 100 can have hidden wheels in the legs that can be deployed to move the unit. This makes moving+installing the unit easy and does not require specialized tools or equipment.
Stability
The 3 legs of the base sub-assembly have been optimized to reduce the rocking of the exercise apparatus 100. The legs are spaced out much further than the previous flat mounting plate which also reduces overall stress on the base sub-assembly.
These legs can have mounting flanges that have clearance to fit a hammer drill, which is used to fasten the base sub-assembly to thick concrete floors.
The entirety of the design can fit within 31″ door frame without disassembling the system.
Overall:
The base and waist sub-assembly frames can have two pulley stages on each, and each pulley can be subjected to a reduced torque than the apparatus of
The underlying design of the pulleys, bushings, shafts and belts can be the same or similar.
Base Sub-Assembly:
The base sub-assembly design can include wheels hidden inside of its tubular legs to allow for moving the unit.
The base sub-assembly can have three mounting legs instead of a flat mounting plate.
The largest pulley can be moved from on top of the base sub-assembly frame to the bottom of it. This can allow for better structural strength of the mounting tube. This can also allow for replacement of the belt in the field.
Waist Sub-Assembly:
Pads 122 can be on the waist sub-assembly frame or torso portion 2 fork to limit wear, sound, and create a better experience for the users when the linear sub-assembly is at its extreme ROMs.
The waist sub-assembly or torso portion 2 at the shoulder joint 76 can have a linear arm mounting bracket or cradle 120 that the linear sub-assembly or linear motion portion 1 can be attached to. This cradle design feature can allow the subassemblies to be shipped separately. The cradle is designed to withstand forces of the shoulder brake transmission 82 while fully tensioned. The cradle allows the top most pulley of transmission 82 to be installed and properly tensioned on the mounting shafts while the linear sub-assembly is removed. The cradle allows for easy assembly, and for future changement, upgrade, service, and repair of the entire linear sub-assembly without disassembly of the other sub-assemblies.
Linear Sub-Assembly:
The linear sub-assembly has been mounted about a pivot location for the shoulder joint 76 close or near the distal end.
By having the pivot for the shoulder joint 76 near the distal end, the design has been optimized for balance through brake placement and lightening of most components in the assembly. The arm goes through the rollers. The linear arm belt or system or belted support can provide a 6× safety factor and also includes a tensioning mechanism to properly tighten the belts.
Balance of the linear arm portion about the shoulder joint 76 can be important for the following reasons: 1) to ensure that the arm stays at or close to a horizontal position when the system is not in use (prevent unsafe or unpleasant ‘dropping’, 2) to ensure a pleasant user experience and reduce the impact that inertia and other factors within machine could have on measured performed data.
Optimized balance can be accomplished by: 1) placing the brake (12-15 lbs) at the front or distal end of the linear stage closest to the user to counterbalance the longer rear end or proximal end of the linear stage assembly; 2) using a (5-9 lb) support rail for the belted linear stage (note that the weight/load req/material/orientation of linear support changed as a result of pivot point change); 3) adding a counterweight (2-5 lbs) mounted to the upper (or in other embodiments, lower) linear stage belt to travel in the opposite direction of the moving proximal or rear end/mounting point (carriage') at the rear or proximal end of the linear stage tube/arm, for the purpose of counteracting gravitational forces of the linear stage tube/arm mounting point (‘carriage’). For example: as the arm (and therefore tube end/carriage/mounting point) travels towards the user during use, the counterweight travels away.
The counterweight on the linear subassembly can be on the top or bottom sides of the mounting structure and the counterweight can be made with wheels, low friction material, or other standard linear motion methods. The magnetic brakes can be replaced with other types of brakes. Motors can also be used to create an active system instead of a passive one. The general dimensions of the majority of components can be changed based on structural and customer requirements. The commercial system standard can have a 6× safety factor, while at home systems can have a 4× safety factor.
While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.
Some embodiments can include incremental encoders or homing Hall Switches for providing accurate position output. Features of the various or different embodiments can be combined together or omitted. The size, ratings and specifications of the various components can vary, depending upon the situation at hand. The limb interface device 70 can have suitable configurations for securing to other parts of the body, such as the head, torso or waist and other limbs such as the legs, feet or ankles.
This application claims the benefit of U.S. Provisional Application No. 62/991,875, filed on Mar. 19, 2020 and U.S. Provisional Application No. 63/122,057, filed on Dec. 7, 2020. The entire teachings of the above applications are incorporated herein by reference.
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