A Pedestal Design for the Total Gym

Transcription


Richard E. Butts
[email protected]
@Richard_Butts
Elevate your paddlesport training!
December 2009
http://www.frontiernet.net/~richeb/
Revision C
 2009 Richard Butts
Page 1
A Pedestal Design for the Total Gym
Contents
Project Overview........................................................................................................................................... 3
Bill of Materials, Tools and Suggestions ....................................................................................................... 5
Pedestal Assembly and Detail Drawings ....................................................................................................... 6
General Views of the Pedestal .................................................................................................................. 6
View of the Pedestal and the Total Gym showing Assembly Details ........................................................ 7
Dimensions of the Base............................................................................................................................. 8
Dimensions of the Angled Support ........................................................................................................... 9
Dimensions of the Top ............................................................................................................................ 10
Dimensions of the Upright ...................................................................................................................... 11
Dimensions of the U-Bolt ........................................................................................................................ 12
Some Close-Up Views of the 2 7/8” x 4” Pedestal and the Platform Weight Bar ........................................ 13
Static Resistance Provided by the Pedestal’s Height .................................................................................. 15
Height & Incline Comparison of the Total Gym 1000 Series and the Total Gym on the Pedestal .......... 15
Graph of the Static Resistance Presented to the User as % of Platform Load and Angle ...................... 16
Examples of Static Resistance vs Platform Load and Angle .................................................................... 16
Calculating the Force and Power Required to do the Prone Push-Down Exercise ..................................... 17
Details of an Example Prone Push-Down................................................................................................ 17
Diagram of the Platform Forces .............................................................................................................. 17
Equations for Force and Power vs. Time for the Example Prone Push-Down Exercise .......................... 18
Calculating the Force and Power vs. Time from the Platform’s Acceleration and Velocity ................... 19
Power Required Per-Person in Tandem Marathon Canoe Paddling....................................................... 20
Comparison of Power: Example Prone Push-Down Exercise vs. 7 MPH Tandem Marathon Canoe ...... 20
Unintentional but Happy Consequences – The seated, single arm lat pull down ...................................... 21
Appendix A: Photos of the Total Gym 1000 Series Showing Angles and Dimensions ................................ 22
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Project Overview
The Total Gym 1000 series is a terrific piece of exercise equipment for strengthening the muscles used in
the canoe and kayak paddling motion. It allows a large variety of arm motions and requires engaging the
torso and back while using the arms. Some people using the Total Gym for paddling-related exercises
find that the exercise resistance available in the product is too small. This project provides details of a
pedestal that increases the exercise resistance. The exercise resistance comes from the angle of the
platform and the weight on the platform. Increasing the exercise resistance can be done either by
increasing the platform’s angle so that a larger percent of the user’s weight is lifted or by adding weight
to the platform via attachment of a bar at the bottom edge of the platform for the addition of barbell
plates or by doing both.
Here are drawings and photos of a pedestal I made to increase the platform’s angle and with it the
exercise resistance. Along with the increased height the pedestal also improves the lateral stability by
increasing the width of the base by 68% (from 16” to 27”). I have used this pedestal for about three
years and I found it is stable and rigid. I’m quite happy with it. The motivation for increasing the
platform’s angle via this pedestal is an alternative to the method used by Mr. Marc Gillespie (principal of
Forge Racing). Marc has the upper end of his Total Gym attached to a steel pole in his basement. The
pole is a structural support of the house, is about 4” in diameter and is commonly used in house
construction in this area. My house also has such support poles but there are none in a location
convenient for placing the Total Gym.
The finished pedestal looks like this:
Notice that this pedestal keeps the vertical orientation of the Total Gym’s vertical support. For that to
happen, the bottom end of the diagonal support is kept in nearly its original location relative to the floor
and relative to the axis of the vertical support. In the photo above you can see the diagonal support has
its lower attachment point moved down to the base of the pedestal from its original position on the
Total Gym’s vertical support.
Revision C
Page 3
You are responsible for safety while using the Total Gym and any modifications you make to it. If you
increase the angle of the platform by simply putting the vertical support on top of something such as a
box then the vertical support won’t be vertical and the Total Gym will be unstable and unreliable. Don’t
use the Total Gym in an unstable or unreliable condition. Be aware that increasing the angle of the
platform causes increased load in the hand grips, cables, pulleys and fasteners. You are responsible for
determining that your hand grips, cables, pulleys and fasteners are capable of handling the increased
load before you decide to use them.
The following pages show the materials, tools and parts used for making a pedestal from 4” x 4”
dimensional lumber. What the lumber yards call 4” x 4” dimensional lumber is actually 3 ½” x 3 ½” when
it arrives in the hands of us users. You will see 3 ½” x 3 ½” on all the drawings. The pedestal shown in the
photo is the one I have used for several years and it is made from a large pallet’s stringer which is 2 7/8”
x 4”. In this paper I’ve taken its design and adapted it to the more common 4” x 4” dimensional lumber
size. In case you’re wondering, I have not used 4” x 4” dimensional lumber and these drawings to build a
pedestal. The pedestal I made is from 2 7/8” x 4” lumber. If you find an error, missing dimension or have
a suggestion about this project please contact me.
A person could get the same static resistance increase by adding weight to the platform instead of
increasing the platform angle. Adding about 54% of your body weight to the platform will be statically
equivalent to increasing the platform angle the amount this pedestal affords. I found the standard Total
Gym is too unstable side-to-side when set to its maximum angle and the platform is moved aggressively.
Before I added more weight I wanted to add side-to-side stability. The platform added stability and
static resistance. Adding weight to the platform is a good idea only if the system is stable. The additional
weight requires that you apply additional force to accelerate it. After developing the pedestal I added a
bar and weights to the platform in the same way others have done. A detailed photo of the bar
attachment is at the end of this document.
You’re welcome to use this design for any non-commercial purpose. If you make one, you have the
responsibility for the quality and care with which you make it, the quality and care with which you
attach the Total Gym to it and the suitability of the whole system for any use you put it to.
In the pages after the design details there is an analysis of force and power involved in the prone pushdown exercise. There is also a simple analysis of the power required for a 7 mph tandem canoe.
Together these analyses provide the explanation of why the top hand’s power is critical to maximizing
the canoe speed.
I hope you find this information useful. Enjoy and train safely.
Rich Butts, Mechanical Engineer
[email protected]
December 2009
This design is drawn in Sketch-Up v7. If you want the model files, contact me.
If you have a project design that you’d like drawn up or analyzed you’re invited
to contact me with your needs.
---------------------------------------------------------- * * * * * * * ----------------------------------------------------------
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Page 4
Bill of Materials, Tools and Suggestions
Bill of Materials
4” x 4” x 10’ Dimensional Lumber, Qty 1.............. (9’ 4” is needed, can be made from one 8’ and one 4’)
2” U-bolts, Qty 2 ............................................... (for fastening the vertical upright’s base to the pedestal)
¼” x 3 ½“ Hex Head Lag Screws, Qty 7 ............................................. (for fastening the pedestal together)
¼” I.D. x ¾” O.D. Flat Washers, Qty 11 ................................... (7 for the Lag Screws and 4 for the U-Bolts)
1 ¼” x 1 ¼” Right Angle Braces, Qty 2 .................. (for positioning the lower end of the diagonal support)
1” Wood Screws, Qty 6 .......................................... (for fastening the Right Angle Braces to the pedestal)
Wood Glue, Qty A/R ..................................................... (as required, for fastening the pedestal together)
Tools
Tape Measure
Carpenters Square
1
/8” Drill Bit .................................................................................. (pilot holes for the ¼” x 3½” lag screws)
¼” Drill Bit ............................................................................ (clearance holes for the ¼” x 3½” lag screws)
1” Auger Drill Bit ...................... (clearance holes for the 7/16” socket used on the lag screws and U-bolts)
Saw ..................... (Hand, Circular, Table or Band – whatever suits you. I used a hand-held circular saw.)
Drill ..... (I used a battery powered portable for the 1/8” and ¼” drills and a ratchet brace for the 1” drill)
7
/16” Socket and Wrench......................................................... (tightening the lag screws and the U-bolts)
Protractor .................................................................................................................................... (optional)
Suggestions
I have not shown pilot hole locations for the lag screws to screw into. You’ll most likely be using a
hand drill to place all the clearance holes. I suggest using the clearance hole as the template from
which to mark the hole location on the mating piece and then drill the pilot holes.
I have no knowledge about what loads and stresses the Total Gym is capable of handling. I have an
approximately five year old Total Gym and for three years I have used it on the Pedestal without
breaking anything. Your results may be different.
I have my Total Gym/Pedestal on a rug instead of on a potentially slippery hard surface.
About two years ago the Total Gym designers, efi Sports Medicine, Inc., changed the handle and cable
attachment design from plastic to metal. At that time Total Gym owners could get the new design at
no cost if they asked for it. I don’t know all the reasons for the design change. Strength and reliability
could be reasons. You might want to update.
Back To Table of Contents
Revision C
Page 5
Pedestal Assembly and Detail Drawings
General Views of the Pedestal
FRONT
BACK
Revision C
Page 6
View of the Pedestal and the Total Gym showing Assembly Details
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Page 7
Dimensions of the Base
A
Section A View of
Clearance Holes
Diameter ¼”
Diameter 1”
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Page 8
Dimensions of the Angled Support
Revision C
Page 9
Dimensions of the Top
Check your U-bolt
center-to-center
distance before
drilling these holes. I
notice the bolt
distance varies about
 1/8”
B
These holes are for the U-Bolts.
See the notes on the U-Bolt
dimensions page before drilling.
A
Section A View of
Clearance Holes
Diameter 1”
Diameter ¼”
Section B View of
Clearance Holes
Diameter ¼”
Diameter 1”
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Page 10
Dimensions of the Upright
Revision C
Page 11
Dimensions of the U-Bolt
Height of the bolt varies with manufacturer.
Typical height is 3" or 3 ½".
The drawing for the TOP gives ½” of thread
for the nut if you have a 3” bolt. And the bolt
will be clamping 1” of wood.
If you have a 3 ½” bolt you might want to
clamp 1 ½” of wood by shortening the depth
of the four 1” diameter holes to 2”.
Oddly enough, a 2” U-Bolt is intended to be used on a 1 ½“ pipe!
If your U-Bolt comes with a flat plate, just remove it. It doesn’t get used.
Revision C
Page 12
Some Close-Up Views of the 2 7/8” x 4” Pedestal and the Platform Weight Bar
The three attachment points of the Total
Gym’s vertical upright to the Pedestal Two U-bolts at the base. One lag screw
through an existing hole in the Total Gym’s
vertical upright. Use the hole located about
13” up from the base of the Total Gym.
Attachment of the diagonal
support to the pedestal
Revision C
Bottom view of the recessed U-bolt’s
fasteners
Page 13
Bottom View of Platform Showing Attachment
of Additional Bar for Barbell Plates
Back View of Pedestal
Revision C
Page 14
Static Resistance Provided by the Pedestal’s Height
The resistance of the Total Gym, like all free weights, has two components – the static resistance and the dynamic resistance.
Static Resistance
The static resistance is the force required to hold the platform load in any position. The static resistance is determined by the
platform load and the platform angle.
Dynamic Resistance
The dynamic resistance is the force required to accelerate the platform load. The dynamic resistance is determined by the total
moving mass and the acceleration of that mass caused by the user’s applied force.
The static resistance is the minimum force the user will experience; the dynamic resistance is determined by the user’s effort; and the sum
of them is the total resistance experienced by the user.
Height & Incline Comparison of the Total Gym 1000 Series and the Total Gym on the Pedestal
Total Gym 1000 Series
Platform’s Guide Rail Length
89”
Guide Rail’s Lowest Height
10 1/4” Rail’s Incline: 6.6
Guide Rail’s Highest Height
Total Gym on Pedestal
Platform’s Guide Rail Length
89”
Guide Rail’s Lowest Height
42”
Rail’s Incline: 28.2
Guide Rail’s Highest Height
Photos in appendix A were made while gathering these dimensions.
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Page 15
Graph of the Static Resistance Presented to the User as % of Platform Load and Angle
90%
Standard: Highest
100%
Standard: Lowest
80%
70%
60%
Resistance as % of Platform Load= Sin(Angle)*100%
Use of the pedestal increases the maximum static resistance by
54%. Raising it from the standard’s maximum at 43% of
platform load to the w/pedestal’s maximum at 65% of the
platform load.
40%
On Pedestal: Highest
50%
On Pedestal: Lowest
% of Platform Load Presented to User as Static Resistance
Static Resistance Presented to User as % of Platform Load and Platform Angle
30%
20%
10%
0%
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Platform Angle, Degrees
Examples of Static Resistance vs Platform Load and Angle
User’s Weight (Lbs)
160
160
185
185
Additional Weight (Lbs)
0
40
0
50
Total Weight (Lbs)
160
200
185
235
Revision C
Platform Angle ()
38.1
38.1
40.9
40.9
Static Resistance (Lbs)
=Sin(Platform Angle) x Total Weight
99
123
121
154
Page 16
Calculating the Force and Power Required to do the Prone Push-Down Exercise
The motion of the prone push-down exercise is very similar to the top hand motion of the canoe stroke. That similarity makes it great for training. It is
possible to calculate how much force and how much power are used to do this exercise. The calculated power can be thought of as the top hand’s
potential for propelling a canoe. Many people advocate the top hand’s
power to be critical in developing canoe speed. That thought leads to
asking: At a given speed of a tandem canoe, what percentage of the
required per-person power is equal to the top hand’s power potential? In
the next few pages I’ll develop an answer to that question and the
2) Platform Moves Up
question of force needed to do this exercise.
For starting out, here is a list of the information I know:
Details of an Example Prone Push-Down
Angle of Platform
User’s Weight
Added Platform Weight
Platform Travel (observation)
Platform Starting Speed (at the bottom)
Platform Ending Speed (at the top)
Travel Time, bottom to top (observation)
Acceleration due to Gravity
38.1
160.0
40.0
18.5
0.0
0.0
0.5
386.4
degrees
lbs
lbs
inches
in/s
in/s
Seconds
in/s2
1) Push Down
Prone Push-Down Exercise on a Total Gym with Pedestal and
Additional Platform Weight
Diagram of the Platform Forces
Here is a simple diagram of the platform and the forces acting on it:
Applied Force as Function of Time = F(t)
Total Platform Mass x Acceleration due to Gravity = Force of Gravity
MTotal x g =Fgravity
38.1
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Page 17
Equations for Force and Power vs. Time for the Example Prone Push-Down Exercise
I want to know what the applied force is as a function of time. There are only two forces that act along the platform’s line of travel. Those are the
applied force and a portion of the force of gravity. Notice that they act in opposite directions, so we can call the direction of the applied force
“positive” and the direction of the portion of the gravity force that acts along the platform’s line of travel “negative”. Let Mtotal represent the total
mass on the platform and g represent the vertical acceleration due to gravity. The portion of the force of gravity that is acting along the platform’s
line of travel is equal to Cosine(90-38.1) x Mtotal x g. Since the cosine and the sine are 90 apart we can write that as sin(38.1) x Mtotal x g. Sir Isaac
Newton pointed out that the sum of all the forces acting on a body and along any one line of action equals the time rate of change of the body’s
momentum (momentum equals mass x velocity) along that line of action. That’s the long way of saying the familiar and simplified “F = ma”. Putting
all that together gets us an equation for the force that the user applies to the platform as a function of time and the acceleration that it gives to the
platform as a function of time:
*This is the familiar “F=ma” and the Greek
letter sigma,, means “sum of the…”+


We can also calculate the power as a function of time by knowing that mechanical power is force multiplied by velocity.
Since we want to know the force as a function of time, we must figure out the acceleration as a function of time. And since we want to know the
power as a function of time, we must know the velocity as a function of time. Fortunately for us the acceleration is related to the velocity:
acceleration is the time rate of change of velocity. So if we know or can estimate the velocity as a function of time, then we can know the force and
power as a function of time. Instead of measuring the velocity vs. time, I will estimate it based on experience from doing the exercise. When doing
this exercise it is noticeable that the platform velocity increases to a peak just before the top. Then it slows quickly to a stop at the top. The force is
large and increasing at the start of the motion. Then it quickly drops to what feels like zero just before the top. Then it quickly rises again at the top of
the travel. From those observations I believe the platform’s velocity vs. time is close to a skewed parabola: a nice smooth velocity vs. time curve that
starts at zero going slowly up to a peak then going quickly back to zero. We can use that observation and the other facts we know to calculate an
estimate of the force vs. time and the power vs. time.
Revision C
Page 18
Calculating the Force and Power vs. Time from the Platform’s Acceleration and Velocity
Velocity Along Rail vs Time
0.0
0.1
0.2
0.3
0.4
0.5
Displacement Along Rail vs Time
20.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
Displacement (inches)
300.0
150.0
0.0
-150.0
-300.0
-450.0
-600.0
-750.0
-900.0
Velocity (inches/second)
0.0
0.1
0.2
0.3
0.4
15.0
10.0
5.0
0.0
0.0
0.5
0.1
Time (Seconds)
Based on experience from doing the prone
push-down exercise this is an estimate of the
velocity vs. time: a skewed parabola.
v(t) = -3552t3+1776t2
This acceleration vs. time is the derivative of the
velocity vs. time equation.
a(t) = -10656t2+3552t
0.2
0.3
0.4
0.5
Time (Seconds)
Time (Seconds)
This displacement vs. time is the integral of the
velocity vs. time equation and it fits the known
fact of 18.5” travel in 0.5 seconds.

Force (Lbs)
Force Applied to Platform vs Time
2.0
300.0
250.0
200.0
150.0
100.0
50.0
0.0
-50.0
-100.0
Power Applied to Platform vs
Time
1.5
Power (H.P.)
Acceleration (inches/second^2)
Acceleration Along Rail vs Time
The peak force is 275 Lbs
which is 2.2x the static
force of 123 Lbs.
Average
Two Arm Power
1.0
Average
One Arm Power
0.5
0.0
0.0
0.1
0.2
0.3
0.4
The average one-arm
power is 0.4 HP
0.5
Time (Seconds)
Revision C
0.0
0.1
0.2
0.3
0.4
0.5
Time (Seconds)
Page 19
Power Required Per-Person in Tandem Marathon Canoe Paddling
How much power does it take to paddle a tandem marathon canoe? Suppose it takes an average, continuous force of 50 Lbs1 to propel a canoe at 7
mph. 7 mph equals 10.3 ft/s. In linear motion, power is force x velocity so the average power is 50 Lbs x 10.3 ft/s = 515 ft-Lbs/s. Converting to Horse
Power, 515 ft-Lbs/s  550 ft-Lbs/s per H.P. = 0.9 H.P. per 2 people. So it requires about 0.5 H.P. per paddler to travel at 7 mph.
1
50 Lbs is very likely to be at the high end of the actual force required to overcome friction drag and wave drag in deep, calm water.
Comparison of Power: Example Prone Push-Down Exercise vs. 7 MPH Tandem Marathon Canoe

Analysis of the example for the prone push-down exercise gave us a result of 0.4 H.P. as the average power from one arm.
Recall that the motion of the prone push-down exercise is very similar to the top hand motion of the canoe stroke.

Analysis of the example for paddling a tandem marathon canoe at 7 mph gave us a result of 0.5 H. P. required per paddler.
Conclusion: The top hand in the canoe stroke is capable of producing a large portion of the power required from a paddler in a tandem canoe.
This simple analysis lends support to what many marathon canoe paddlers already know - effectively using the power of the top hand is
a critical ingredient to maximize the canoe speed.
Knowing that effective use of the top hand’s power is critical to maximizing the canoe speed leads to the question - What conditions
enable effective use of the top hand’s power?
1. The top hand must be directly above the blade for the entire duration of the power stroke.
2. The blade must remain at a fixed distance (laterally) from the canoe’s keel for the entire duration of the power stroke.
3. The blade must be fully submerged and perpendicular to the canoe’s keel for the entire duration of the power stroke.
In practice it means – When the catch* occurs, the top hand must already be directly over the blade and it must immediately begin
powering the canoe forward, continuing until the end of the power stroke.
* The catch is that moment at the end of the recovery phase when the blade is quickly and fully submerged. It is the start of the power
stroke.
Comment:
This comparison makes the implicit assumption that the power expended in one rep. of the prone push-down exercise can be repeated
for each of the many, many strokes of paddling a canoe. That is not likely to be true. Perhaps 1/3 to 1/2 of the calculated power could be
sustained. Also in calculating the power required to propel the canoe, the force used is likely at the high end of the actual requirement
which may be between 30 to 50 Lbs. Even considering these reductions, the conclusion stays the same.
Revision C
Page 20
Unintentional and Happy Consequences – The seated, single arm lat pull down
The pedestal has made possible doing a seated, single arm lat pull down. It is easy to reach up and pull down on one of the handles while sitting on a
low seat opposite the Total Gym’s platform. To replicate the top arm’s paddling motion just take your arm across your body and grab the handle then
press it straight down keeping your knuckles pointed forward. Holding onto a loop of rope that is around your foot will position your bottom hand
approximately at the start-of-stroke location. When the total gym was at its factory height the handles were a little too low and the base was not
wide enough to be stable during this exercise. To make this motion useful for training you should have additional weight added to the platform. One
way to do that is with the addition of a bar to the platform and barbell plates as shown earlier in this document. Here are a few photos that show the
arrangement and motion. Notice that my right hand is pulling the handle down on my left side and outboard of my left leg.
Revision C
Page 21
Appendix A: Photos of the Total Gym 1000 Series Showing Angles and Dimensions
Total Gym 1000 Series: Highest Position – General View
Total Gym 1000 Series: Lowest Position – General View
Revision C
Total Gym 1000 Series: Highest Position – Rail Height
Total Gym 1000 Series: Lowest Position – Rail Height
Page 22
Total Gym 1000 Series: Diagonal Support Attachment Height
Revision C
Total Gym 1000 Series: Platform Rail Length
Page 23

A Pedestal Design for the Total Gym

Transcription

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