Multi-functional fitness chair for light weight trainer

Multi-functional fitness chair for light weight trainer
Multi-functional fitness chair
for light weight trainer
Fan Rong
Wu Peng
Department of Mechanical Engineering
Blekinge Institute of Technology
Karlskrona
Sweden
2016
Bachelor of Science Thesis in Mechanical Engineering
in cooperation with
Blekinge Institute of
Technology
Shanghai Second
Polytechnic University
2
Abstract
Nowadays, physical inactivity has become a global problem. According
to the research, about 5.3 million deaths all over the world in 2008 could be
attributed to inactivity [1]. However, it is enough to do a little exercise every
day to reduce the risk of premature deaths by as much as 30 percent. Due to the
increasing working pressure, people do not have enough time to go to gym and
do exercises, which means that the design of multi-functional fitness chair is
necessary so that people can do exercise at home at any time.
There have already been many similar household fitness products in the
market, but most of them take up large space and the training part is very simple.
In comparison, the multi-function fitness chair designed in this thesis combines
several fitness equipment together in one chair, so it would save a lot of space,
and yet provides possibility to perform versatile exercise.
The product was designed in Autodesk Inventor 2015, and finite element
analysis was performed in Inventor 2015 and for checking the strength and
safety of the design.
Keywords: Fitness chair, Multi-function fitness equipment, Enhanced
access to fitness, Autodesk Inventor 2015, Finite Element Simulation.
3
4
Acknowledgements
Our deepest gratitude goes first and foremost to Md. Shafiqul Islam, our
supervisor, for his constant encouragement and guidance. He has walked us
through all the stages of the development of this thesis. Without his consistent
and illuminating instruction, this thesis could not have reached its present form.
Secondly, we would like to express our heartfelt gratitude to Professor
Wlodek Kuleza, who led us into the world of composition. We are also greatly
indebted to the professors and teachers from our home university. They taught
us the fundamental knowledge of the mechanical engineering, and make the
possibility of the completion of this thesis.
Finally, our thanks would go to our beloved family for their loving
considerations and great confidence in us all through these years. We also owe
our sincere gratitude to our friends and our fellow classmates who provided us
with their help and time in listening to us and helping us work out our problems
during the difficult course of the thesis.
We would like to express our gratitude to all those who helped us during
the documentation of this thesis.
Fan Rong
Wu Peng
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6
Contents
Abstract.................................................................................... 3
Acknowledgements .................................................................. 5
Contents ................................................................................... 7
List of figures ......................................................................... 10
List of tables ........................................................................... 12
List of symbols ....................................................................... 13
List of acronyms..................................................................... 15
1 Chapter: Introduction ..................................................... 17
2 Chapter: Survey of related work ..................................... 19
2.1
Portable Sit-up Machine.................................................................. 19
2.2
Rowing machine ............................................................................. 20
2.3
Lat pull ............................................................................................ 22
2.4
Leg extension .................................................................................. 23
2.5
Existed multi-functional fitness chair- Peak Pilates MVe® Fitness
Chair........................................................................................................ 25
2.6
Summary ......................................................................................... 26
3 Chapter: Problem statement, objectives and main
contribution ........................................................................... 28
3.1
3.2
4
Problem statement........................................................................... 28
Objectives and main contribution ................................................... 28
Chapter: Solution ............................................................ 30
4.1
Solution1 ......................................................................................... 30
4.2
Solution 2 ........................................................................................ 31
4.2.1The sleeve was replaced with the dual-shaft linear rail .................. 31
4.2.2The gears box to make the length of pulling rope and the
deformation of springs different ..................................................... 32
4.2.3Spring box ....................................................................................... 32
4.2.4Ratchet ............................................................................................ 32
4.2.5Sit-ups structure .............................................................................. 32
5
Chapter: Chapter: Details of the final solution ............... 34
5.1
5.2
5.3
Design of the base ........................................................................... 35
Design of the seat and the back....................................................... 36
Design of the leg support ................................................................ 37
7
The choose of the wire rope ............................................................ 39
5.4
5.5
Design of the spring box ................................................................. 40
5.6
Design of the connecting part of the spring .................................... 42
5.7
Design of the connecting part between the back and slider ............ 42
5.8
Design of the gears box................................................................... 43
5.9
Dual-shaft linear rail ....................................................................... 44
5.10 Cylinder- linear rail .......................................................................... 46
5.11 Ratchet and pawl ............................................................................. 47
5.11.1
The design of ratchet gearing.................................................. 49
5.11.1.1 The shape of the ratchet gearing......................................... 49
5.11.1.2 The determination of module and number of teeth ............ 49
5.11.1.3 The dimensions of the ratchet gearing................................ 49
5.12 Material choice................................................................................ 51
6
Instruction........................................................................ 54
6.1
Abstract ........................................................................................... 54
6.2
Product overview ............................................................................ 54
6.3
Main exercises................................................................................. 55
6.3.1Lat pull ............................................................................................ 55
6.3.2Rowing exercise .............................................................................. 56
6.3.3Leg extension .................................................................................. 57
6.3.4Sit-up exercise................................................................................. 58
6.3.4.1 Without weights ...................................................................... 58
6.3.4.2 With weights ........................................................................... 59
6.4
Extra exercises ................................................................................ 60
6.4.1Musculus Biceps Brachii Curl ........................................................ 62
6.4.2Cable Pushdown.............................................................................. 62
6.5
Weights ........................................................................................... 63
7
Chapter: Hand calculation............................................... 64
7.1
7.2
7.3
7.4
8
Welding ........................................................................................... 64
Gear calculation .............................................................................. 68
Cylindrically helical tension spring design ..................................... 73
The choice of spring........................................................................ 76
Chapter: FEM simulation ................................................ 77
8.1
8.2
8.3
Welding simulation ......................................................................... 77
Gear simulation ............................................................................... 78
Spring simulation ............................................................................ 79
9 Chapter: Conclusion and future work ............................. 81
Reference ................................................................................ 82
8
Appendix 1: ............................................................................ 85
Drawing of the full equipment assembly ................................ 85
Appendix 2: ............................................................................ 86
Drawing of main components ................................................ 86
9
List of figures
Figure 1.1 Obesity in the UK [2] .................................................................... 17
Figure 2.1 Portable Sit-up Machine JS-060h [3] ............................................ 19
Figure 2.2 Different muscles in stomach [5] .................................................. 20
Figure 2.3 Rowing machine [6] ...................................................................... 21
Figure 2.41 Start of the “Drive” [7] ................................................................ 21
Figure 2.52 The “Drive” [7]............................................................................ 22
Figure 2.63 The “Finish” [7]........................................................................... 22
Figure 2.7 The training part of lat pull [8] ...................................................... 23
Figure 2.8 Cybex VR1 Lateral Pulldown [9] .................................................. 23
Figure 2.9 Optima Series Leg Extension/Curl [10] ........................................ 24
Figure 2.10 Working muscle in leg extension [11]......................................... 24
Figure 2.11 Peak Pilates MVe® Fitness Chair [12]........................................ 25
Figure 2.12 MVe Fitness Chair exercises [13] ............................................... 26
Figure 3.1 FW-188 household multi- functional fitness equipment [14] ........ 28
Figure 4.1 Previous product ............................................................................ 30
Figure 4.2 Sleeve slider................................................................................... 31
Figure 4.3 Slider.............................................................................................. 32
Figure 5.1 Multi-Use Adjustable Dumbbell Chair [16] .................................. 35
Figure 5.2 The base of the chair...................................................................... 36
Figure 5.3 Gaming chair [17].......................................................................... 37
Figure 5.4 The seat and the back..................................................................... 37
Figure 5.5 Leg support .................................................................................... 38
Figure 5.6 GLCE365-Leg-Curl- Extension [18].............................................. 38
Figure 5.7 SWR 7×19 wire rope [19] ............................................................. 39
Figure 5.8 Breaking load in different diameter [19] ....................................... 39
Figure 5.9 Different types of the end terminations [19] ................................. 40
Figure 5.10 Design of the spring box.............................................................. 40
Figure 5.11 Whole view of spring box ........................................................... 41
Figure 5.12 Internal structure of the spring box ............................................. 41
Figure 5.13 The connecting of the spring ....................................................... 42
Figure 5.14 Design of the connecting part of the spring................................. 42
Figure 5.15 Design of the connecting part between the back and slider ........ 43
Figure 5.16 The whole structure ..................................................................... 43
Figure 5.17 Design of the gears box ............................................................... 44
Figure 5.18 Specification of external dual-shaft linear rail [20]..................... 45
Figure 5.19 The dual-shaft linear rail [20] ...................................................... 45
Figure 5.20 The dual-shaft linear rail and the cylinder-linear rail .................. 46
10
Figure 5.21 Specification of cylinder- linear rail [20] ..................................... 47
Figure 5.22 Cylinder linear rail series [20] ..................................................... 47
Figure 5.23 Internal ratchet gearing [22] ........................................................ 48
Figure 5.24 Different shapes of the ratchet gearing ........................................ 49
Figure 5.25 Design dimension of the ratchet gearing ..................................... 50
Figure 5.26 Ratchet and pawl ......................................................................... 51
Figure 6.1 Components of the whole product................................................. 54
Figure 6.2 Lat pull exercise............................................................................. 56
Figure 6.3 Rowing exercise ............................................................................ 57
Figure 6.4 Leg extension................................................................................. 58
Figure 6.5 Sit-up without weights................................................................... 59
Figure 6.6 Sit-up with weights ........................................................................ 60
Figure 6.7 Musculus biceps brachii curl [24]h ............................................... 61
Figure 6.8 Cable Pushdown [25] .................................................................... 61
Figure 6.9 Musculus biceps brachii curl ......................................................... 62
Figure 6.10 Cable Pushdown .......................................................................... 63
Figure 7.1 Structure of welding ...................................................................... 65
Figure 7.2 Parameters of the gears [27] .......................................................... 73
Figure 7.3 Mechanical properties of 65Mn [28] ............................................. 74
Figure 7.4 Types of the spring [29] ................................................................ 76
Figure 8.1 Welding function in Inventor ........................................................ 77
Figure 8.2 Welding stress ............................................................................... 78
Figure 8.3 Gear stress...................................................................................... 79
Figure 8.4 The deflection of the spring by 100 N ........................................... 79
Figure 8.5 The deflection of the spring by 150 N ........................................... 80
11
List of tables
Table 2-1 Different working muscles in different exercises........................... 26
Table 5-1 Lists of main parts .......................................................................... 34
Table 5-2 Datum of the fitness chair [16] ....................................................... 35
Table 5-3 Assessment of the type ................................................................... 36
Table 5-4 Dimensions of the ratchet gearing .................................................. 50
Table 5-5 Mechanical Properties of Aluminum 6061-T4 [23] ....................... 51
Table 7-1 Known datum of gears.................................................................... 68
Table 7-2 Main parameter of different springs ............................................... 76
Table 8-1 The deflection at ultimate load for different types of spring .......... 79
12
List of symbols
Symbol
Quantity
Unit
݉
Module
ܼ
Number of teeth
݀௔
Tip diameter

‫݌‬
Circular pitch

݄
Tooth height

ܽଵ
Working length of the pawl

ܾ
Width of the ratchet

݄ଵ
Tooth slant

‫ݎ‬௙
Ratchet dedendum circle radius

‫ݎ‬ଵ
Ratchet addendum circle radius

‫ܮ‬
The length of the pawl

‫ݎ‬ଵ
Ratchet addendum circle radius

‫ܮ‬
The length of the pawl

ߪ
Stress
ƒ
‫ܫ‬
Moment of inertia
݉ସ
‫ܥ‬
Spring index
݀
Diameter of wire

ߣ
Deflection at ultimate load

߬௠௔௫
Maximum cyclic shear stress
ƒ
ܵ௖௔
Fatigue strength safety factor
߬଴
Pulsating cyclic shear fatigue limit of the spring
material
13
ƒ
ܵி
ܲ
Design safety factor of fatigue strength of the
spring
Input power
݊ଵ
Pinion speed
‫ݑ‬
Gear ratio
‫ܭ‬௧
Load factor
ܶଵ
Torque of the pinion
߶ௗ
Tooth width coefficient
ܼா
Material influence coefficient
”Ȁ‹
ή 
ଵ
ߪு௟௜௠ଵ
Fatigue strength limit of the pinion
‫ܽܲܯ‬ଶ
ƒ
ߪு௟௜௠ଶ
Fatigue strength limit of the wheel
ƒ
‫ܭ‬ுοଵ
Contact fatigue life factor
‫ݒ‬଴
Circumferential speed
݉ Τ‫ݏ‬
ܾ
Face width

݄‫כ‬௔
Addendum Coefficient
݄௙
Dedendum

14
List of acronyms
Acronym
Unfolding
FEM
Finite Element Method
CAD
Computer aided design
15
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1 Chapter:
Introduction
With the development of the society, our living condition is much more
comfortable than before. However the good condition also bring a lot of health
problem, on the other word, lacking exercise can cause many chronic diseases
[1]. Except the elderly, more and more young people are suffering from sub
health problems. As for the students, the lack of exercise bring about the
descending of the students' body ability, and they are more likely to get sick.
According to the research, overall 64% of adults in the UK are overweight or
obese, with a Body Mass Index of 25 or over. Around 8% of deaths are
attributed to obesity related illness in the UK [2].
Figure 1.1 Obesity in the UK [2]
As for the office workers, having Irregular diet and life pressure also
overload their body. When young people realize their health problems, they
start to go to the gym or buy lots of fitness equipment in order to start exercising.
Although there are many people doing exercise, most of them only last for few
months. Besides, they may have difficulties which may interfere with them. For
the students, they may not afford to go to the gym. And for the workers, their
schedule always changed which may disrupt their plan of doing exercise, and
after finishing the busy work, many people prefer to go home to have a rest than
going to the gym. Thus there are few people insist on doing sports every day.
17
Besides if people choose to buy lots of fitness equipment to do sports at home,
the equipment may occupy a lot of space and spend a lot of money.
Therefore, in order to solve these issues, our group attempt to design a
chair which aims to get a full body workout by spending the least amount of
money, it can exercise the waists, legs, shoulders and other parts of the body
only by using this chair wherever you like. We think that the exercise intens ity
is more suitable to the young people, and they may occupy less space and cost
less money.
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2 Chapter:
Survey of related work
2.1 Portable Sit-up Machine
For sitting in a chair for a long time, most of office workers have the
lumbar spine (lower back), besides that, more and more people are facing too
much pressure in the work, mostly having no time to have a healthy diet,
sometimes even eating unhealthy food like some fast food. The Portable Sit-up
Machine JS-060h [3] aims to help people having waist and abdomen exercises.
From the training point of view, the training effect of this Sit-up machine is
limited, because the back of the chair restores the original position only by the
restoring force of the spring. However, using this equipment can exactly reduce
the back pressure after a long time sitting. On the contrary, if the back can have
an opposite movement direction, like the training equipment in the gym, in this
way, people can training their waist and abdomen.
Figure 2.1 Portable Sit-up Machine JS-060h [3]
Nowadays, more and more people begin to do sit-up, in order to exercise the
abdominal muscles. Mr. Olympia Arnold Schwarzenegger, a professiona l
bodybuilder recommends people to do sit-up exercises, because through the situp exercise, it can strengthen the core and stabilizing muscles [4].
The primary muscle targeted in a pull up is Rectus Abdominis. The rectus
abdominis can be said to be the wall of the abdominal muscles and are paired
long muscles which connect the lower rib cage and the hips. It also creates six
19
pack effect. The functions of these muscles are tensing the abdominal wall,
flexing the trunk and stabilize the pelvis [5]. Doing sit-up exercise can also
exercise External Oblique, which attach to the rib cage and the pelvis. In
addition, Tensor Fasciae Late and Rectus Femoris can also be exercised during
the sit- up exercise.
Figure 2.2 Different muscles in stomach [5]
2.2 Rowing machine
One of the best amenities in the gym is the rowing machine. Modelo D, a
rowing machine [6], you can exercise different parts of your body in differe nt
posture. It can not only works on the upper body, but also works on the lower
body, besides that, it can also exercise your abdominal muscle. For example,
when it works on the upper body, 75 percent of the power comes from your
legs and hips. In this way, you can tone your legs and firm your thighs, as long
as you row properly and regularly. The rowing machine is good way to improve
cardiovascular fitness.
20
Figure 2.3 Rowing machine [6]
There are many reasons that people are choosing to do indoor exercises by
the rowing machine. The first one is people in different ages can use rowing
machine, it was designed to bring benefits to the masses. The second reason is
it can train the total body, not only for the upper-body, but also for the lowerbody, the rowing machine gets nine major muscle groups worked such as quads,
core, shoulders, back, hamstrings and so on. The third reason is it is an effective
aerobic exercise, no matter what the age is, aerobic exercise is one of the most
important contributor to the total health, for instance, a regular aerobic exercise
can make the immune system stronger than before. And the last reason is it is
easy to learn, a basic rowing exercise can be learned in 10 minutes or less.
A basic rowing exercise can be divided into three process, and in differe nt
process, the working muscles are also different [7].
1.
Start of the “Drive”
In this process, the working muscles are Erector, Spinae, Rhomboids,
Quadriceps, Gastrocnemius and Soleus, and Hamstrings.
Figure 2.41 Start of the “Drive” [7]
2.
The “Drive”
In this process, the working muscles are Erector Spinae, Rectus Abdominis,
Triceps, Rhomboids, Deltoids, Trapezius, Pectoralis Major, Wrist Extensors
and Flexors, Quadriceps, Glutes, Hamstrings, and Gastrocnemius and Soleus.
21
Figure 2.52 The “Drive” [7]
3. The “Finish”
In this process, the working muscles are Erector Spinae, Wrist Extensors and
Flexors, Triceps, Biceps, Deltoids, Pectoralis Major, Rectus Abdominis,
Internal and External Oblique, Quadriceps, and Hamstrings.
Figure 2.63 The “Finish” [7]
2.3 Lat pull
The lat pull machine is very common in the gym, this equipment can be used
for training biceps and shoulders, and this is also an effective exercise to make
the muscle support the shoulder joint stronger, in addition, it is important to
reduce sports-related injuries. The first step is adjusting user's sitting posture,
the second step is grasping the bar which is wider than the shoulder width. Then
slowly pull the bar down to the upper chest. When finished, slowly stand up
and allow the weight stack to return. During the whole exercise process, the
major working muscles are, Latissimus Dorsi, Teres major, Sternal portion of
pectoralis major, Pectoralis minor, Rhomboids, and Biceps.
22
Figure 2.7 The training part of lat pull [8]
We have done some investigate on the internet, lots of lat pull machines are
designed for the gym, because all of them need a large space, like one of the lat
pull machine, Cybex VR1 Lateral Pulldown, a professional training machine,
the dimensions of this machine is width 1223 , length 1901 , height
2201 [9].
Figure 2.8 Cybex VR1 Lateral Pulldown [9]
2.4 Leg extension
The leg extension is a relatively simple exercise, which works at only one
joint, so it means it is a basic and limited motion. Sitting on the machine with
the knees at a 90 degree angle and the back should be straight, lifting the weight
until the legs are almost straight, however, in the whole exercise, the knees
23
should be kept a slight bend in order to protect the joint from excessive wear
and tear. The simplicity of the leg extension makes it easy to learn.
Figure 2.9 Optima Series Leg Extension/Curl [10]
The exercise of leg extension is a key exercise in strengthening the patellar
ligament and the quadriceps attachment for the knees, so the leg extension
machines are very common in the gym. Optima Series Leg Extension/Curl is a
professional machine which for the leg extension. The primary muscle targeted
in a pull up is Quadriceps.
Figure 2.10 Working muscle in leg extension [11]
The correct leg extension form.
24
1.
Sit on the leg extension machine and keep the back straight, it means
the back should stick to the back of chair throughout the whole
movement.
2.
Adjust the pedal above the feet and much below the knees, which should
be comfortable and appropriate.
3.
Adjust the weight which is suitable to the trainer.
4.
Start to raise legs and halt just before the legs are straight, the whole
movement should be slowly, otherwise it will do damage to the knees.
5.
Squeeze the quadriceps for a second slowly bring down the legs and
stop just before the knees are perpendicular.
6.
Do 3-4 sets with 10-15 repetitions each.
2.5 Existed multi-functional fitness chair- Peak Pilates
MVe® Fitness Chair
Pilates chair is an existed professional chair for fitness, it is sleek and metal,
stable, portable and stackable which up to 5 for high for space saving. This
chair can be folded and easily fits into a closet, under the bed or put into a car.
Figure 2.11 Peak Pilates MVe® Fitness Chair [12]
The Pilates chair is lightweight, but solidly built and is suitable for all body
sizes. The function of the Pilates fitness chair is, sculpting legs, arms, buttocks,
thighs and other parts of body, so this chair is ideal for one on one training or
some small group classes. The MVe fitness chair facilitates the performance of
25
many Pilates exercises, the following figure is some of the MVe fitness chair
exercises.
Figure 2.12 MVe Fitness Chair exercises [13]
A group of researchers have done a research and the objectives of the
research is to assess the feasibility and efficacy of delivering Pilates exercises
for resistance training to breast cancer survivors using the MVe Fitness Chair.
Twenty-six female breast cancer survivors were invited to participate in this
research, and the result shows that the MVe Fitness Chair is feasible for use in
breast cancer survivors [13].
2.6 Summary
Table 2-1 Different working muscles in different exercises
Fitness
machine
Working muscles
Rectus Abdominis
External Oblique
Sit-up
Tensor Fasciae Late
Machine
Rectus Femoris
26
Erector, Spinae, Rhomboids,
Quadriceps,
Gastrocnemius
Hamstrings.
and
Soleus,
Trapezius, Pectoralis Major,
Wrist Extensors and Flexors.
Rowing
machine
Latissimus Dorsi
Teres major
Sternal portion of pectoralis
major
Lat pull
Pectoralis minor
Rhomboids
Biceps.
Quadriceps
Leg
extension
l
27
3 Chapter:
Problem statement, objectives and
main contribution
3.1 Problem statement
In the market, varieties of household fitness equipment have already existed,
however most of them have a same problem, taking a lot of space. For instance,
FW-188 multi- functional fitness equipment, a household fitness equipment, a
complete set of equipment take a large space [14]. The average floor area per
capita in Sweden in 2008 is 58݉ଶ Τܿܽ‫[ ݌‬15]. It means, in most situation, there
are not a lot of space to place household fitness equipment, besides that, the
training part is very simple, one equipment corresponds to a certain training
part.
Figure 3.1 FW-188 household multi-functional fitness equipment [14]
In our design, we combine several kinds of fitness equipment together in one
chair, in this way, we can save a lot of space, to most family it is a good choice.
3.2 Objectives and main contribution
According to the previous part, we can conclude that there is a contradictory
point in the household fitness equipment field, a professional household fitness
28
equipment need to take a lot of space, on the contrary, a simple, normal
household fitness equipment is small, however only can training several parts
of bodies. A number of people think, training the same parts of body every day
is more efficient. This is one of the worst exercise mistakes, these mistakes are
destroying bodies’ metabolism, keeping flabby, weak and injury-prone. Human
are creatures of habit and tend to stick to things which are familiar with and
good at. But when it comes to the training, people should keep changing
training parts if the trainer what to make progress, in this way, it can keep
metabolism running on high.
So our group want to design a household multi-functional fitness chair for
the people who wants to have light weight training to keep fit at home or for
some fitness training beginners. This kind of household multi-functional fitness
chair combines with a variety of fitness equipment, so it only takes a little space.
Since this product is designed for light weight training, so there is no need
to use barbell weights to provide force, we want to use springs instead of
dumbbell weights, this is an efficient way to deduce the probability of the
accident happens, which hit by a dumbbell, besides it can also save space.
29
4 Chapter:
Solution
4.1 Solution1
Figure 4.1 Previous product
In the preliminary design, it has not enough functions and useless structures.
This fitness chair used common chair with the spring structure providing
force for sit-up exercise and leg rod setting on the front of the chair for leg
extension. The structure has been shown in the Figure 4.1.
The advantage of the design is that it is lighter than these in the gym.
Moreover, it can be used in the office or some small space. Users just lay on
the back of the chair to do some exercises instead of going to the gym.
However, it is limited in the function and effect. What is more important, it
is difficult to combine the fitness parts with the part which provides forces. And
then, in that part which provides forces, it is lack of the up and down stability
because the wheels were not fixed on the ground. When doing sit- up exercise,
it is easy to find that users cannot exercise the abdominal muscles because they
do not use the power of the waist completely but the back power.
30
4.2 Solution 2
According to disadvantage the preliminary design and multifunction, an
innovation design was come up with. It also depends the spring structure to
provide different forces for fitness exercises. In order to solving the lack of the
stability in the spring part which provides force, the liner rails replace wheels
and it more stable than the past in the structure. It will be shown in the Figure33.
What is more, some other function for fitness has been added to this design,
for example, lat pull, rolling exercise, musculus biceps brachii curl and table
pushdown. The instruction for using will been shown in the next literature.
After discussing, this design was adopted.
4.2.1 The sleeve was replaced with the dual-shaft linear rail
However, there are some problems in the structure. When doing rolling
exercise, the seat must be moved forth and back with the body of user but here
it just was fitted over the bar of the chair holder by sleeve. It can cause wear
between sleeve and that bar and reduction of the product durability. According
to this reason, the dual-shaft linear rail should be the best choice.
Figure 4.2 Sleeve slider
31
Figure 4.3 Slider
4.2.2 The gears box to make the length of pulling rope and the
deformation of springs different
Because of using the same kind of springs to output different forces, a
problem, that the deformation of springs is limited in a small range but the
length of pulling rope is larger, must be considered. In order to achieve this
goal, the gears box was designed after brainstorming.
4.2.3 Spring box
The different user needs different weights while doing exercises so here are
2 kinds of springs. The issue is how to link these springs on the fitness structures.
Under such conditions, the spring box was designed.
In this design, it also solves the swing up and down of springs.
4.2.4 Ratchet
Here, the back must be disconnected with the spring structure and fixed at a
certain angle while doing other exercises except sit-ups. In this design, the
ratchet is inserted into the back and combined with the seat.
4.2.5 Sit-ups structure
In previous design, the user lies on the back and pushes the back which
connects with the spring structure to do sit-ups. After investigating the gym,
some people suggest that the abdominal muscle are tight when doing Sit-ups
32
but it does not in that way. According to some other ways to do Sit-ups, the
new method was gotten.
In this solution, feet must be fixed on somewhere so the pedal to set feet on
is added.
33
5 Chapter: Chapter:
Details of the final solution
After the group meeting and brainstorming, the product have been added
more fitness function on it. For example the sit-up exercise, lat pull, leg
extension, rowing exercise and some other exercises. The product can be
roughly divided into several main parts, and the following table 5-1 is the lists
of them.
Table 5-1 Lists of main parts
Part number
Name
Quantity
1
Base
1
2
Seat and back
1
3
Leg support
1
4
Telescopic rod
1
5
Rtchet and pawl
2
6
Linear rail
3
7
Rocker mechanism
1
8
Gears box
1
9
Spring box
4
10
Leg fixing rod
1
11
Cylinder- linear rail
2
12
Dual-shaft linear rail
2
13
Slider
1
14
Chair handle
1
34
5.1 Design of the base
It is similar to some existed fitness chair, the most important factor of the
base is strength, In order to make the base have a higher strength, two
crossbeams are added to the front and back of the base, besides, at the both
sides of the crossbeams, there are four anti-skid pads. One function of the antiskid pads is increasing the friction force between the crossbeams and the floor,
and the other function is reduce the damage to the floor, the main material of
the fitness chair is carbon steel, the whole weight of the chair is a big force,
which is exerted to the floor, this might do damage to the floor, that is why we
add four anti-skid pads.
In order to estimate the possible prize of the product, we investigated some
similar items on the internet.
Figure 5.1 Multi-Use Adjustable Dumbbell Chair [16]
Table 5-2 Datum of the fitness chair [16]
Price
̈́ͳ͹Ͳ
Size
Length: 1300 
Width: 320 
Height: 800 
35
weight
150 ‰
Figure 5.2 The base of the chair
5.2 Design of the seat and the back
Before the design of the seat and the back, our group have a discussion about
how the seat and the chair like, there are two different choices, one is the
common shape of the seat and the back, like the exercise chair in the gym, and
the other is gaming chair, it is known to us that the gaming chair is designed for
the E-sport match, and be famous for its comfort, one of the group member
explain why he wants to design the back and the seat base on the gaming chair,
no one is willing to treat exercise as a burden, using a comfortable chair is more
likely to reduce the exhaustion after finish exercises. Then our group have a
brainstorm, which aims to find a proper solution.
Table 5-3 Assessment of the type
Type
Economy
Safety
Exercise
chair
Gaming
chair
3
3
1
2
Comfort Design
Practicability
Total
1
3
10
3
2
8
After the brainstorm, we decide to design the seat and the back like a
traditional exercise chair. From the table we can find that the weakest point is
the comfort, so we want to do some improvements to the back and the seat,
choosing soft material like sponge, and also thicken the seat and the back, make
it more comfortable and softer, in this way, it is suitable for long-time exercise.
36
Figure 5.3 Gaming chair [17]
Figure 5.4 The seat and the back
5.3 Design of the leg support
The leg support is one of training part in our design, and it has two functio ns.
The first one is having leg extension exercises. There is a hook, which can
connect with a wire rope, and at the other side of the rope is the spring. Springs
are the source of the force, when the trainer having leg extension exercise, he
needs to put the leg under the pedal of the support, in order to make it more
comfortable, there are also two sponges around the support, then start to raise
legs and halt just before the legs are straight, during the whole process, the leg
support stretch the springs by the wire rope, it will be introduced in the next
37
part. The second function of the leg support is the base of long pole, this part
will be introduced in the next part.
Figure 5.5 Leg support
The design of the leg extension part comes from this product. However there
are also some disadvantages. In this product, the source of the force is the
barbell weights. In order to have different forces, different sizes of the barbell
weights are needed, and they may take too much space. Another disadvanta ge
is that people have difficulty in replacing the barbell weights. Comparing to the
spring, we find that changing springs is much easier, people can just by hanging
up another spring.
Figure 5.6 GLCE365-Leg-Curl-Extension [18]
38
5.4 The choose of the wire rope
The wire rope is a type of cable which consists of several strands of material
wire twisted into a helix, it is one of the most important component in the
product, because the strength of the wire rope determine whether the product is
safe or not. After having a serious of research, both the strength and the price
of the wire rope in different companies, finally the wire rope made in SWR is
chosen. First of all, the type of cross – sectional should be decided, ͹ ൈ ͳͻ is
very popular in diameters from 3mm to 16mm, and is used on a variety of
applications, especially being used in the gym equipment as it has a very tough
coating. The following figure shows the breaking load in different diameter.
Figure 5.7 SWR 7×19 wire rope [19]
Figure 5.8 Breaking load in different diameter [19]
Finally, a 4mm 7x19 Galvanised Wire Rope coated to 5mm in Clear Nylon
is chosen for the product. Besides, the end terminations for the wire rope should
also be chosen, otherwise, there is no place to connect the wire rope and the
hook.
39
Figure 5.9 Different types of the end terminations [19]
After having a look about the wire rope in the gym, it is found that the
Thimble Eye is more common in the gym, so the end terminations have been
chosen.
5.5 Design of the spring box
In order to make the product lighter and simpler than those equipment in the
gym, the chair uses springs instead of the dumbbell weights to provide forces
which the user needs to achieve fitness effect as can be seen in the Figure 5.10
Figure 5.10 Design of the spring box
Moreover, the function of this fitness chair is 6 in 1, it means springs must
output different weights when doing exercises. Actually, when doing exercises
for different parts of the body, it needs different weights.
On the other hand, different people need different weights. However,
according to the calculation and analysis, if only using one group of springs
with the same spring constant and sizes, it cannot output different forces.
Now, 4 kinds of springs are selected to solve it. Thus, the aim is to make a
design springs box to set springs and let springs output different forces as can
be seen in the Figure 5.11.
40
Figure 5.11 Whole view of spring box
There is a slide way to fix the end of spring on the front plate. For example,
setting the slider which is fixed with the end of spring into the slide way from
the bigger central hole and drive it to the fixed point above the hole along the
slide way.
In order to reduce the spring swing up and down while pulling springs, it is
necessary to design a pipeline to reduce the swing in the box, which can be seen
in the Figure 5.12. There needs 4 spring boxes and it depends on how many
springs there is.
Figure 5.12 Internal structure of the spring box
Here it is necessary to point out that each kind of spring is made up in groups
of 4 or 2. In this way, providing different forces. Showing at following Figure
5.13.
41
Figure 5.13 The connecting of the spring
5.6 Design of the connecting part of the spring
On the other end of the spring, it is fixed on the other slider which can insert
into the sleeve around the shaft of the connecting rod. In previous ideas, this
connecting rod was fixed on the two wheels but it will move up and down when
pulling it. After a further brainstorming, a better method is found to optimize
the production and the modification can be seen in the Figure 5.14. Here are 2
cylinder- linear rails to instead of wheels to limit 2 degree of freedoms up and
down. Let the connecting rod be fixed on the slide moving on the rail. Thus it
can achieve the purpose to pull springs.
Figure 5.14 Design of the connecting part of the spring
5.7 Design of the connecting part between the back and
slider
On the multi-functional fitness chair, every part must be fully used. For
instance, when doing sit-up exercise, the seat back is used as can be seen in the
Figure-5.16.
42
Figure 5.15 Design of the connecting part between the back and slider
Due to only one outputting- forces point, the way to connect the back and
springs is more important. Firstly, design a curved connecting rod to make the
seat back rotate around the shaft and the other end of the rod is fixed on the
slider that slide on the rail fixed on the incline beam of the chair frame. Besides,
the bottom of the slider is connected with springs by connecting rod. The detail
of this part design has been shown in the following Figure-5.16.
Figure 5.16 The whole structure
5.8 Design of the gears box
At the beginning of design, this part was not come up but some problem was
found when designing spring. Normally, when doing lat pull exercise, the
length of pulling the rope is half a meter as long as the deformation of springs.
However, according to the measurement and actual research, the deformatio n
43
of spring is less than half a meter. In this case, the gears box is designed as is
shown in the Figure-5.17.
Figure 5.17 Design of the gears box
Here two gears whose drive ratio is 2 are used. The bigger one connects the
wire rope and smaller one connects the springs. Thus, if rope is pulled half a
meter, the deformation of springs is a quarter meters.
5.9 Dual-shaft linear rail
Two dual-shaft linear rails are used in the base of the chair. These two dualshaft linear rails have the same functions but are installed in different places,
one is connected with the seat, due to the rowing exercise, the seat should move
smoothly. Another place using a dual-shaft linear rail is the slider, it can said
that the slider is the most important part in the whole equipment, the frictio n
between the slider and base of the chair should as small as possible, otherwise,
it will affect the fitness effect. Thus using dual-shaft-linear rails are necessary.
In the next part, we will introduce the superiority of dual-shaft linear rail and
the specification of external dual-shaft linear rail.
Using dual-shaft linear rail has many advantages. For its high precision, the
repetition error can be within three microns. The speed of the dual-shaft linear
rail is five times faster than other existing products and with a lower noise. For
its high resistance to grinding, the surface of steel shaft is hardened to greatly
improve resistance to wear due to grinding. In addition, the dual-shaft linear
44
rail has the same quality of other linear rail but at lower price. Generally
speaking, the dual-shaft linear rail are always used in laser machine industry,
industrial machinery and some other high-speed transportation equipment.
Figure 5.18 Specification of external dual-shaft linear rail [20]
Figure 5.19 The dual-shaft linear rail [20]
The source of the table and the figure is from the Shenzhen Enkel technology
co., LTD in China, this company is expertized in R&D, manufacturing and
45
selling of linear guide rails and other components for industrial motion
application. According to the parameters in the table, we choose the model
OSG-10N, and the sketch of the dual-shaft linear rail in Inventor is totally
followed with the figure 5-20.
Figure 5.20 The dual-shaft linear rail and the cylinder-linear rail
5.10 Cylinder-linear rail
Similarly, the cylinder-linear rail is used support and guide moving parts,
doing reciprocating linear motion in a given direction. Meanwhile, reaching a
high positioning accuracy.
The cylinder- linear rail is used at the bottom base of the chair, which
connected with a connecting rod, and the springs can be hanged on this
connecting rod, the function of the cylinder-linear rail is to guide the springs
moving in the horizontal direction.
We also choose the cylinder- linear rail manufactured by the Shenzhen Enkel
technology co., LTD.
46
Figure 5.21 Specification of cylinder-linear rail [20]
Figure 5.22 Cylinder linear rail series [20]
The model we choose is SBR20SA, the dimensions of SBR20SA are showed
in the figure 5.21.
5.11 Ratchet and pawl
When having different exercises, there have different requirements of angle
to the chair back. For example, during the lat pull, the back of the chair should
47
have a certain angle. However, to different people, this certain angle is differe nt
from person to person. Compare to the lat pull, throughout the whole process
of leg extension, the back of the chair should keep straight all the time,
otherwise it will do damage to the knees. In this case, we need to find a way to
fix the back of the chair. The back of the chair can have different angles and
more important, it cannot rotate backward. The chair which is used in Roller
Coaster inspired us, then we search for the principle of it. Finally we decide to
use ratchet gearing to fix the back of the chair.
Ratchet and pawl is an intermittent motion mechanism, which consists of
rocker, pawl and external ratchet. The function of the ratchet gearing is to
prevent the ratchet wheel from rotating backward. The ratchet is widely used
in many mechanical equipment, one of the most common product is the
ratcheting socket wrench.
Ratchet gearing has many different types. Due to the limited space, we use
internal ratchet gearing. The pawl is fixed inside the ratchet wheel, and the
advantage of using internal ratchet gearing is that it can save a lot of space. In
addition, considering that the dimension of the chair is not very large, it is good
to choose internal ratchet gearing.
Figure 5.23 Internal ratchet gearing [22]
48
5.11.1 The design of ratchet gearing
5.11.1.1 The shape of the ratchet gearing
Figure 5.24 Different shapes of the ratchet gearing
Comparing with these types of---the asymmetric trapezoid has strong load
capacity and it can work when the load is very large while the asymmetr ic
triangle and asymmetric round can only be allowed when the load is not large
enough.
Throughout the whole process of exercises, the trainer lean against the back
of the chair all the time, so in this project, we decide to use the ratchet gearing,
which the shape of it is asymmetric trapezoid.
5.11.1.2 The determination of module and number of teeth
Similar to the gear, most of the dimensions of the ratchet gear are based on
the module. However the standard module of the ratchet gear depends on the
addendum circle (݀௔ ).
 ൌ ݀௔ Τ‫ݖ‬
The number of teeth (œ) depends on the using condition and movement
requirement. To some common feed ratchet gearing, we can determine the
number of teeth by the smallest rotation angle of the ratchet gear, then we can
use formula to calculate the module.
5.11.1.3 The dimensions of the ratchet gearing
After we determine the module and the number of teeth, we calculate other
dimensions of the ratchet gearing. The following table shows some main
dimensions.
49
Figure 5.25 Design dimension of the ratchet gearing
Table 5-4 Dimensions of the ratchet gearing
Symbol
Quantity

Module
Number of teeth
Formula
Value
1, 1.5, 2, 2.5, 3, 3.5, 4, 5,
6, 8, 10
ൌ ʹߨ Τߠ௠௜௡
4
20
݀௔
Tip diameter
݀௔ ൌ ݉ ή ‫ݖ‬
80
’
Circular pitch
’ ൌ Ɏ ޏ
12.57
Š
Tooth height
Š ൌ ͲǤ͹ͷ
3
ƒൌ
4
ܽଵ ൌ ሺͲǤͷ̱ͲǤ͹ሻܽ ൌ ͲǤ͸ܽ
2.4
Ƚ ൌ ʹͲι
ʹͲι
„ ൌ ሺͳ̱Ͷሻ ൌ Ͷ
16
݄ଵ ൌ ݄Τ…‘• ߙ
3.2
ƒ
ܽଵ
Working length of the
pawl
Ƚ
„
Width of the ratchet
݄ଵ Tooth slant
‫ݎ‬௙
Ratchet dedendum
circle radius
1.5
50
‫ݎ‬ଵ
Ratchet addendum
circle radius
The length of the pawl
2
ൌ ʹ’
25.14
Figure 5.26 Ratchet and pawl
5.12Material choice
The choice of material of the multi- functional fitness chair is one of the most
important part in the whole design. The mechanical properties of the material
determine the stability and the security of the product. In addition, the
properties will also effect the results of the hand calculations and the simulatio n.
Comparing to the normal chair, the multi- functional fitness chair focus more
on the stability. So in this part, we are going to choose the material under three
requirements. Aluminum 6061 is the final material which is chosen for the main
material of the multi- functional fitness chair.
1.
The intensity of the material
This is the first factor need to be considered. As mentioned before, the
intensity of the material determines whether the chair is safe or not. The
following table shows the mechanical properties of Aluminum 6061-T4.
Table 5-5 Mechanical Properties of Aluminum 6061-T4 [23]
Mechanical Properties
Metric
Comments
Hardness, Brinell
65
AA; Typical; 500 g load; 10 mm bal
51
Hardness, Knoop
88
Converted from Brinell
Value
Hardness
Hardness, Vickers
75
Converted from Brinell
Value
Hardness
Ultimate Tensile
Strength
ʹͶͳƒ AA; Typical
Tensile Yield Strength
ͳͶͷƒ AA; Typical
Elongation at Break
ʹʹΨ
AA; Typical;
Thickness
1/16 in. (1.6 mm)
Elongation at Break
ʹͷΨ
AA; Typical;
Diameter
1/2 in. (12.7 mm)
Modulus of Elasticity
Poisson's Ratio
Fatigue Strength
͸ͺǤͻ
ƒ AA; Typical; Average of tension and
compression. Compression modulus
is about 2% greater than tensile
modulus.
0.33
Estimated from trends in similar Al
alloys.
ͻ͸Ǥͷƒ AA; 500,000,000 cycles completely
reversed
stress;
RR
Moore
machine/specimen
Machinability
ͷͲΨ
0-100 Scale of Aluminum Alloys
Shear Modulus
ʹ͸
ƒ
Estimated from similar Al alloys
Shear Strength
ͳ͸ͷƒ AA; Typical
Through the research, the Aluminum 6061-T4 has an ultimate tensile
strength of ʹͶͳƒ and yield strength of at least ͳͳͲƒ . After the
simulation, combining with these main datum, we can make sure that the
product we designed is safe enough.
2. The weight of the material
52
Although he chair has two crossbeams at the bottom, and four anti-skid
pads at the both sides of the crossbeams,, the function of the anti-skid
pads is to reduce the damage to the floor, in the other word, reduce the
force from the product to the floor, if the total weight of the chair is too
big, it will also hurt the floor, it means, using light material can
effectively avoid this situation happens.
3.
The price of the material
Under normal circumstances the price of the material and the intens ity
of the material are the two opposite factors. The material with high
intensity, means it have a higher requirement for casting, and it is
obvious that the price will higher than the normal one. Therefore, what
should we do is to find a balance between these two main factors.
53
6 Instruction
Figure 6.1 Components of the whole product
6.1 Abstract
Nowadays, more and more people do not have enough time to do exercises,
thus, the lack of exercise cause a series of health problems. This multifunctional fitness chair is designed for the people who wants to have light
weight training to keep fit at home and for some fitness training beginners. The
product has different forms, this instruction will show people how to transform
the product into different forms and which is the working muscles in differe nt
exercises.
6.2 Product overview
This product combines with a variety of fitness equipment, so it enables
people to do different kinds of exercises at home. Through different exercises,
different parts of muscles can be exercised. Some details about which muscles
can exercised through exercises will be introduced in the next part.
54
The trainer can have lat pull, rowing exercise, leg extension, sit-up
exercise and some other exercises.
6.3 Main exercises
6.3.1 Lat pull
1.
Adjust the seat of the chair, by using the locking screw 1. After the seat
moving into a comfort position, then screw up the locking screw to fix
the seat.
2.
During the whole process of lat pull, the back of the chair should be
vertical all the time, otherwise, it will not only affect the training effect,
but also do damage to your back.
3.
The connecting rod 1 cannot be used in this exercise, so we just remove
the connecting rod from the slider, and then fix the connecting rod 1 in
the back of the chair by using a pin.
4. Using a ratchet and pawl to control the angle of the back, moving the
back and makes it vertical. However, when the back moves over the
vertical angle, just pull out the end cap of the ratchet and pawl. The end
cap is connected with the pawl claw, after we pull out the end cap, the
back can rotate freely.
5.
The function of the leg fixing rod is to fix thighs, if the load is too large,
a leg fixing rod can keep people from being pulled up. The leg fixing
rod can also be adjusted by a pin. Make the leg fixing rod in a correct
position.
6.
Adjust the telescopic rod by using locking screw 2 in a confortable
position which can reach the handle.
7.
Using the back springs. According to your ability to adjust the type and
quantity of spring.
55
Figure 6.2 Lat pull exercise
6.3.2 Rowing exercise
1. Different from the lat pull, the seat of the chair should move on the dualshaft linear rail smoothly, we need to loosen the locking screw 1.
2. During the rowing exercise, we also need not use connecting rod 1,
fixing it in the back of chair like the process be introduced in the lat pull
part.
3. Using a ratchet and pawl to fix the back at any angle. The requireme nts
of the angle is not high, so just adjust the back as you like.
4. Loosen the locking screw 3 to put the telescopic rod on the level. When
the telescopic rod lays on the leg support, screw up the locking screw 3
to fix the rod.
5. We also can use locking screw 2 to adjust the length of the telescopic
rod.
56
6.
Because the leg fixing rod will prevent the kneel in the rowing exercise,
so we need to loosen the pin which fix the leg fixing rod and lay it on
the telescopic rod.
7.
Putting your legs on the pedal.
8.
Using the back springs. According to your ability to adjust the type and
quantity of spring.
Figure 6.3 Rowing exercise
6.3.3 Leg extension
1.
Adjust the seat of the chair by using the locking screw 1. After the seat
moving into a comfort position, then screw up the locking screw to fix
the seat.
2.
In the leg extension, it is similar to the lat pull, the back of the chair
should also be vertical all the time. Fixing the connecting rob 1 and
adjusting the ratchet and pawl.
3.
It does not matter that whether using leg fixing rob to fix the thighs or
not. If you do not want to use leg fixing rob, changing the position it by
using pin.
4.
Using the back springs. According to your ability to adjust the type and
quantity of spring.
57
5. Putting the feet under the sponge 3.
6. Holding the handle of the chair
Figure 6.4 Leg extension
6.3.4 Sit-up exercise
In order to make our product more widely applicable to different groups of
people, there are two different forms to have sit-up exercise. One is doing situp exercise without weights, like the normal sit-up machine, the angle of the
back can be adjusted as you like. The other one is doing sit-up exercise with
weights, this form of sit-up exercise is suitable for the people who want to have
further exercise.
6.3.4.1 Without weights
1. Adjust the seat of the chair by using the locking screw 1, at the position
that the feet can reach the pedal, then screw up the locking screw to fix
the seat.
58
2.
Although in this sit-up exercise, there is no need to use springs here, the
connecting rod 1 also need to be fixed in the back of the chair, in order
to increase the stability of the product.
3.
Using ratchet and pawl to control the angle. The bigger the angle, the
more obvious the effect of exercise.
4.
Putting the feet into the pedal to fix it.
Figure 6.5 Sit-up without weights
6.3.4.2 With weights
Different from the sit-up without weights, the force provided by the spring
act as weights in this exercise. This form of exercise is more suitable for the
people who want to have further exercise.
1.
In this form of sit-up exercise, people need to turn their face to the back.
Using arms to grip the sponge 1, through the abdominal muscles to push
the back forward, in this case, the abdominal muscles can be exercised.
2.
Adjusting the angle of the sponge 1, ensure that the sponge is in front of
the chest, then lock it by using the pin at the back of the chair.
3.
Pull out the end cap of the ratchet and pawl, enables the back of the chair
can rotate freely.
59
4. The function of the connecting rod 1 is connecting the back of the chair
and the slider. At the other side of the slider is connecting rod 2, through
the slider, the spring can provide forces to prevent the movement of the
back.
5. Since the trainer is facing to the back, the feet can be fixed by the sponge
2.
6. Using the front springs. According to your ability to adjust the type and
quantity of spring.
Figure 6.6 Sit-up with weights
6.4 Extra exercises
Using the same equipment but with different posture can exercise differe nt
parts of muscles. Similarly, this product can also provide some extra exercises,
like the Musculus Biceps Brachii Curl and the Cable Pushdown to exercise arm
muscles. Besides the long handle we introduce in the figure, we also provide
other types of handle for different exercises, like the short handle, V-bar and
rope attachment.
60
Figure 6.7 Musculus biceps brachii curl [24]h
Figure 6.8 Cable Pushdown [25]
61
6.4.1 Musculus Biceps Brachii Curl
1. Raising the sponge 3, keeping it vertical and taking off the hook.
2. Hang up the hook to the short handle or the rope attachment, at the other
side of the rope which is connected with the connecting rod 2.
3. Fixing the connecting rod 1 in the back of chair, otherwise the back will
rotate through the slider while doing exercise.
4. Using the back springs. According to your ability to adjust the type and
quantity of spring.
Figure 6.9 Musculus biceps brachii curl
6.4.2 Cable Pushdown
This exercise is similar to the lat pull, the difference between them is the
posture of the trainer. Doing Cable Pushdown need the trainer stand in front of
the telescopic r od. However, the lat pull need the trainer at a sitting posture.
62
Figure 6.10 Cable Pushdown
Through the Cable Pushdown, Triceps Brachii Lateral Head, Triceps Brachii
Long Head and Triceps Brachii Medial Head will be exercised [26].
6.5 Weights
Considering that in different exercises, different weights are needed. So it
means the weights should be optional. For the product, there two different kinds
of springs can be chosen, which each of the spring can provideͳͲͲ andͳͷͲ
weights. Because of the stability, the number of springs that are used must be
even. There areʹͲͲ,͵ͲͲ ͶͲͲ and͸ͲͲ four different weights can be
chosen, which is more suitable for different users.
63
7 Chapter:
Hand calculation
7.1 Welding
Joints subjected to bending
According to solid mechanics both normal stresses and shear stresses will
rise at bending. These can be calculated from:
ߪ௕ ൌ
ெ್
‫( ݕ כ‬1)
ூೣ
் ‫כ‬ௌ
ɒ௕ ൌ ூ
ೣ ‫כ‬௕
(2)
Symbol
Quantity
‫ܫ‬௫
Moment of inertia about the neutral axis. The calculation is done
it simply to consider the a-dimension is tilted in the girdle plane,
figure 20 II
The distance from neutral axis to the plane where the stress
should calculated.
Shear force
›
„
Static torque for the part of the cross-sectional area that is outside
the reference plane.
Cross-sectional width of calculation plane.
For the ring-shaped cross-sections that weld in fig 1 forms get from
equations (1) and (2) a stress distribution in the height according Figure 1 a.
As follows of this is that ߪ௕ become maximal at the extreme fibers and ɒ௕
become maximum in neutral plane. Where one stress has its maximum is thus
while the second is 0.
Apart from very short beams (L in figure 1 c very small) we can usually
ignore and let be the design criterion. For the ring-shaped cross-section, such
as weld in figure 20. However, we must also check section B (see fig. 1 b),
64
because here both and will be occur with relatively large amount.
Looking at a cross-section of the upper weld, fig 1 I, we find that the stress
in the weld must be divided into component forces and in order to fulfill with
fig 11.
Figure 7.1 Structure of welding
ߪ
߬
ߪ௕ ൌ ୄ ൅ ୄ
ξʹ ξʹ
ߪୄ ൌ ߬ୄ ,
ʹ ‫ߪ כ‬ୄ
ߪ௕ ൌ
ξʹ
ߪ
ߪୄ ൌ ߬ୄ ൌ ௕
ξʹ
ߪ௝ ൌ ටߪୄ ଶ ൅ ͵߬ ୄ ଶ ൌ ߪ௕ ‫ ʹ כ‬ൌ ͳǤͳߪ௧௜௟௟
For the welds in Figue. 1 is designated as the strength table
ͳ
ͳ
ሺ‫ܪܤ‬ଷ െ ܾ݄ଷ ሻ ൌ
ሾሺܾ ൅ ʹܽሻሺ݄ ൅ ʹܽሻଷ െ ܾ݄ଷ ሿ
‫ܫ‬௫ ൌ
ͳʹ
ͳʹ
௛
And in section (fig. 1 b) becomes ‫ ݕ‬ൌ ଶ ൅ ܽ
When the attachment is ‫ܯ‬௕ ൌ ‫ܮ כ ܨ‬
65
In the section B calculated ߪ௕ in the same way as in section A, but
௛
with‫ ݕ‬ൌ ଶ
As shown in figure 1 ƒ is almost same for the entire height h and relative ly
small at the top and bottom welds. Thus one makes the simplification that
assumes that all the shear force T only transfer of life welds (i.e. those with
்
height h) and is evenly distributed over the length. Therefore ɒ௕ ൌ ௛ ‫כ‬ଶ௔
This stress will be parallel withܶ, i.e., it will correspond in fig 1 c.
The stress in section B is now obtained from equation 4
ߪ௝ ൌ ටߪୄ ଶ ൅ ͵߬ୄ ଶ ൅ ͵߬ ‫ צ‬ଶ
Symbol
Value
Unit
݄
40

ܾ
70

݄ᇱ
35

ܾᇱ
65

ܽ
5

‫ܨ‬
686
‫ܮ‬
400

66
Solution:
ܽ ൌ ͷ
Safety value for beam bar
‫ܯ‬௕ ൌ ‫ ܮ כ ܨ‬ൌ ͸ͺ͸ ൈ ͶͲͲ ൈ ͳͲିଷ ൌ ʹ͹ͶǤͶܰ ή ݉
Beam˖
ߪ௕ ௠௔௫ ൌ
‫ܯ‬௕ ݄
ʹ͹ͶǤͶ
ͶͲ ൈ ͳͲିଷ
‫ כ‬ൌ
‫כ‬
ͳ ሺ
‫ܫ‬௫ ʹ
ʹ
ଷ
ଷሻ
ିଵଶ
ͳʹ ͹Ͳ ൈ ͶͲ െ ͸Ͷ ൈ ͵Ͷ ൈ ͳͲ
ൌ ͸͹ǤͲͶͷ’ƒ
Weld
ͳ
ͳ
ሺ‫ ܪܤ‬ଷ െ ܾ݄ଷ ሻ ൌ
ሾሺܾ ൅ ʹܽሻሺ݄ ൅ ʹܽሻଷ െ ܾ݄ଷ ሿ ൌ ͶǤ͸ ൈ ͳͲି଻
ͳʹ
ͳʹ
Section A
‫ܫ‬௫ ൌ
‫ܯ‬௕ ݄
‫ כ‬൬ ൅ ܽ൰ ൌ ͳͶǤͻͳ͵‫ܽ݌ܯ‬
‫ܫ‬௫
ʹ
ߪୄ ൌ ߬ୄ
ߪ
߬
ߪ
ߪ௕ ൌ ୄ ൅ ୄ ൌ ʹ ୄ
ξʹ ξʹ
ξʹ
ʹ
ξ
ൌ ɒ௠௔௫
ൌ
ߪ
ɐ௠௔௫
ୄ
ୄ
ʹ ௕
ߪ௕௠௔௫ ൌ
ߪ௝ ൌ ටߪୄ ଶ ൅ ͵߬ୄ ଶ ൌ ߪ௕ ‫ ʹ כ‬ൌ ξʹߪ௕ ൌ ξʹ ൈ ͳͶǤͻͳ͵ ൌ ʹͳǤͲͻͲ‫ܽ݌ܯ‬
Section B
‫ܯ‬௕ ݄
‫ כ‬ൌ ͳͳǤͻ͵Ͳ‫ܽ݌ܯ‬
‫ܫ‬௫ ʹ
ߪ
ͳͳǤͻ͵Ͳ
ൌ ͺǤͶ͵͸‫ܽ݌ܯ‬
ߪୄ ൌ ߬ୄ ൌ ௕ ൌ
ξʹ
ξʹ
‫ܨ‬
͸ͺ͸
ൌ
ൌ ͳǤ͹ͳͷ‫ܽ݌ܯ‬
߬‫ צ‬ൌ
݄ ‫ ܽʹ כ‬ͶͲ ൈ ʹ ൈ ͷ ൈ ͳͲି଺
ߪ௕௠௔௫ ൌ
ߪ௝௕ ൌ ටߪୄ ଶ ൅ ͵߬ୄ ଶ ൅ ͵߬‫ צ‬ଶ ൌ ͳ͹ǤͲʹͶ‫ܽ݌ܯ‬
67
7.2 Gear calculation
Table 7-1 Known datum of gears
Known
Value
Unit
Input power
0.2
Pinion speed
180
‫ݎ‬Τ݉݅݊
Gear ratio
2.0
Working life
Provided work 300 days a year, two hours per day
Solution˖
˖
1. Choice of gear, accuracy, material, number of teeth
1) According to fig’ Transmission Scheme. Spur gear is the best choice.
2) As general working machine, low speed is needed, so 7 Accuracy
(GB10095-88) is more suitable.
3) Material choice, according to table 10-1, the material of Pinion is
quenched and tempered steel No.45, hardness is 250HB; the material of Wheel
is normalizing steel No.45, hardness is 210HB.
4) Number of teeth
Pinion: ‫ݖ‬ଵ ൌ ʹͶ
Wheel: ‫ݖ‬ଶ ൌ Ͷͺ
2. Design the tooth contact strength
According to design calculate formula (10-9a)
68
య ‫ܶܭ‬
‫ ݑ‬േ ͳ ܼா ଶ
൬
൰
݀ଵ௧ ൌ ʹǤ͵ʹ ඨ ଵ Ȉ
ሾߪு ሿ
߶ௗ
‫ݑ‬
(1) Determine every numerical in the formula
1) Load factor ‫ܭ‬௧ ൌ ͳǤ͵
2) Calculate the Torque of the pinion
ܶଵ ൌ
ͻͷǤͷ ൈ ͳͲହ ܲଵ ͻͷǤͷ ൈ ͳͲହ ൈ ͲǤʹ
ൌ
ൌ ͳǤͲ͸ ൈ ͳͲସ ܰ Ȉ ݉݉
ͳͺͲ
݊ଵ
3) According to the table 10-7 we choose the Tooth width coeffic ie nt
߶ௗ ൌ ͳǤͲ
4) According to the table 10-6, we find the Material influe nce
భ
coefficient ܼா ൌ ͳͺͻǤͺ‫ܽ݌ܯ‬మ
5) According to the tooth surface hardness fig 10-21d [2], 10-21c [2],
Contact fatigue strength limit of the pinion isߪு௟௜௠ଵ ൌ ͸ͲͲ‫ ;ܽ݌ܯ‬Contact
fatigue strength limit of the wheel is ߪு௟௜௠ଶ ൌ ͷ͸Ͳ‫ܽ݌ܯ‬.
6) Calculate the Stress cycles based on the formula 10-13
ܰଵ ൌ ͸Ͳ݊ଵ ݆‫ܮ‬௛ ൌ ͸Ͳ ൈ ͳͺͲ ൈ ͳ ൈ ͸ͲͲ ൈ ͷ ൌ ͵ǤʹͶ ൈ ͳͲ଻
͵ǤʹͶ ൈ ͳͲ଻
ܰଶ ൌ
ൌ ͳǤ͸ʹ ൈ ͳͲ଻
ʹ
7) According to the fig 10-19 we choose the Contact fatigue life factor
‫ܭ‬ுοଵ ൌ ͲǤͻͲ
‫ܭ‬ுοଶ ൌ ͲǤͻͷ
8) Calculate the contact fatigue allowable stress
Choose the Failure Probability 1%, safety factor ൌ ͳ, according to the
formula 10-12
‫ߪ ܭ‬
ሾߪு ሿଵ ൌ ுοଵ ு௟௜௠ଵ ൌ ͲǤͻ ൈ ͸ͲͲ ൌ ͷͶͲ‫ܽ݌ܯ‬
‫ݏ‬
‫ܭ‬ுοଶ ߪு௟௜௠ଶ
ሾߪு ሿଶ ൌ
ൌ ͲǤͻͷ ൈ ͷ͸Ͳ ൌ ͷ͵ʹ‫ܽ݌ܯ‬
‫ݏ‬
(2) Calculate
1) Calculate the pinion’s reference diameter ݀ଵ , into a smaller value
ሾ
of ߪு ሿ
69
య ‫ܶܭ‬
ߤ േ ͳ ܼா ଶ
൬
൰ ൌ ͵ʹ݉݉
݀ଵ௧ ൌ ʹǤ͵ʹ ඨ ଵ ή
ሾߪு ሿ
݀
ߤ
2) Calculate the Circumferential speed ‫ݒ‬଴
ߨ݀ଵ௧ ݊ଵ
ߨ ൈ ͵ʹ ൈ ͳͺͲ
ൌ
ൌ ͲǤ͵Ͳʹ݉Ȁ‫ݏ‬
͸Ͳ ൈ ͳͲͲͲ
͸Ͳ ൈ ͳͲͲͲ
3) Calculate the Face width
‫ݒ‬଴ ൌ
„ ൌ ߶ௗ Ȉ ݀ଵ௧ ൌ ͵ʹ݉݉
4) Calculate the ratio of face tooth width and tooth height
Module ݉ ௧ ൌ
ௗభ೟
௓భ
௕
௛
ଷଶ
ൌ ଶସ ൌ ͳǤ͵͵݉݉
Tooth depth Š ൌ ʹǤʹͷ݉ ௧ ൌ ʹǤʹͷ ൈ ͳǤ͵͵ ൌ ͵݉݉
ܾ ͵ʹ
ൌ
ൌ ͳͲǤ͸͹
݄
͵
5) Calculate the load coefficient
‫ ݒ‬ൌ ͲǤ͵Ͳʹ݉Ȁ‫ݏ‬
Choose the dynamic load factor as ‫ܭ‬௏ ൌ ͳǤͳʹ based on ൜ ଴
͹‫ݕܿܽݎݑܿܿܣ‬
Spur gear, ‫ܭ‬ுఈ ൌ ‫ܭ‬ிఈ ൌ ͳ
Find the Using coefficient ‫ܭ‬஺ ൌ ͳǤʹͷ in table 10-2
ܽ‫ݐݎ݋݌݌ݑݏ ݕ݈݈ܽܿ݅ݎݐ݁݉݉ݕݏ‬
Get ‫ܭ‬ுఉ ൌ ͳǤͶͲbased on ൜
͹‫ݕܿܽݎݑܿܿܣ‬
௕
According to the௛ ൌ ͳͲǤ͸͹, ‫ܭ‬ுఉ ൌ ͳǤͶͲ find the ‫ܭ‬ிఉ ൌ ͳǤ͵ͳ in fig 1013; so the load coefficient:
‫ ܭ‬ൌ ‫ܭ‬஺ ‫ܭ‬௏ ‫ܭ‬ுఈ ‫ܭ‬ுఉ ൌ ͳǤʹͷ ൈ ͳǤͲʹ ൈ ͳ ൈ ͳǤͶͲ ൌ ͳǤ͹ͺͷ
6) According to the actual load factor to correct the calculated pitch
diameter
య ͳǤ͹ͺͷ
య ‫ܭ‬
݀ଵ ൌ ݀ଵ௧ ඨ ൌ ͵ʹ ൈ ඨ
ൌ ͵ͷǤͷ͸͹݉݉
‫ܭ‬௧
ͳǤ͵
7) Calculate the module
70
ൌ
݀ଵ ͵ͷǤͷ͸͹
ൌ
ൌ ͳǤͶͺ݉݉
ܼଵ
ʹͶ
2. Check by root bending strength
According to design calculate formula (10-4)
‫ܨܭ‬௧ ܻி௔ ܻௌ௔
൑ ሾߪி ሿ
ܾ݉
(1) Determine every numerical in the formula
ߪி ൌ ߪி଴ ܻௌ௔ ൌ
1) Load coefficient ‫ ܭ‬ൌ ͳǤ͹ͺͷ
2)
ʹܶଵ ʹ ൈ ͳǤͲ͸ ൈ ͳͲସ
ൌ
ൌ ͷͻ͸ǤͲ͸ܰ
‫ܨ‬௧ ൌ
݀ଵ
͵ͷǤͷ͸͹
10-5
3) Get ܻி௔ଵ ൌ ʹǤ͸ͷ, ܻி௔ଶ ൌ ʹǤͷͷ and ܻௌ௔ଵ ൌ ͳǤͷͺ, ܻௌ௔ଶ ൌ ͳǤ͸ͳby fig
4) Face width
„ ൌ ߶ௗ Ȉ ݀ଵ௧ ൌ ͵ʹ݉݉
5) Module
ൌʹ
6) Calculate root bending strength
‫ܨܭ‬௧ ܻி௔ଵ ܻௌ௔ଵ ͳǤ͹ͺͷ ൈ ͷͻ͸ǤͲ͸ ൈ ʹǤ͸ͷ ൈ ͳǤͷͺ
ൌ
ൌ ͸ͻǤ͸ͳ‫ܽ݌ܯ‬
ܾ݉
͵ʹ ൈ ʹ
‫ܻ ܻ ܨܭ‬
ͳǤ͹ͺͷ ൈ ͷͻ͸ǤͲ͸ ൈ ʹǤͷͷ ൈ ͳǤ͸ͳ
ൌ ௧ ி௔ଶ ௌ௔ଶ ൌ
ൌ ͸ͺǤʹͷ‫ܽ݌ܯ‬
ܾ݉
͵ʹ ൈ ʹ
ߪிଵ ൌ
ߪிଶ
7) According to the fig ͳͲ െ ͳͺሾଶሿ , get the bending fatigue life factor
‫ܭ‬ிேଵ ൌ ͲǤͻ͵, ‫ܭ‬ிேଶ ൌ ͲǤͻ͹
8) According to the fig 10-20(b), 10-20(c), get bending fatigue limit
ߪிாଵ ൌ ͷͺͲ‫ ܽ݌ܯ‬and ܵி ൌ ͳǤͶ
ߪிாଶ ൌ ͶͷͲ‫ ܽ݌ܯ‬and ܵி ൌ ͳǤͶ
9) Root bending fatigue allowable stress
71
‫ܭ‬ிேଵ Ȉ ߪிாଵ ͲǤͻ͵ ൈ ͷͺͲ
ൌ
ൌ ͵ͺͷǤ͵‫ܽ݌ܯ‬
ܵி
ͳǤͶ
Ȉߪ
ͲǤͻ͹ ൈ ͶͷͲ
‫ܭ‬
ሾߪிଶ ሿ ൌ ிேଶ ிாଶ ൌ
ൌ ͵ͳͳǤ͹ͻ‫ܽ݌ܯ‬
ܵி
ͳǤͶ
ሾߪிଵ ሿ ൌ
3. Calculate gear geometry
(1)Reference diameter
Pinion: ݀ଵ ൌ ܼ݉ଵ ൌ ʹ ൈ ʹͶ ൌ Ͷͺ݉݉
Wheel: ݀ଶ ൌ ܼ݉ଶ ൌ ʹ ൈ Ͷͺ ൌ ͻ͸݉݉
(2) Face width
„ ൌ ߶ௗ Ȉ ݀ଵ௧ ൌ ͵ʹ݉݉
(3) Addendum Coefficient
݄‫כ‬௔ ൌ ͳ
(4) Addendum
݄௔ ൌ ݄௔‫ כ‬ή ݉ ൌ ͳ ൈ ʹ ൌ ʹ
(5) Headspace coefficient
‫ כ ܥ‬ൌ ͲǤʹͷ
(6) Dedendum
݄௙ ൌ ሺ݄‫כ‬௔ ൅ ‫ כ ܥ‬ሻ݉ ൌ ሺͳ ൅ ͲǤʹͷሻ ൈ ʹ ൌ ʹǤͷ݉݉
(7) Full-height tooth
݄ ൌ ݄௔ ൅ ݄௙ ൌ ʹ ൅ ʹǤͷ ൌ ͶǤͷ݉݉
(8) Tip diameter
Pinion: ݀௔ଵ ൌ ݀ଵ ൅ ʹ݄௔ ൌ Ͷͺ ൅ Ͷ ൌ ͷʹ݉݉
Wheel: ݀௔ଶ ൌ ݀ଶ ൅ ʹ݄௔ ൌ ͻ͸ ൅ Ͷ ൌ ͳͲͲ݉݉
72
(9) Root diameter
Pinion: ݀௙ଵ ൌ ݀ଵ െ ʹ݄௙ ൌ Ͷͺ െ ͷ ൌ Ͷ͵݉݉
Wheel: ݀௙ଶ ൌ ݀ଶ െ ʹ݄௙ ൌ ͻ͸ െ ͷ ൌ ͻͳ݉݉
(10) Base diameter
Pinion: ݀஻ଵ ൌ ݀ଵ …‘• ߙ ൌ Ͷͺ ൈ …‘• ʹͲι ൌ ͶͷǤͳͲͷ݉݉
Wheel: ݀஻ଶ ൌ ݀ଶ …‘• ߙ ൌ ͻ͸ ൈ …‘• ʹͲι ൌ ͻͲǤʹͳͲ݉݉
(11) Pitch
‫ ݌‬ൌ ߨ݉ ൌ ͸Ǥʹͺ͵
Figure 7.2 Parameters of the gears [27]
7.3 Cylindrically helical tension spring design
1. Consider the spring will provide 100N and 150N when the spring
completely tensioned, and the deflection at ultimate load required to be about
250mm.
2. So choose the low manganese spring steel 65Mn as the spring material.
73
Figure 7.3 Mechanical properties of 65Mn [28]
3. Spring index:
Choose ൌ ͷ̱ͺ generally
Consider the spring deflection need to be maintain the requirement under the
given forces.
ൌͺ
Estimates take diameter of wire ݀ ൌ ʹǤͷ݉݉
According to the Table 16-3, get the wire’s allowable stressߪ஻ ൌ ͳ͸ͷͲ‫ܽ݌ܯ‬.
4. Calculate the diameter of wire
‫ ܨ‬ൌ ͳͷͲܰ
ͳͷͲ ൈ ͳǤͳͺͶ ൈ ͺ
‫ܥܭ ܨ‬
ൌ ͳǤ͸ ൈ ඨ
ൌ ʹǤ͵Ͷͺ݉݉
݀ ᇱ ൒ ͳǤ͸ඨ ௠௔௫
ሾ߬ሿ
ͲǤͶ ൈ ͳ͸ͷͲ
Choose the next standard value ݀ ᇱ ൌ ʹǤͷ݉݉
‫ ܨ‬ൌ ͳͲͲܰ
ͳͲͲ ൈ ͳǤͳͺͶ ൈ ͺ
‫ܥܭ ܨ‬
ൌ ͳǤ͸ ൈ ඨ
ൌ ͳǤͻͶ͸݉݉
݀ ᇱ ൒ ͳǤ͸ඨ ௠௔௫
ሾ߬ሿ
ͲǤͶ ൈ ͳ͸ͲͲ
Choose the next standard value ݀ ᇱ ൌ ʹǤͲ݉݉
5. Calculate the deflection at ultimate load
‫ ܨ‬ൌ ͳͷͲܰ
74
ͺ݊‫ ܦ‬ଷ ‫ ܨ‬ͺ݊‫ ܥ‬ଷ ‫ ܨ‬ͺ ൈ ͺͲ ൈ ͺଷ ൈ ͳͷͲ
ൌ
ൌ
ൌ ʹͶͺǤͺ͹݉݉
ߣൌ
‫ ݀ܩ‬ସ
‫݀ܩ‬
͹ͻ ൈ ͳͲଷ ൈ ʹǤͷ
‫ ܨ‬ൌ ͳͲͲܰ
ͺ݊‫ ܦ‬ଷ ‫ ܨ‬ͺ݊‫ ܥ‬ଷ ‫ ܨ‬ͺ ൈ ͳͲͲ ൈ ͺଷ ൈ ͳͲͲ
ൌ
ൌ
ൌ ʹͷͻǤʹͶ݉݉
‫݀ ܩ‬ସ
‫݀ܩ‬
͹ͻ ൈ ͳͲଷ ൈ ʹǤͲ
6. Checking Fatigue strength
ߣൌ
When the load changed from 0 to maximum, calculate the minimum and
maximum cyclic shear stress generated by spring internal material.
ͺ‫ܦܭ‬
ͺ ൈ ͳǤͳͺͶ ൈ ʹͲ
Ȉ ‫ܨ‬௠௔௫ ൌ
Ȉ ͳͷͲ ൌ ͷ͹ͺǤͺͻ‫ܽ݌ܯ‬
ଷ
ߨ݀
ߨ ൈ ʹǤͷଷ
ͺ‫ܦܭ‬
ͺ ൈ ͳǤͳͺͶ ൈ ͳʹ
Ȉ ‫ܨ‬௠௔௫ ൌ
Ȉ ͳͲͲ ൌ ͶͷʹǤʹͷ‫ܽ݌ܯ‬
߬௠௔௫ ൌ
ଷ
ߨ݀
ߨ ൈ ʹǤͲଷ
ͺ‫ܦܭ‬
Ȉ ‫ܨ‬௠௜௡ ൌ Ͳ
߬௠௜௡ ൌ
ߨ݀ ଷ
Fatigue strength safety factor:
߬ ൅ ͲǤ͹ͷ߬௠௜௡
ܵ௖௔ ൌ ଴
൒ ܵி
߬௠௔௫
߬௠௔௫ ൌ
Where
߬଴ -Pulsating cyclic shear fatigue limit of the spring material
ܵி -Design safety factor of fatigue strength of the spring
ܵி ൌ ͳǤ͵̱ͳǤ͹
‫ ܨ‬ൌ ͳͷͲܰ
ܵ௖௔ ൌ
ͲǤͶͷ ൈ ͳ͸ͷͲ ൅ Ͳ
ൌ ͳǤ͵ʹ ൒ ܵி
ͷ͹ͺǤͺͻ
‫ ܨ‬ൌ ͳͲͲܰ
ͲǤͶͷ ൈ ͳ͹ͲͲ ൅ Ͳ
ൌ ͳǤ͸ͻ ൒ ܵி
ͶͷʹǤʹͷ
7. Checking static stress intensity
ܵ௖௔ ൌ
Static strength safety factor:
ܵௌ௖௔ ൌ
߬௔
߬௠௔௫
75
൒ ܵௌ
7.4 The choice of spring
The springs for the gym equipment are different from the normal springs. So
the spring should be manufactured according to the parameter by hand
calculation. For our product, two springs are needed, which different in
parameter.
Table 7-2 Main parameter of different springs
Weights
ͳͲͲ
ͳͷͲ
Mean diameter of coil
ͳ͸
ʹͲ
Diameter of wire
†
ʹ
ʹǤͷ
Spring index
ͺ
ͺ
Number of active coils

ͳͲͲ
ͺͲ
Length of the spring
‫ܮ‬଴
ʹͲͲ
ʹͲͲ
Full loop side
Full loop side
Types of ends
Figure 7.4 Types of the spring [29]
76
Figure 7-4 shows the types of the spring which manufactured by a Chinese
company, Dongguan TinFin Hardware Products Co. This company offers
customers products with competitive price and good quality. That is why this
company are chosen.
8 Chapter:
FEM simulation
8.1 Welding simulation
Before having stress analysis, we need to use welding function in Inventor
2016 at first, as the previous welding hand calculation shows that the a
dimension is 5, then we use welding function to combine two bars together.
Figure 8.1 Welding function in Inventor
When having sit-up exercise, the trainer faces to the back of the chair, and
almost the whole weight is exerted to the back of the chair. We assume that the
force is 700, which is perpendicular to the back.
After the welding simulation in Inventor, we found that the result by
simulationͳͺǤͳͻƒ is similar to the hand calculationͳ͹ǤͲʹͶƒ . The
following figure is the result by simulation.
77
Figure 8.2 Welding stress
8.2 Gear simulation
Then the FEM is simulated in Inventor. There is a ͸ͲͲ force on the
meshing part of two gears, the maximum Von Mises Stress simulate by FEM
is ͳ͵͸Ǥͻƒ , comparing with the result in hand calculatio n, ሾߪிଶ ሿ ൌ
͵ͳͳǤ͹ͻ‫ ܽܲܯ‬which is larger than the result by FEM, it means it is strong
enough.
Besides, it can be seen in figure 8-3, the Von Mises Stress in the tooth root
is͸ͺǤͶƒ, according to the result of root bending strengthߪிଵ ൌ ͸ͻǤ͸ͳ‫ܽܲܯ‬,
the result by FEM is͸ͺǤͶƒ, which is similar to the root bending strength. It
can be proved that both the result by hand calculation and the result by FEM
are correct.
78
Figure 8.3 Gear stress
8.3 Spring simulation
Through the simulation by Inventor, the deflection at ultimate load for each
type of spring is shown in the following table, comparing them with the result
by hand calculation.
Table 8-1 The deflection at ultimate load for different types of spring
ͳͲͲ
ͳͷͲ
Hand calculation
ʹͷͻǤʹͶ
ʹͶͺǤͺ͹
FEM
ʹ͸ͲǤ͸
ʹͶͺǤ͸
Figure 8.4 The deflection of the spring by 100 N
79
Figure 8.5 The deflection of the spring by 150 N
From the table 8.1, there is no difference between the results by hand
calculation and the results by FEM. So it can be said that both of the results are
correct.
80
9 Chapter:
Conclusion and future work
In order to make the final product more likely to be manufactured, more
details of the product are focused on. From every screw to every part of the
product are designed following the measurement result. Like the distance
between the chair to the pedal, the length of the legs from different people are
measured.
Neither of group members is professional fitness, so an investigation is
necessary. Before the design, a large number of fitness equipment in the gym
in Karlskrona are investigated, not only the operation of the fitness equipme nt,
but also the functions of them. Besides, combining the information on the
internet and the interview from professional fitness, some training sites and the
working muscles have been known.
However, the product also have some disadvantages. As a mechanic a l,
fitness equipment, the security is the most important factor, it means every parts
of the product need to be tested, both the security and the stability. Due to the
limitation of the time, only some main parts are tested in this report, if the
product need to be manufactured, a further test is essential.
There is no doubt that a mechanical structure is more safety than a structure
with electric technique. However using electric technique can make the product
have a higher functionality. In order to further our product, an electric technique
will be added, connecting a deformation sensor with the spring, through a series
of data collection, data integration and data conversion. Finally get a quantity
about the burning calories, and reflect on a monitor to show the user which is a
good way to know the training effect.
81
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Appendix 1:
Drawing of the full equipment assembly
85
Appendix 2:
Drawing of main components
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