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Transcript of Joint Torque Reduction of a Planar Redundant Manipulator Thesis
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The University of Nottingham
Faculty of Engineering
Department of Electrical and Electronic Engineering
JOINT TORQUE REDUTION OF ! "#!N!R REDUND!NT
$!NI"U#!TOR%
AUTHOR : SYED ARHAM ABBAS RIZVI
ID : 010554
SUPERVISOR : Dr. SAMER YAHYA
MODERATOR : Dr. LIM CHIN KEONG
DATE : APRIL, 11, 2014
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T!r" #$%r &r'($)* &r'&'+% +-/!**$" ! &%r*!% -!/$* ' *$ r$-!r$/$*+ ' *$
"$3r$$ ' &achelor of Engineering
Acknowledgement
First and foremost, I would like to thank the Almighty for giving me strength and determination so that I was
able to complete my project.
Without a doubt, I would like to thank Dr. amer !ahya, as without his knowledge and complete support I
would not have been able to accomplish the task set out to me. And his cheerful attitude every time I met him
motivated me to further my project. "hank you for all of your hard work and time dedicated on me.
"his thesis, without any further thought is dedicated to my wonderful parents who have given me full support in
all issues I have undergone in life. "hey sacrificed a lot just to let me study and have a better future. I would like
to thank my beloved sister who supported in times of need so that I would be able to complete this project.
I thank my friends for always being with me and giving me the re#uired courage in order for me to complete my
project as well as my thesis.
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Table of ContentsAcknowledgement 1
Abstract 3
Introduction 4
Objectives 5
Progress and Achievements 5
Thesis Structure
!iterature "eview #
"ypes of $anipulator %
"ypes of &oints '
$otors (sed In $anipulators )
"ypes of "ransmission ystems in $anipulators *+
onventional $anipulators **
"endon-based "ransmission ystem *
/elt-based "ransmission ystem *'
0ear-based "ransmission ystem *)
1ydraulic23neumatics-based "ransmission ystem
$ethodolog% &4
$anipulator Design and 3ro 4ngineer $odelling 5
/evel-0ear "ransmission ystem 5
"endon-3ulley "ransmission ystem 6+
alculations 6
"esults 3'
/evel-0ear $anipulator 6)
"endon $anipulator 7*
onventional $anipulator 76
omparing the designs 75
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(iscussion and Anal%sis 4)
*onclusion 5+
,urther -ork 5+
"e.erences 51
A//endi0 53
Abstract
A manipulator is an engineering tool that allows a user to manipulate their environment via it. As there are a
variety of manipulators which are used for specific task according to their design and si8e, it has come to notice
that the overall design can be improved in terms of efficiency i.e. power output to power input.
"his project is about the design of a new mechanism which would be more efficient compared to theconventional manipulator as the weight of the mobile i.e. the links would be reduced, as the stepper motor,
which are usually placed at the link would now be placed at the base, thus the weight of the motor would now be
removed which contributes the most to the link9s weight. :arious transmission systems can be used instead of
the conventional design but there are limitations in those designs as to how much tor#ue they can transmit, how
much area they cover, etc. "hus the bevel gear and tendon transmission system were modelled and compared to
the conventional design.
"he tendon based transmission had the minimum mass thus the tor#ue re#uired to move it was lowest. At the
position where the tor#ue re#uired is ma;imum, a tor#ue of *.
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Introduction
In this world, energy is a very valuable and finite resource and new ways to harness it are being researched and
developed. "he whole process of energy is being developed to be more efficient so that energy in all its forms
can be harnessed more efficiently thus more energy is available to be used. >esearch and Development
departments of every company are finding out new ways to make their devices use less power than their
previous models to perform the same task thus increasing their efficiency and thus needing less energy on theoverall thus more people would be able to use them.
"o decrease the energy used in devices, new technology is developed and new methods of to convert the energy
into useful work are researched. "he most widespread form of energy in this world is electricity as it is a key
factor in industriali8ation, urbani8ation ?creation of new 8ones for people to live a life in a healthy lifestyle@,
economic growth and increasing the #uality of lifestyle of people.
4lectricity is mostly created by combusting hydrocarbons in the form of petroleum and natural gas or using coal
as the raw resource. As these are finite resource and research shows that their #uantity is decreasing and would
eventually finish in a predicted 5+ years9 time. "he figure below shows the types of resources and how much
they contribute to the creation of power on a global scale.
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37%
21%
25%
8%
9%
Petroleum Coal Dry Natural Gas Renewable Resources Nuclear-Electrcty
,I 12+1 A global creation o. /ower according to resource t%/e in &++)2 1
Devices everywhere are getting more efficient and so are manipulators. $anipulators have been modified
countless times and in numerous different ways so that they are able to provide the same power output with less
input power. In this project, the same thing is to be done so that the manipulator modelled would have an overall
better efficiency than the manipulators already in use.
$any models of manipulators were designed which would theoretically re#uire less tor#ue to operate and thesewere compared to each other and the best design was chosen. "his design was then compared to the normal
manipulator design. "he results showed that theoretically, the design would improve the efficiency of the
manipulator. Further discussion would be done in the methodology section.
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Also as normal manipulators have the motors at the link, the mass of the overall manipulator would increment
considerably with each degree of freedom ?DF@ thus for the tor#ue re#uired to be minimum, the DF of the
manipulator are kept to the minimum so that the manipulator can perform its re#uired tasks. "his decreases the
manipulator9s workspace giving it less freedom of movement. If there are obstacles in the manipulator9s path,
then the manipulator might be hindered if the obstacle blocks the workspace. "his can be improved with
increased DFs but a conventional manipulator is not able to achieve that as efficiency is lost as the mass of the
manipulator is increased for the task which can be done by a less DF manipulator. "hus a new design of the
manipulator is needed to perform the task with increased DFs so it can have a larger volume for its workspaceso that obstacle hindrance would be minimi8ed.&
Obecti!es
"he objectives of this project are as followsB
*. >esearching the designs of the manipulators and their advantages and disadvantages over other models.
. $odelling a robot manipulator design in C3ro-4. "his was changed from the software olidworks as the
university does not have the license for the software.6. 3erform simulations on the design.
7. alculate the dynamic e#uations of a $anipulator
5. ompare the modelled design with the motors at link design.
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T"esis $tructure
"his paper is organised into a few topics which are listed below as followsB
Abstract
"his part describes the reason for creating more efficient designs.
Introduction
/riefly introduces the topic and gives a very short usage detail of the manipulator
bjectives
0ives the things to be achieved during the duration of the project
3rogress and Achievements
0ives information of what was achieved in the project.
"hesis tructure
0ives a brief description of each title in the thesis
Eiterature >eview
3rovides the information of where all the information was collected from for the designs of the
manipulators.
$ethodology
0ives the details of how the design was modelled, how the calculations were prepared and processed and
how the designs were compared.
Discussion and Analysis
4;plains the result of the comparison between the models
onclusion
0ives a small e;planation of the overall achievements of the research and what could be done on it in the
future.
>eferences
"his section gives the list of citation of the source of knowledge which were collected and combined in this
paper.
Appendi;"his section provides the mathematical formulas and the results from $athematica.
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&iterature 'e!iew
"his will detail all the information gathered to create the design which was finalised and all the other models.
T%/es o. $ani/ulators
"here are main types of manipulators which are used. "here are the serial and planar manipulators.3
3lanar manipulators have separate kinematic chains that are linked to the moving platform and the ground at the
same time. "hey have an advantage over their serial counterparts as they are able to produce more precise
movement and they are able to carry higher loads and they have a better build as they have better rigidity. "hey
can also produce higher velocity and accelerations thus being able to perform the task faster and more
effectively. erial $anipulators have simple forward kinematics while the inverse kinematics for them is #uite
difficult whereas for parallel manipulators, the forward kinematics is harder than the inverse kinematics.
,I12+& A t%/ical (O, serial /arallel
mani/ulator2 4
3lanar 3arallel $anipulators perform translations along the ; and y a;es and the rotation around the 8 a;is.
"hey have the advantage of micro-minimi8ation and pick and place operations as their kinematics operations are
easier to perform than their non-planar counterparts.&
3arallel $anipulators have a comple; closed loop chain mechanism thus the kinematic analysis of the parallel
manipulator is more difficult than the serial counterpart.
"he serial parallel manipulator shown in FI0*.+ has both the advantages of erial and 3arallel $anipulators
from rigidity to workspace. "hese type of manipulators haven9t been investigated deeply though.&
erial manipulators on the other hand are the simplest type of manipulators and have been used in almost all the
application as they are easy to design, model and create. A link model of the manipulator is shown in FI0*.+6.
"hey consist of links and joints and are connected in series to one another.
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,I12+3 The link model o. a serial 3 (O, mani/ulator25
T%/es o. 6oints
&oints are the referred to two bodies as they are connecting bodies and providing them a motion relative to one
another. "hese two bodies can be said to be frames of reference. "he *stframe is to be fi;ed while the ndframe
is to be mobile. "hey are fundamental to a robot as without them, the robot would just be a rigid structurewithout any motion.
T)*es of+oints
T)*es of,otion
-egree of.reedom 'elati!e Position
Re!olute Rotatonal 1 D"# $nular &s'lacement ()*Prsmatc $+al 1 D"# ,near &stance
crewRotatonal an&$+al 1 D"#
$nular &s'lacement an& ,near&stance
'.ercal Rotatonal 3 D"# $nular &s'lacement () an& /*
Rotatonal Rotatonal 1 D"#
$nular &s'lacement
(rotaton alon a+al a+s*"rt.oonal $+al 1 D"#
,near &stance alon a 90 anular&s'lacement rom 1strame
TA712+1 !ist o. joints and their con.iguration2
,I12+4 6oint (iagrams2 #
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$otors used in $ani/ulators
$otors are the main energy conversion devices ?electrical energy to mechanical energy@ used in
manipulators and they are the most e;pensive parts of the manipulator normally. "hey convert electrical
impulses to angular rotation. "here are a variety of motors ranging from eries D $otor to A >eluctance
motors and they are used for their respective applications. "he motor used in manipulator mainly is the
stepper motor.
As most applications re#uire precise movement at specific velocities, the stepper motor provides the finest
movement range in all the motor types '2tepper $otors provide angular motion at specific steps
depending on the number of poles in the stator and the rotor of the motor. "he same numbers of pole pairs
are re#uired on the rotor as on a single stator. "he angle of one step is e#ual to
Step Angle=NsNrNs Nr
360
WhereB
=s G =umber of teeth on stator core. =r G =umber of teeth on rotor core.
"hese motors are #uite heavy as more accurate motors would re#uire more poles and a high tor#ue
producing motor would need more powerful magnetic field. "hus better performance would result in
additional weight which we are trying to reduce in the mobile part of the manipulator body.
"hese motors re#uire a system which includes a ontroller, Amplifier and the motor itself ). "he controller
needs to be able to produce 3W$ ?i.e. pulses@ and an 1-bridge circuit would be re#uired to produce
movement in both clockwise and counter-clockwise motion. "his would work as an electrical switch to
change direction which can be written in the programming instead of a mechanical switch which would
re#uire mechanical interference to change the direction of motion. "he Amplifier increases the power of thepulses so that the motor can be powered up by it. As not all amplifier are compatible with stepper motors so
they need to be compatible with each other to control the motor properly. Finally, the stepper motor is
needed to convert the power in the amplified pulses to mechanical work.
tepper motors are relatively cheap, produce a high tor#ue at low speeds and work in all sorts of
environments thus they are #uite reliable as they provide what is needed from them but at high speeds, the
tor#ue produced is significantly reduced and resonance might occur at low speeds.
"he specifications re#uired to choose the motor are as follows 1+11B
*. Dynamic "or#ueB "or#ue developed when in motion.
. 3hase InductanceB Eimits phase-current rise time and thus Dynamic "or#ue.
6. 1olding "or#ueB "or#ue to prevent involuntary motion by static load.
7. "or#ue tiffnessB $otor9s ability to resist angular displacement within a step.
5. >otor InertiaB >esists motor accelerations.
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"here are many types of configurations in which a motor can be placed in a manipulator and these have their
advantages and disadvantages over their counterparts. "he following is a list of configurations which have
been used in serial planar manipulators. "ransmission systems are used to transfer the power from the
$otors to the &oints so that the rotary movement in the motor can be converted to the specific movement
re#uired at the joint.
$otor at Eink transmission system.
"endon - based transmission system.
/elt - based transmission system.
0ear - based transmission system.
3neumatics21ydraulics - based transmission system.
A detailed e;planation of each of these transmission systems is given below in the order shown above.
"he tor#ue re#uired for the manipulator would be based on the weights of the link and the joints which include
the transmission ?depending on the design@ and motors.
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,I12+5 The link diagram o. a 3 l ink mani/ulator2
m*, m and m6 are the masses of the links and the transmission system parts which go along the links. "he link
weight is taken to be acting in the centre of the link as we are assuming the mass is evenly distributed.
All of the designs shown above would have different masses depending on the system they are using and they
would have limitation of the tor#ue which they would be able to transfer.
*onventional $ani/ulator
,I12+ A mani/ulator with motors at the base2 13
In this design, the motors will contribute to the joint weight and as
there is no transmission system as the motor is directly connected to the
link thus there is no additional inertia which the motor would have to overcome when moving its respective
link.
"he motor is the heaviest part of the manipulator and thus the motor at the previous joint would have to be
more powerful as it would be supporting the weight of the motor and thus higher tor#ue would be re#uired
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thus the parts in that motor need to be more powerful thus a larger motor is re#uired and thus consecutive
motors would be larger than the previous.
"he motors in this design would get smaller with each consecutive link thus each joint would provide a
smaller tor#ue thus if a larger tor#ue is re#uired at that joint, the previous motor would be re#uired to be
larger even though the higher tor#ue is not needed over there and is only need due to the additional weight of
the larger motor.
,I12+# A sim/ler illustration o.
a conventional mani/ulator2 13
H
Tendon 8 based transmission s%stem
,I12+' A sim/le tendon based design2
"his model uses tendons to transfer the force from the motors to the links as shown in FI0*.+%. It converts
a;ial displacement to rotational displacement as the tendons are pulled from each direction to rotate the link
in the direction of the pulling force. "he force is not applied at the joints but at a distance from the joints thus
a tor#ue is applied at
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Force ; os?@ ; is?J@?y-a;is@
Force ; in?@
Force applied
by tendon
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,I12+) The .orce s/lit into its com/onents2 13
"he force which would create the rotational motion
would be the y a;is component of the force on the tendon. "he ;-a;is component of this force would act at the
joint which would increase the friction between the link bars and the joint rod as the force and this would cause
hindrance to the motion of the manipulator. "his is called the joint stiffness.
,I121+ The e..ect o. .riction on this s/eci.ic
design2
$ore than one actuator ?or larger actuators@ can be used for joints without changing the dynamics of the
manipulator.
"hus the total force produced by the motor would not be utili8ed to produce the rotational motion. "he efficiency
of the transmission system is fairly low but this is balanced by the reduced weight at the links as the motors are
replaced from the links to the base of the manipulator.
,I1211 Tendon8Pulle% (esign One2013
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?@
J?;-a;is@ Force ; os?@
K. Force ; os?@ ; os?J@
Friction G LMFcos?@&oint >od
Force ; os?@
Eink /ar
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Number of Pulleys=Number ofJoints
In this design, the tension of the taut wire produces the force which causes friction between the tendon and the
pulley and hence the tendon is able to transmit the tor#ue from the motor to the joint. As the tendon for the joint
6 is passing through the pulleys * and , there is a tor#ue produced in the *stand ndjoint thus there would be
unnecessary motion at these joints thus, when programming the controller for this joint, there must be a feedback
system which would have to compensate for the irrelevant motion thus the programming would get more
complicated and hence the flaw in the design.
,I121& Tendon8 Pulle% design two2013
"his design tries to remove the irrelevant motion by using two pulleys instead of one for each tendon at the
joints where motion is not needed. Instead of the tendons stretching at opposite sides of the pulley, they are now
placed on the same side of two pulleys thus compensating for the motion of each other.
,I1213 The conce/t o. the design2013
Number of pulleys=(number of joints)2
As the pulleys increase, the overall weight of the manipulator increases. "his additional weight would not hinder
the manipulators movement at a small scale. As we increase the si8e of the manipulator, a larger tor#ue would be
re#uired to move the manipulator hence increasing the force thus increasing the shear on the pulley. As shear
Page16
"or#ue ?clockwise@
"or#ue ?anti-clockwise@
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increases, the material with lower shear modulus would deform under the force "his would be conflicting with
the design itself as the design was to decrease the
As we increase the si8e of the manipulator, a larger tor#ue would be re#uired to move the manipulator hence
increasing the force thus increasing the shear being applied on the pulley. As shear increases, the materials with
lower shear modulus would deform under the force thus materials with higher shear modulus are re#uired.
According to FI0*.*7, the density of the materials increases linearly with increasing shear modulus thus for
higher tor#ue application, this design would not be as effective as the weight would rise sharply.
"he width of each link would increase with the increase of joints of the manipulator thus this would lead to abulky design which is not ideal for most applications.
Page1#
Force"his is one instance of the
force on the pulley. "here
would be forces tangent toevery point of
circumference of the
pulley.
"his parallel force causesdeformation along the surface of the
shape.
3ulley
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-ensit) 2kg m435100 1000
earmouus
a
031
1
10
100
,I1214 (ensit% o. $aterial vs Shear $odulus2
Instead of using pulleys, a single ball bearing could be used instead. "his would decrease the bulkiness of the
design and at higher tor#ue, the weight of this design would be less than the double pulley design. As seen in
FI0*.**, there would be a bearing at each non-tor#ue transmitting pulley.
,I1215 A diagram o. a bearing2 14
"he bearing in this mechanism is used to isolate the rotational motion of one part from another and it decreases
the friction between them significantly.
Page1%
uter race
Inner race
/alls
age
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"his is caused by the mechanism which includes simple spheres, two races and a cage which holds the spheres in
their place as shown in FI0*.*5. "he spheres i.e. balls come in contact with both the races. "he race which is
connected to the mobile part would be moving at the same velocity and thus the point of the ball in contact with
the race would also move at that velocity thus causing rotation. "he other race would be attached to a stationary
object. "hus the balls would be revolving around the a;is of the bearing. As the balls a rolling, they have a
significantly lower co-efficient of friction and thus it would seems like that the two objects are sliding besides
each other.
9ame o. $echanism -eight :Small Scale;
Tendon Eowest
Tendon8Pulle% Eower ?In-effective design@
Tendon8(ouble Pulle% 1igher
Tendon87earing Pulle% 1ighestTA712+& $echanism vs -eight
9ame o. $echanism -eight :!arge Scale;
Tendon Eowest
Tendon8Pulle% Eower ?In-effective design@
Tendon87earing Pulle% 1igher
Tendon8(ouble Pulle% 1ighestTA712+& $echanism vs -eight
When compared to the conventional design, the highest payload ?when the arm is hori8ontal i.e. the worst case in
terms of gravitational support@ of the designs shown above are significantly higher when the same driving
system is used thus only changing the transmission. "his is proven in CDesign and 4;periment of oupled
"endon $anipulators thus these design are more efficient as they provide more useful output tor#ue at the same
input tor#ue as the weight of the manipulator is decreased.
"he material used for the tendons is also an issue as for higher tor#ue applications, the material needs to have
higher tensile strength and thus higher (" so that the tendon would not break during the application or deformplastically.
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Tensile strengt" 2,Pa501 1 10 100 1000
Pri
ce2,7'3kg5
10
100
1000
Polyester4E-lass ber6 non-crm' abrc com'oste6 uas-sotro'c lamnate
Polyester45wt% E-lass ber6 wo!en abrc com'oste6 ba+al lamnate
Polyester4E-lass ber6 'ultru&e& com'oste ro&6 un&rectonal
,I121 The gra/h o. Tensile Strength vs Price2
3olymers are normally used for tendon materials as they are fle;ible thus they are able to bend easily ."hus the
best material would be polyester24-glass fiber as this would be under $!>*+2kg whereas Nevlar which is
usually chosen for tendons which costs around $!>
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7elt < 7ased transmission s%stem2
"his transmission system has the same concept as the tendon- based transmission. Instead of using tendons and
pulleys, belts are used with pulleys and gears. /elt drives can absorb shock and vibrations on the system as wellas a degree of misalignment in the driver and the driven object.
/elts can be of two types, flat or :ee beltsB
Flat beltsB"hese belts provide high power at high speeds when the scale of the transmission is large so the
system is bulky and thus are suitable for small systems which re#uire large tor#ue. "hese belts re#uire large
amount of tension to transmit power properly which increases the load proportionally. "hese belts tend to move
about the a;is of rotation so a centering mechanism is used to keep them at place. As the force which makes it
possible to transmit the force from the belt to the machine element is friction aloneO at high speeds and when thesystem has large inertiaO slippage would occur, this would not be suitable. "he material used in these belts need
to have a high friction co-efficient so that the grip of the belt is improved so it would be able to transmit theforce efficiently.15
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,I121# A t%/ical .lat belt2
:ee beltsB "hese belts have a different shape as wedges are created along the shape of the belt which would give
them better hold on the machine element which it is connected to.
,I121' A =ee :Timing; belt2 1#
"hese belts provide the best dynamic characteristics i.e. the traction force, speed of movement and load on
bearing. "he shape of the e;trusion on the belt is trape8oidal as this would provide a good angle of approach and
e;iting angle and the edges of the shape are rounded so that the force does not cause wear on the belt due to
constant shear. And thus due to the shape of the belt, the lifetime of the belt is also prolonged.
"he material of these belts could have a lower frictional co-efficient as the majority of the force is transmitted as
contact force as shown in FI0*.*'.
,I121) The .orces between a =ee belt and a ear2
Page22
"he downward
force from the belt
acting on the gear.
Force from belt directed on the teeth of the gear
Force from belt transferred due to friction
between the two machine elements.
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"he overall system for the belt2gear and belt2pulley are similar to the tendon2pulley mechanism.
ear 8 based transmission s%stem2
0ears are the most common machine elements used to transfer power. "hus there is a couple of different type of
gears used in manipulator transmission.1#
*. 3arallel A;isB "hese include spur gears and helical spur gears and their teeth are perpendicular to thesurface. "hey are used to connect to a;is of rotation.
,I12&+ Two gears connecting their a0es2
. 3erpendicular A;isB "his is further classified into Intersecting A;is ?traight and piral /evel 0ear and
Face 0ears@ and =on-Intersecting A;is ?Worm 0ear and 1ypoid 0ear@ which e;plains by itself.
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,I12&1 7evel gears connecting their a0es2
6. rossed A;isB "he a;es of these gears are neither parallel
nor perpendicular to each other.
,I12&& Two helical connecting their a0es2
7. 3lanetary 0ear ystemB
,I12&3 A Planetar% ear with all the elements labelled201%
f these gears, the perpendicular gears are used in the transmission system due to the transfer of power in
perpendicular direction to the joint rotation a;is.
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,I12&3 The mechanism used in Samer >ah%a et al2 in their /a/er201(
In amer !ahya et al.9s design, all the joints were controlled by a single motor. "his would thus create the same
angular movement at each joint and individual joint movement is not possible in this design. "he overall tor#ue
usage of this design was less than of the conventional manipulator design.
/evel 0ears vs Worm 0ears for transmitting power at a right angleB&+
According to iemens research team, the bevel gears are more efficient at transmitting tor#ue and have a longer
life-time than their counterpart, the worm gear.
,I12&4 The advantages and disadvantages o. di..erent t%/e o. gears2
Column1 8elical ear 9e!el ear
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$ani/ulator (esign and Pro ngineer $odelling
$any designs were thought of in the start and during the period of the project. f those designs only a couple of
designs were selected.
"he following designs were selected on the basis of their mechanism and the ability of 3ro-4ngineer to model
and simulate them.
The 7evel8ear transmission s%stem2
"his mechanism utili8es the ability of the bevel gear mechanism to transfer tor#ue at a right angle and converts it
into a mechanism which can transfer tor#ue from a source to any angle via a link. "his mechanism uses bevels
gears and bearings for conveying tor#ue to the links and not allowing the transmission system to create motion
in unnecessary links respectively. "his design was modelled after understanding the design of amer !ahya et
al.9s design in their paper C&oint "or#ue >eduction of a "hree Dimensional >edundant 3lanar $anipulator. A
few modifications were made on it as the design used by them utili8ed a single motor which would control all
the links motion thus individual link control was not feasible.
7evel ear $echanism
"he mechanism is basically set on a single a;is of rotation and the bearing creates relative motion of the link
shaft and the bevel gear so the rotation of the gear does not affect the rotation of the shaft. "his gear is connectedto another gear perpendicular to it thus this makes the bevel gear.
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:ertical A;is *
:ertical
A;is
/evel 0ear 7
/evel 0ear
6
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,I12&' The design o. the mechanism2
17evel ear 1B&B3B4 "he bevel gear ?7 bevel gears as shown@
&"he bearings ? as shown@
3"he hollow shaft connecting the gears.
4"he gear holder.
5"he a;is of rotation of joint rod, bearings, the gear connecting hollow shaft.
"he bevel gears 1 and &are connected to each other by gear meshing as are the bevel gears 3 and 4. "he design
does not allow the transfer of tor#ue from the gears to the joint shaft which would be inserted in between the
bearings. "his is done by the action of the bearings which stops the transfer of tor#ue from the gears to the joint
shaft. Part3is there so that the bevel gears & and 3are able to transfer tor#ue between each other. If there was
not Part3, the tor#ue would not be transferred and the two bevel gear systems would separate systems which
would be connected by the joint shaft which would have been inconvenient. Part 4 is placed so that the bevel
gears 1 and 4do not move in the direction of the a;is 5O the a;is of the joint shaftO thus they would always be
fi;ed in their position so that there are no obstacles when moving the manipulator.
Instead of the two bearings, a single bearing can be used instead as it would provide the same function.
"here are three joints in the manipulator designed thus there are < bevel-gear mechanisms in the manipulator.
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/evel 0ear
/evel 0ear
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,I12&) The design bevel8gear transmissions%stem2
"he bevel-gear mechanism shown in FI0*.' is only for joints where the tor#ue from the motor is not needed
thus there are of these mechanisms on &oint * and * on &oint .
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/evel 0ear 1ori8ontal A;is
:ertical A;is
/evel 0ear *
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,I123+ 7evel ear $echanism :ear to 6oint Sha.t TorCue Trans.er;
"he mechanism shown above is for transferring the tor#ue from gear 1to gear &which is connected to the joint
shaft thus effectively transferring the tor#ue from the motor to the joint shaft which was meant to be accelerated.
"here is * of these mechanism on each of the joints as which these mechanisms, the manipulator would be
unable to move as no tor#ue transfer would be taking place.
"hese mechanisms are connected to their consecutive mechanisms via shafts which would connect the verticala;is of one mechanism to the vertical a;is of the ne;t mechanism thus each of the bevel gears in one line would
be connected to each other and would move with the same rotational velocity as the gear ratio of the whole
mechanism is *B*.
Due to the gears being of *B* ratio ?i.e. the same si8e@, the a;ial distance of the manipulator would be large. "o
reduce this, the gears on the hori8ontal a;is need to be larger than the gears on the vertical a;is thus the a;ial
space needed to place all the mechanism on the joints would be less thus all the vertical a;is gear would be
smaller compared to the hori8ontal a;is gears at each joint thus effectively reducing the a;ial space occupied by
the manipulator.
"his mechanism could hence be used in manipulator with more joints as the a;ial si8e of the manipulator can be
controlled instead of increasing with each additional joint. "he manipulator base is connected to the stationarybase via a bearing thus allowing the whole manipulator to be able to rotate thus giving it freedom in 6
dimensions.
"he materials used in this design were used in order to reduce the mass of the overall design thus reducing theweight and hence the overall tor#ue needed to move the manipulator while trying to not change the part
properties so much that the parts would fail while in motion.
"he parts for this design were as followsB
Parts ,aterials -ensit) kgm@*,nAs $e-.ar&ene& wrou.t alumnum 2900
Bransmsson Ro& ,ow Carbon teel 7850Gear $e-.ar&ene& wrou.t alumnum 2900Gear ;ol&er $e-.ar&ene& wrou.t alumnum 2900
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7oung>s modulus 26Pa51e-5 1e-: 03001 0301 031 1 10 100
-ensit)2kgm
435
100
1000
10000
As the manipulator is not very huge, the tor#ue re#uired to move it would be not huge thus aluminum could be
used without the fear of deformation.
"he materials for a manipulator are directly related to the si8e of the manipulator as a larger manipulator would
re#uire an overall larger tor#ue and thus would need gears which are re#uired to transfer larger tor#ue so the
material of the gear would need to have a larger young9s modulus and thus the density of the material would
increase ?as shown in the graph below@.
,I1231 !inearit% o. (ensit% and >oungDs $odulus2
As 3: can be used to create a small manipulator while a large scale manipulator would fail if it uses the samematerial as the small manipulator.
Pro*erties ?nits&ow Carbon
$teelAge@"ardened wroug"t
aluminum
Prce >R4A 18 75
el& tren.t >Pa 510-10 300-395Bensle tren.t >Pa 550-20 500-580
Com'resscetren.t
>Pa500-10 300-395
ouns >o&ulus G'a 8-80 200-215
Castablty
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>ac.nablty Goo& ery Goo&
Fel&ablty ery Goo& Goo&
TA712+5 Pro/erties o. Aluminum and Steel2
!imitations
As said, the designing of the model was supposed to be done on olid works but due to the license of olid
works not being available to the university, the modelling was done in 3ro-4ngineer.
3ro-4ngineer in the university did not include the module in 3ro-$echanism which defines bevel gear
connection as it had only standard and rack and pinion connection.
,I123& T%/es o. ear *onnections available in Pro8$echanism2
Tendon8
Pulle%
Transmission
S%stem
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,I1233 The basic design o. the Tendon $ani/ulator2
"he basic concept of this manipulator is derived from the fact that tendons can transfer force and pulleys can be
used to change the direction of the force.
In this, the tendon wraps around the joint pulley ?i.e. the tendon goes around the pulley for 6
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Pro*erties ?nits e!lar 14(@aramid Bber
Densty A4m@ 1:70Prce >R4A :00
Bensle trent. >'a 3:00ouns >o&ulus G'a 180
Possons Rato 03
#le+ural >o&ulus GPa 180Elonaton % stran 12
>ec.ancal ,oss Co-ecent 0008-001TA712+ Pro/erties o. Eevlar 14)8aramid .iber2
"his design would produce a manipulator which would achieve a light-weight design thus it would have a low
moment of inertia. "his would then re#uire low energy consumption thus improving efficiency. As the weight of
the manipulator is less, the pay-load to weight ratio would be higher.
Parts ,aterials -ensit) kgm@*,nAs $e-.ar&ene& wrou.t alumnum 2900
Bransmsson Ro& ,ow Carbon teel 7850
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*alculations
"he calculations for the manipulator used the Denavit-1artenberg parameters.&4&5&
"he manipulators designed had 6 links thus 6 DFs and thus 6 joints in the D-1 parameter table. All the joints in
the manipulator are revolute
+oints D a d +oint 'ange
1 )1 0 l1 0 (-*90H to 85H
2 )2 0 l2 0 (-*90H to 90H
3 )3 0 l3 0 (-*90H to 90H
TA712+' (8@ Parameters .or the $ani/ulator2
Parameter
-eBnition
EiF Rotaton anle rom I-1to Iabout J-1EDiF $nle o rotaton rom J-1to Jabout IFaiG Distance from intersection of Pi-*Q Rito the origin of i coordinate along Ri.
EdiF Dstance rom orn o (-1* coor&nate to ntersecton o J-1K IalonJ-1
TA91G/(H -eBnitions of t"e -@8 ParametersG
.
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,I1235 The design o. the mani/ulator2
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l6
l
l*rigin ;-a;is
y-a;is
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,I123 Einematics Parameters o. a $ani/ulator2
With the D-1 parameters, we need to find the tor#ue e#uation which is given as follows.
=D ( ) (t)+h ( , )+c ()
In this e#uationB
G "or#ue of the $anipulator
D ( )=The Accelertionrelte! "nerti
h ( , )=The #entrifugl#oriolis
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c( )=The$r%ity term
,inding the Acceleration related Inertia $atri0 Term
D ( )=
(D 11 D 12 D 13
D21 D 22 D 23D31 D 32 D 33)
O D?i j@
4ach of these terms is the value for the tor#ue of the jthlink transferred to joint i.
4ach term of D?i j@ is given as follows ?where j is replaced by k@B
If iGk, it will be Diiwhich will be related to the acceleration of joint i where the driving tor#ue " iacts while
when i is not e#ual to k, Dikis related to the reaction tor#ue induced by the acceleration of joint k and acting at
the joint i or vice versa.
Where &iis the 3seudo-Inertia $atri; of link i, dependent on the mass distribution of link i and are e;pressed
with respect to the i thframe.
Where (jk is the effect of motionof joint j on all the points on the
link i.
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Where (LAB s t.e trans'ose o t.e MLA w.c. s !en as ollows
Trnspose
(1 2 3
b1 b2 b3
c1 c2 c 3)=
(1 b1 c1
2 b2 c2
3 b3 c 3)"he i-*"iin the previous e#uation is given by the following e#uationB
"his is the same for all rotary joints.
"he Sj isgiven by the following matri; for rotary jointsB
&i=(0 1 0 01 0 0 0
0 0 0 0
0 0 0 0)"hus the D-1 parameters are inputted in the i-*"i and thus by following the procedure shown above, the
Acceleration related Inertia matri; can be found.
ince the Inertia matri; is symmetric and "r?A@ G "r?A"@, DikG Dki.
,inding the ravit% "elated $atri0 Term
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c ( )=c 1
c 2
c 3
4ach of these terms is given by the following e#uationB
Where
iriG (l
2
0
0
1
) which is the displacement of point I from the link co-ordinate frame i.
i G gravity loading term due to the links
,inding the *entri.ugal and *oriolis $atri0 Term
h ( , )=(h1h2h3
)Where hiis found out by the following termB
Where hikmis given by the following e#uationB
Where (jkmis given by the following e#uationB
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Where "r? @ is the trace of the matri; which is the sum of the main diagonal of the matri;.
Tr (A )=( 1 2 34 5 67 8 9
)=1+5+9"he co-efficient hikmis related to the velocity of the joint variables and is defined by the e#uation given above.
"he two indices k and m are related to the velocities of joint k and m, whose dynamic interplay induces a
reaction tor#ue at joint i. "hus, the first inde; I is always related to the joints where the velocity-induced reactiontor#ues are felt.
For kGm, hikkis related to the centrifugal force generated by the angular velocity of joint k and felt at the joint i,
while when k is not e#ual to m, hikmis related to the oriolis force generated by the velocities of joint k and m
and is felt at joint i.
"hus, the entrifugal and oriolis $atri; term can be found and now the tor#ue values for each joint can be
found out.
ome of these co-efficient can be 8ero. "his can be due to the following reasonsB
*. "he kinematic design of the manipulator can eliminate some dynamic coupling between joint motions.
. ome of the velocity-related dynamic co-efficient only have a dummy e;istence i.e. in the entrifugal
and oriolis related $atri; "erm.
6. Due to particular variation in the link configuration during motion, some dynamic co-efficient may
become 8ero at particular instance of time.
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'esults
"he manipulators were simulated on 3ro-4ngineer to find out the tor#ue re#uired for the manipulators at each
angle.
0ravity and all the friction between the parts were taken into account during the simulations. "he tor#ue re#uired
at the joints was found out every joint for the manipulator
In the simulations on 3ro-4ngineer, the following simulations were done to find out the tor#ue re#uired for the
manipulator without any end loadB
*. "he tor#ue re#uired when the $anipulator is at its hori8ontal position ?i.e. the position which re#uires
the ma;imum tor#ue@.. "he tor#ue re#uired when the $anipulator is vertical position. ? the minimum tor#ue re#uired at the
joints@
6. "he tor#ue re#uired when the joints of the manipulator are moving from their ma;imum angular position
to minimum position and vice versa. All of them move at the same angular velocity.
7. "he tor#ue re#uired when the *stlink is hori8ontal while the ndand the 6rdlink are rotating at the same
velocity.
5. "he tor#ue re#uired when the *stand the ndlink are hori8ontal while the 6 rdlink is rotating at a given
velocity.
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). "he tor#ue re#uired when the *stand the ndlink are vertical while the 6rdlink is rotating at a given
velocity.
"hese simulations are done for each of the manipulator i.e. the bevel gear manipulator, the tendon manipulator
and the conventional manipulator.
>esults for 7-) are given in the appendi;.
0 01 02 03 0: 05 0 07 08 09 1
0
05
1
15
2
25
3
TorCue ,or 6oints (uring @oriHontal Position
ont 1
,near (o
ont 2
,near (o
ont 3
,near (o
Time?sec
TorCue :9m;
7evel ear $ani/ulator
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0 01 02 03 0: 05 0 07 08 09 10
0
0
0
0
00
0
0
+oint Torue w"en t"e ,ani*ulator is *er*endicular to t
Time
Tor=ue
,I123# TorCue at 6oints reCuired to sta% at the horiHontal /osition2
,I123' TorCue reCuired .or being still during the =ertical /osition.
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-1 1 3 5 7 9 11 13 15
-3
-2
-1
0
1
2
3
Nont 1 Nont 2 Nont 3
Time? Seconds
TorCue ? 9m
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,I123) TorCue vs Time .or rotating joints
All the joints were rotating at a steady *+ degree2second speed. "hus the ndjoint had a speed of +
degree2second and the 6rdjoint had an angular speed of 6+ degree2second.
0 001 002 003 00: 005 00 007 008 009
0
02
0:
0
08
1
12
1:
1
18
Time? Second
Tor=ue3Im
Tendon $ani/ulator
,I124+ TorCue reCuired .or the mani/ulator .or it to sta% in its horiHontal /osition2
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0 001 002 003 00: 005 00 007 008 009 01
0
0
0
0
0
0
0
0
0
ont 1
ont 2
ont 3
Time? Seconds
TorCue? 9m
,I1241 TorCue reCuired .or the $ani/ulatorDs vertical /osition2
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,I124& TorCue vs Time .or rotating joints2
0 2 : 8 10 12 1: 1 18
-15
-1
-05
0
05
1
15
Non
Non
Non
Time? Second
TorCue? 9m
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*onventional $ani/ulator
0 01 02 03 0: 05 0 07 08 090
1
2
3
:
5
7
8
Nont 1 Nont 2 Nont 3
Time? seconds
TorCue? 9m
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0 1 2 3 : 5 7 8 9 100
0
0
001
001
001
001
001
Time? seconds
TorCue? 9m
,I124& TorCue .or @oriHontal Position2
,I124& TorCue reCuired .or the =ertical Position2
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0 2 : 8 10 12 1: 1
-8
-
-:
-2
0
2
:
8
Nont 1 Nont 2 Nont 3
TorCue ? 9m
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,I1243 The TorCue vs Time gra/h .or rotating joints2
*om/aring the $ani/ulator (esigns
,or @oriHontal Position
0 001 002 003 00: 005 00 007 008 0090
05
1
15
2
25
3
Con!entonal $rm Ben&on $rm
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0 2 : 8 10 12 1: 1 18
-8
-
-:
-2
0
2
:
8
an'ulator Con!entonal >an'ulator Ben&on >an'ulator
Time ? Seconds
TorCue ? 9m
,or "otating 6oints
,I1245 The TorCue .or 6oint 1 .or each $ani/ulator2
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,I124 The TorCue .or 6oint & .or each $ani/ulator2
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0 2 : 8 10 12 1: 1 1
-25
-2
-15
-1
-05
0
05
1
15
2
25
an'ulator Con!entonal >an'ulator Ben&on >an'ulator
TorCue? 9m
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,I124# The TorCue .or 6oint 3 .or each $ani/ulator
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0 2 : 8 10 12 1: 1
-03
-02
-01
0
01
02
03
an'ulator Con!entonal >an'ulator Ben&on >an'ulator
TorCue ? 9m
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-iscussion and Anal)sis
As seen from FI0*.77 which displays the tor#ue re#uired by the manipulator to be in the hori8ontal position
which is shown below. "his position re#uires the ma;imum tor#ue, as the moment of each link is highest as
gravity is acting perpendicular to the hori8ontal links, thus the hori8ontal distance from the centre of mass of the
link to the link joint is ma;imum creating the largest tor#ue ?momentum@.
,I124'
The
horiHontal /osition o. the mani/ulators2
"he manipulator above is the bevel gear manipulator shown in the hori8ontal position.
"he vertical position is perpendicular to this position as such gravity would be acting parallel to the vertical links
thus the hori8ontal distance from the moment of the link to the joint would be minimum.
"he rotation of the manipulator was done between the two e;treme positions.
"he results we got from the simulations showed us that manipulators with the transmission systems would
re#uire less tor#ue at the links to create the same motion as the conventional manipulator. "he tor#ue re#uired by
the manipulator is directly proportional to the mass of the manipulator. As the mass of the manipulator increases,
the tor#ue increases thus in a larger scale of the manipulator where a larger motor is needed the difference in thetor#ue re#uired would diverge further and the transmission system would yield a higher efficiency as the base
manipulator movement would re#uire less input power as less tor#ue is needed to move the manipulator.
"hese transmission systems can be implemented in planar manipulators with more DFs as we have discussed
how to decrease the a;ial si8e ?width@ of the manipulator so as the links increase the a;ial si8e does not increase
proportionally.
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&o
&o
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"hese manipulator designs would be able to use the same motor si8e at each link whereas the conventional
manipulator would re#uire a smaller motor with each increasing link as the previous motor needs to support the
ne;t motor.
1aving the same motor si8e at each link in the conventional design would not be logical as the base tor#ue
re#uired to move the manipulator would increase drastically.
Conclusion
"he main objective of the project was to reduce the joint tor#ue of a manipulator. For this, e;tensive research
needed to be done to find out the types of methods to reduce the tor#ue re#uired at the link for a manipulator.
"he method to reduce the joint tor#ue of a manipulator which was chosen was the use of a transmission system
and usage of lighter materials so that the overall design had a lower mass. "he manipulators were designed with
their respective transmission systems.
"hese were then modelled in 3ro-4ngineer. Dynamic simulations were then run on these manipulators using the
mechanism module of 3ro-4 and by giving re#uired constraints, the tor#ue was found out for each of the joints
of the manipulators.
Further calculations were done to show the dynamic model of the planar manipulator. "his helped in
understanding the manipulator design and the effect of Inertia, 0ravity, the entrifugal and oriolis 4ffect on the
manipulator when it is accelerating, moving at a constant speed or stays at rest.
"he manipulators designed were then compared with the conventional manipulator design. "he difference in the
tor#ue was seen as the conventional manipulator had an overall larger joint tor#ue re#uirement than the
manipulators using the transmission systems.
It was seen that the bevel gear transmission system would have a higher tor#ue re#uirement than the tendon-pulley transmission system but both of these manipulators had an overall less tor#ue re#uirement than the
conventional design.
All aims and objectives which were stated for this project were fulfilled.
.urt"er Jork
Due to the unavailability of olidworks, the simulations of the design of the tendon were done on 3ro-4ngineer
so the tendons were not added in the simulations and only the joints were simulated with the overall parts. "he
simulation can be done with the tendons attached in the simulations to get more accurate results.
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"he designs can be created in hardware and then simulated to get real worlds results as the budget was
insufficient as the tendon and bevel gear manipulator combined would have cost way above the given budget of
$!> 6++.
'eferences
T*U. Dennis ui. ?+*@. "he un9s the limit. Young Scientist Journal. 5 ?*@, oboticsVNinematicsVandVDynamics2erialV$anipulatorV3ositionVNinematics.
TAccessed *5 April *7U.
T
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T*U. Indian Institute of "echnology Nanpur. +*7.IN&R("1C&I(N &( S'RIA2 ARM. T=EI=4U Available atB
httpB22home.iitk.ac.in2adutta2$anualVserialVarm.pdf. TAccessed *5 April *7U.
T*6U. hugen $a, higeo 1irose, and 1iroshi !oshinada , .$, .1, 1.!, *))6. Design and 4;periments for a
oupled "endon-Driven $anipulator . Control S#stems I''', *62*, pg6+-6eduction of a
"hree Dimensional >edundant 3lanar $anipulator . Sensors 5Basel6, *2. 0on8ale8, ..0 Eee, *)'%.Robotics/ Control, Sensing, -ision and Intelligence. *st ed.
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ons.
T%U. >achid $anseur. >bot $odelling and Ninematics. *st ed. International. Da :inci 4ngineering 3ress.
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http://en.wikibooks.org/wiki/Robotics_Kinematics_and_Dynamics/Serial_Manipulator_Position_Kinematicshttp://en.wikibooks.org/wiki/Robotics_Kinematics_and_Dynamics/Serial_Manipulator_Position_Kinematicshttp://www.coppeliarobotics.com/helpFiles/en/jointDescription.htmhttp://www.comsol.com/multibody-dynamics-modulhttp://www.comsol.com/multibody-dynamics-modulhttp://www.haydonkerk.com/Resources/StepperMotorTheory/tabid/192/Default.aspxhttp://www.haydonkerk.com/Resources/StepperMotorTheory/tabid/192/Default.aspxhttp://yertiz.com/cnc/steppermotor.pdfhttp://www.embedded.com/print/4378311http://www.coppeliarobotics.com/helpFiles/en/jointDescription.htmhttp://www.comsol.com/multibody-dynamics-modulhttp://www.comsol.com/multibody-dynamics-modulhttp://www.haydonkerk.com/Resources/StepperMotorTheory/tabid/192/Default.aspxhttp://yertiz.com/cnc/steppermotor.pdfhttp://www.embedded.com/print/4378311http://en.wikibooks.org/wiki/Robotics_Kinematics_and_Dynamics/Serial_Manipulator_Position_Kinematics -
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A**endi:
0raphs for >esult 7-). All the graphs have "or#ue on their y-a;is and time on the ;-a;is.
"he se#uence which will followedB
7. &oint * is kept in the hori8ontal position while &oint and &oint 6 rotate through their joint rangeB
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http://www.pfeiferindustries.com/timing-belt-pulley-pitch-diameter-outside-diameter-charts-i-12-l-en.htmlhttp://www.carparts.com/transmission.htmhttp://home.iitk.ac.in/~adutta/Manual_serial_arm.pdfhttp://www.impactbearing.com/deep-groove-ball-bearings.htmlhttp://www.pfeiferindustries.com/timing-belt-pulley-pitch-diameter-outside-diameter-charts-i-12-l-en.htmlhttp://www.pfeiferindustries.com/timing-belt-pulley-pitch-diameter-outside-diameter-charts-i-12-l-en.htmlhttp://www.gearsandstuff.com/types_of_gears.htmhttp://www.carparts.com/transmission.htmhttp://www.industry.usa.siemens.com/drives/us/en/energy-efficient-ac-gear-motors/Resources/Pages/Worm-vs-Bevel-Gear-Motor-Comparison.aspxhttp://www.industry.usa.siemens.com/drives/us/en/energy-efficient-ac-gear-motors/Resources/Pages/Worm-vs-Bevel-Gear-Motor-Comparison.aspxhttp://www.festo.com/net/SupportPortal/Files/42076/Festo_Biomechatronic_Footprint_en.pdfhttp://www.festo.com/cms/en_corp/9655_10219.htm#id_10219 -
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*alculations
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