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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
48
MODELING AND VALIDATION OF PROTOTYPE OF
SELF STABILIZING TWO WHEELER USING
GYROSCOPE
Akshay Khot1
, Nishad Kumbhojkar2
1,2
Department of Mechanical Engineering, Sinhgad College of Engineering,
Pune, Maharashtra, India
ABSTRACT
This paper focuses on the concept of developing the two wheeler car & it’s validation with
the help of prototype. This paper deals with an experiment carried out to produce gyroscopic effect
on an in-house prototype. The prototype is a two wheel vehicle in which rotating discs imparted act
as gyroscope to produce a counter balancing force (gyroscopic effect) when the vehicle prototype
looses balance on either sides. Thus the vehicle stabilizes itself. This paper also gives a brief of a
concept vehicle developed on similar grounds with an added feature. Wherein even if an external
force is applied to the system the force sensors deployed in it sense the force and develop a force of
similar magnitude but in opposite direction due to presence of two gyroscopes used in the vehicle,
thus the vehicle does not loose it’s balance even if the external force is applied to it.
Keywords: Gyroscope; Gyroscopic effect; self stabilize.
1. INTRODUCTION
The gyroscopic effect is widely used in air or sea vehicles such as air planes and ships,
wherein always external disturbing couple is acting on the vehicle [1]. Thus, for the stability of such
vehicles it is essential to neutralize the effect of external disturbing couple which can be done by
applying equal and opposite couple .Accordingly, to generate equal and opposite reactive couple it is
essential to vary the magnitude and direction of velocity of precession.
In the case of two wheelers this phenomenon can be effectively used for stabilizing &
balancing the vehicle by means of a rotating disc i.e. a gyroscope. Consider a body rotating in a
plane (plane YZ, Fig.1) & spinning about an axis (axis OX) and it’s axis of rotation or spin is made
to precess in another perpendicular plane (plane XZ). The couple is induced (reactive gyroscopic
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 12, December (2014), pp. 48-54
© IAEME: www.iaeme.com/ IJARET.asp
Journal Impact Factor (2014): 7.8273 (Calculated by GISI)
www.jifactor.com
IJARET
© I A E M E
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
49
couple, Fig.2) on the rotating or the spinning body across the axis of rotation or spin in a third
mutually perpendicular plane (plane XY).
The converse of the above also holds good i.e..Whenever a body is rotating in a plane (plane
YZ) about an axis (axis OX) and a couple is applied on a rotating body across axis of rotation or spin
in another perpendicular plane (plane XY), the rotating or spinning body starts precessing in third
mutually perpendicular plane (plane XZ) as shown in the adjoining fig: 1. This phenomenon is
known as gyroscopic effect [2].
Fig.1: Concept of gyroscopic principle
Fig 2: Directions of vectors & couples
The active gyroscopic couple represents rate of change of angular momentum, and this
couple must be applied to disc across the axis of spin to cause it to precess in the horizontal plane.
When the axis of spin precess itself or is made to precess the shaft on which the disc is mounted
applies reactive gyroscopic couple (Fig: 2). This reactive gyroscopic couple thus produced by the
gyroscope is equal to the external disturbance but it is in opposite direction. Thus this couple
neutralizes the effect of disturbance & stabilizes the object.
(Active couple) = - (Reactive couple) (1)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
50
2. PROTOTYPE DETAILS
The objective of this model is to prove the fact that the body can be balanced on only two
wheels in idle condition. The gyroscopic principle can be successfully used for creation of a
prototype of a two wheel vehicle, and thus observing gyroscopic phenomenon on the same.
The prototype was created using following parts:
1. Wooden Frame
2. Wooden plank
3. DC Motor
4. Four CDs(compact discs)
5. Wooden pencil
6. Round wheels
2.1 Construction
The wooden frame used is bolted on the bottom wooden plank as shown in Fig.3 Trolley
round wheels are fitted to the wooden plank at the bottom, the holes in the frame are drilled in order
to fit the gimble of the gyroscope (wooden pencil),the DC motor supported on a piece of wood is
placed on the gimble. The only pre-requisite for this setup to work is that the mass distribution, the
mass should be dominant on the upper side (setup should be top heavy) of the gimble The centre of
gravity is thus just above the gimble axis, CDs used as gyroscope are fitted to the shaft of the motor
as shown in the Fig: 3.
Fig. 3: Prototype of Two Wheeled Gyroscope
(side view)
Fig. 4: Wooden Frame Assembly
2.2 Working
Once the motor starts rotating the CDs fitted on the motor shaft start rotating, the rotation of
the CD leads to the production of the gyroscopic effect (as mentioned for disc in introduction) thus,
when the wheels loose their balance due to the active gyroscopic couple a counter acting reactive
gyroscopic couple is produced in the opposite direction due to gyroscopic effect thus stabilizing the
prototype, This occurs on both left as well as right hand side.
Thus, due to rotation of the gyroscope a counteracting reactive gyroscopic couple leads to the
stabilization of the prototype.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
51
The motor & gimble axle assembly is designed such a way that it is having heavy top. That
means the center of gravity lies above the gimble axle. So the motor & gyroscope assembly tries to
attain the position such that the C.G. of core will move downwards (Fig. 4). But at the same time the
motor & gimble assembly is arranged within the frame having bearing reaction at ends. So only
possible way for motor to attain the stability is to either lean forward or backward. So when the
motor is started the body is about to fall on either side & also the motor assembly is leaning this
causes the precession of spin axis. Due to this precession, according to right hand rule the reactive
gyroscopic couple acts on the frame which nullifies the effect of the disturbing couple & thus
stabilizes the vehicle. After few rotations & oscillations of motor, the motor & frame attains the
stationary position and gyroscope is subjected to pure rolling motion about the spin axis.
2.3 Mathematical evaluation
Consider the couple acting on the vehicle due to the unbalance condition, i.e., weight of
prototype is distributed on two wheels only is ‘C’. Due to this couple the body of prototype tends to
fall on either of the side.
C = Disturbing Couple
Let,
I be the moment of inertia of discs about the axis of rotation.
ω be the angular velocity of motor.
As mentioned in section 2.2 the motor has tendency to lean forward or backward due to
which the precession of spin axis takes place say it takes place by angle ‘Ө’ in time ‘t’. So the
reactive couple acting on the frame due to gyroscope is given by equation
C= I× ω× d Ө/dt
But,
d Ө/dt = ωp
Where,
ωp is the angular velocity of precession of spin axis.
The only variable in this above equation is ωp this precession velocity changes as the angle of
precession changes. Therefore its observed that as the vehicle comes to near stabilization state the tilt
of the gyroscope is oscillating within small angular range. That means the reactive couple is almost
equal & opposite to the disturbing couple.
Also the motor selected for this experiment can be replaced by another motor with different RPM &
the characteristics can be validated again.
3 OUTCOME
As mentioned in section 2.3 the prototype core in near stabilization zone tends to oscillate
within small angular range but at high frequency which leads to the stabilization of the body. If the
material used is not good enough to sustain these high frequency oscillations then the body may
shake little bit in stabilized state. The only issue with the prototype is that it shakes a bit when the
motor is set running, the reason for this being the cheap and flexible material used for the
prototype& CDs which are used as gyroscope that cannot be balanced properly, However the basic
principle of stabilization using gyroscope can be successfully demonstrated. We will now be
working on creation of a mobile prototype (remote controlled) where it can balance effectively even
in motion.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
52
4 FUTURE PROSPECTS
The above mentioned prototype thus focuses upon using gyroscopic principle (CDs as
gyroscope) for stabilization of a 2-Wheeler.
However this concept is rather implemented on a large scale to develop a Motor-bike concept
vehicle developed by Lit motors which offers the advantages of both car (comfort, safety) & bike
(enhanced mileage, less occupancy). This concept car is rather an evolution of the earlier used
gyroscopic vehicles into a modern electric vehicle that stabilizes on its own.
The vehicle has two spinning wheels/discs that are imparted on back side of the vehicle, they
mainly act as gyroscope and the precession of which is responsible for the stability of the vehicle.
Thus, the concept car developed by Lit motors is self stabilizing, however it has one more added
feature i.e. even if any external force is applied to the vehicle it comes back to its original position,
i.e. it not only stabilizes but also balances itself on its own against any disturbances in stationary as
well as moving condition.
Fig 5: C-1 a Motor bike concept vehicle
Fig 6: Components in the vehicle
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
53
The self balancing phenomenon is possible only because of the high level electronic system
imparted in the vehicle that gives the necessary signal to the gyroscope to produce a counter-
balancing effect as per the applied external force so that the vehicle comes back to the initial position
after getting displaced.
Two gyroscopes used in the concept car with high level electronics are shown in Fig: 7. this
gyroscopes axis of rotation is made to precess depending upon the direction of the external force
(disturbances) where the angle & direction of precession is decided as per the magnitude & direction
of the external force (disturbances).
Fig 7: Gyroscopes imparted in the vehicle However the speed of vehicle during cornering is the
point of focus for the company. Also the vehicle performance on bad road conditioned is not
disclosed yet by company officials.
5 CONCLUSION
The gyroscopes which are conventionally used in airplanes and ships mainly for stabilization
purpose can be effectively used for self stabilization of a two wheeled vehicle. The prototype
mentioned above was thus designed and fabricated to validate the same point. The concept with
advanced electronics is further evolved to development of a concept car by Lit motors that not only
stabilizes but also self balances even if the external force(s) is applied.
6 REFERENCES
1. N. B. Totala, Kanchan Rode, “Miniscale modelling of gyroscopic effect with application to
ship steering”, IOSR-JMCE, Vol.-11,JAN 2014, PP 47-56
2. S.S Rattan, ”Theory of Machines” , Gyroscope, PP 5.1-5.40
3. R.S Khurmi, J.K Gupta “Theory of Machines”, Gyroscope
4. Stephen C. Spry* and Anouck R. Girard∗, “ Gyroscopic Stabilization of Unstable Vehicles:
Configurations, Dynamics, and Control”
5. Kyle.D.Chapkin, Donghoon Kim,Austin .B.Probe,Peter Jorgenson,Carl C.Runco,Ahemad
H.Bani-Yonnes,John E.Hurtado “Gyroscopic Stabilization of Unsatble Vehicles”
ELSEVIER USRG 2012.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME
54
6. Beznos, A.V., Formalky, A.M., Gurfinkel, E.V., Jicharev, D.N., Lensky, A.V., Sativsky,
K.V. andTchesalin, L.S., ”Control of Autonomous Motion of Two-Wheel Bicycle with
Gyroscopic Stabilization”,Proceedings of the 1998 IEEE International Conference on
Robotics and Automation, Leuven, Belgium, May 1998, pp. 2670-2675.
7. Samoilescu, G. and Radu, S., ”Stabilizers and Stabilizing Systems for Ships”, Constantin
Brancusi University 8th International Conference, Targu Jiu, May 24-26, 2002.
8. Nukulwuthiopas, W., Laowattana, S. and Maneewarn, T., ”Dynamic Modeling of a One-
Wheel Robot using Kane’s Method”, Proceedings of the IEEE ICIT 2002 Conference,
Bangkok, Thailand, pp. 524-529.
9. Ahmed, J., Miller, R.H., Hoopman, E.H., Coppola, V.T., Bernstein, D.S., Andrusiak, T. and
Acton, D., ”An Actively Controlled Moment Gyro/Gyro Pendulum Testbed ”, Proceedings of
the 1997 IEEE International Conference on Control Applications, Hartford, CT, October 5-7,
1997, pp. 250-252
10. P. Alexander M.E. , T. Sudha M.E. , M. Omamageswari M.E., “Automatic Gear
Transmission In Two Wheelers Using Embedded System” International Journal of Advanced
Research in Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 164 - 175,
ISSN Print: 0976-6480, ISSN Online: 0976-6499.
11. Rahul M. Sherekar and Anand N.Pawar, “A Review: Rapid Prototyping Techniques For
Designing And Manufacturing of Customized Anatomical Implants” International Journal of
Mechanical Engineering & Technology (IJMET), Volume 5, Issue 3, 2014, pp. 77 - 90, ISSN
Print: 0976 – 6340, ISSN Online: 0976 – 6359.

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Self-Stabilizing Two Wheeler Model Using Gyroscope Experiment and Validation

  • 1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 48 MODELING AND VALIDATION OF PROTOTYPE OF SELF STABILIZING TWO WHEELER USING GYROSCOPE Akshay Khot1 , Nishad Kumbhojkar2 1,2 Department of Mechanical Engineering, Sinhgad College of Engineering, Pune, Maharashtra, India ABSTRACT This paper focuses on the concept of developing the two wheeler car & it’s validation with the help of prototype. This paper deals with an experiment carried out to produce gyroscopic effect on an in-house prototype. The prototype is a two wheel vehicle in which rotating discs imparted act as gyroscope to produce a counter balancing force (gyroscopic effect) when the vehicle prototype looses balance on either sides. Thus the vehicle stabilizes itself. This paper also gives a brief of a concept vehicle developed on similar grounds with an added feature. Wherein even if an external force is applied to the system the force sensors deployed in it sense the force and develop a force of similar magnitude but in opposite direction due to presence of two gyroscopes used in the vehicle, thus the vehicle does not loose it’s balance even if the external force is applied to it. Keywords: Gyroscope; Gyroscopic effect; self stabilize. 1. INTRODUCTION The gyroscopic effect is widely used in air or sea vehicles such as air planes and ships, wherein always external disturbing couple is acting on the vehicle [1]. Thus, for the stability of such vehicles it is essential to neutralize the effect of external disturbing couple which can be done by applying equal and opposite couple .Accordingly, to generate equal and opposite reactive couple it is essential to vary the magnitude and direction of velocity of precession. In the case of two wheelers this phenomenon can be effectively used for stabilizing & balancing the vehicle by means of a rotating disc i.e. a gyroscope. Consider a body rotating in a plane (plane YZ, Fig.1) & spinning about an axis (axis OX) and it’s axis of rotation or spin is made to precess in another perpendicular plane (plane XZ). The couple is induced (reactive gyroscopic INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME: www.iaeme.com/ IJARET.asp Journal Impact Factor (2014): 7.8273 (Calculated by GISI) www.jifactor.com IJARET © I A E M E
  • 2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 49 couple, Fig.2) on the rotating or the spinning body across the axis of rotation or spin in a third mutually perpendicular plane (plane XY). The converse of the above also holds good i.e..Whenever a body is rotating in a plane (plane YZ) about an axis (axis OX) and a couple is applied on a rotating body across axis of rotation or spin in another perpendicular plane (plane XY), the rotating or spinning body starts precessing in third mutually perpendicular plane (plane XZ) as shown in the adjoining fig: 1. This phenomenon is known as gyroscopic effect [2]. Fig.1: Concept of gyroscopic principle Fig 2: Directions of vectors & couples The active gyroscopic couple represents rate of change of angular momentum, and this couple must be applied to disc across the axis of spin to cause it to precess in the horizontal plane. When the axis of spin precess itself or is made to precess the shaft on which the disc is mounted applies reactive gyroscopic couple (Fig: 2). This reactive gyroscopic couple thus produced by the gyroscope is equal to the external disturbance but it is in opposite direction. Thus this couple neutralizes the effect of disturbance & stabilizes the object. (Active couple) = - (Reactive couple) (1)
  • 3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 50 2. PROTOTYPE DETAILS The objective of this model is to prove the fact that the body can be balanced on only two wheels in idle condition. The gyroscopic principle can be successfully used for creation of a prototype of a two wheel vehicle, and thus observing gyroscopic phenomenon on the same. The prototype was created using following parts: 1. Wooden Frame 2. Wooden plank 3. DC Motor 4. Four CDs(compact discs) 5. Wooden pencil 6. Round wheels 2.1 Construction The wooden frame used is bolted on the bottom wooden plank as shown in Fig.3 Trolley round wheels are fitted to the wooden plank at the bottom, the holes in the frame are drilled in order to fit the gimble of the gyroscope (wooden pencil),the DC motor supported on a piece of wood is placed on the gimble. The only pre-requisite for this setup to work is that the mass distribution, the mass should be dominant on the upper side (setup should be top heavy) of the gimble The centre of gravity is thus just above the gimble axis, CDs used as gyroscope are fitted to the shaft of the motor as shown in the Fig: 3. Fig. 3: Prototype of Two Wheeled Gyroscope (side view) Fig. 4: Wooden Frame Assembly 2.2 Working Once the motor starts rotating the CDs fitted on the motor shaft start rotating, the rotation of the CD leads to the production of the gyroscopic effect (as mentioned for disc in introduction) thus, when the wheels loose their balance due to the active gyroscopic couple a counter acting reactive gyroscopic couple is produced in the opposite direction due to gyroscopic effect thus stabilizing the prototype, This occurs on both left as well as right hand side. Thus, due to rotation of the gyroscope a counteracting reactive gyroscopic couple leads to the stabilization of the prototype.
  • 4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 51 The motor & gimble axle assembly is designed such a way that it is having heavy top. That means the center of gravity lies above the gimble axle. So the motor & gyroscope assembly tries to attain the position such that the C.G. of core will move downwards (Fig. 4). But at the same time the motor & gimble assembly is arranged within the frame having bearing reaction at ends. So only possible way for motor to attain the stability is to either lean forward or backward. So when the motor is started the body is about to fall on either side & also the motor assembly is leaning this causes the precession of spin axis. Due to this precession, according to right hand rule the reactive gyroscopic couple acts on the frame which nullifies the effect of the disturbing couple & thus stabilizes the vehicle. After few rotations & oscillations of motor, the motor & frame attains the stationary position and gyroscope is subjected to pure rolling motion about the spin axis. 2.3 Mathematical evaluation Consider the couple acting on the vehicle due to the unbalance condition, i.e., weight of prototype is distributed on two wheels only is ‘C’. Due to this couple the body of prototype tends to fall on either of the side. C = Disturbing Couple Let, I be the moment of inertia of discs about the axis of rotation. ω be the angular velocity of motor. As mentioned in section 2.2 the motor has tendency to lean forward or backward due to which the precession of spin axis takes place say it takes place by angle ‘Ө’ in time ‘t’. So the reactive couple acting on the frame due to gyroscope is given by equation C= I× ω× d Ө/dt But, d Ө/dt = ωp Where, ωp is the angular velocity of precession of spin axis. The only variable in this above equation is ωp this precession velocity changes as the angle of precession changes. Therefore its observed that as the vehicle comes to near stabilization state the tilt of the gyroscope is oscillating within small angular range. That means the reactive couple is almost equal & opposite to the disturbing couple. Also the motor selected for this experiment can be replaced by another motor with different RPM & the characteristics can be validated again. 3 OUTCOME As mentioned in section 2.3 the prototype core in near stabilization zone tends to oscillate within small angular range but at high frequency which leads to the stabilization of the body. If the material used is not good enough to sustain these high frequency oscillations then the body may shake little bit in stabilized state. The only issue with the prototype is that it shakes a bit when the motor is set running, the reason for this being the cheap and flexible material used for the prototype& CDs which are used as gyroscope that cannot be balanced properly, However the basic principle of stabilization using gyroscope can be successfully demonstrated. We will now be working on creation of a mobile prototype (remote controlled) where it can balance effectively even in motion.
  • 5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 52 4 FUTURE PROSPECTS The above mentioned prototype thus focuses upon using gyroscopic principle (CDs as gyroscope) for stabilization of a 2-Wheeler. However this concept is rather implemented on a large scale to develop a Motor-bike concept vehicle developed by Lit motors which offers the advantages of both car (comfort, safety) & bike (enhanced mileage, less occupancy). This concept car is rather an evolution of the earlier used gyroscopic vehicles into a modern electric vehicle that stabilizes on its own. The vehicle has two spinning wheels/discs that are imparted on back side of the vehicle, they mainly act as gyroscope and the precession of which is responsible for the stability of the vehicle. Thus, the concept car developed by Lit motors is self stabilizing, however it has one more added feature i.e. even if any external force is applied to the vehicle it comes back to its original position, i.e. it not only stabilizes but also balances itself on its own against any disturbances in stationary as well as moving condition. Fig 5: C-1 a Motor bike concept vehicle Fig 6: Components in the vehicle
  • 6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 53 The self balancing phenomenon is possible only because of the high level electronic system imparted in the vehicle that gives the necessary signal to the gyroscope to produce a counter- balancing effect as per the applied external force so that the vehicle comes back to the initial position after getting displaced. Two gyroscopes used in the concept car with high level electronics are shown in Fig: 7. this gyroscopes axis of rotation is made to precess depending upon the direction of the external force (disturbances) where the angle & direction of precession is decided as per the magnitude & direction of the external force (disturbances). Fig 7: Gyroscopes imparted in the vehicle However the speed of vehicle during cornering is the point of focus for the company. Also the vehicle performance on bad road conditioned is not disclosed yet by company officials. 5 CONCLUSION The gyroscopes which are conventionally used in airplanes and ships mainly for stabilization purpose can be effectively used for self stabilization of a two wheeled vehicle. The prototype mentioned above was thus designed and fabricated to validate the same point. The concept with advanced electronics is further evolved to development of a concept car by Lit motors that not only stabilizes but also self balances even if the external force(s) is applied. 6 REFERENCES 1. N. B. Totala, Kanchan Rode, “Miniscale modelling of gyroscopic effect with application to ship steering”, IOSR-JMCE, Vol.-11,JAN 2014, PP 47-56 2. S.S Rattan, ”Theory of Machines” , Gyroscope, PP 5.1-5.40 3. R.S Khurmi, J.K Gupta “Theory of Machines”, Gyroscope 4. Stephen C. Spry* and Anouck R. Girard∗, “ Gyroscopic Stabilization of Unstable Vehicles: Configurations, Dynamics, and Control” 5. Kyle.D.Chapkin, Donghoon Kim,Austin .B.Probe,Peter Jorgenson,Carl C.Runco,Ahemad H.Bani-Yonnes,John E.Hurtado “Gyroscopic Stabilization of Unsatble Vehicles” ELSEVIER USRG 2012.
  • 7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online), Volume 5, Issue 12, December (2014), pp. 48-54 © IAEME 54 6. Beznos, A.V., Formalky, A.M., Gurfinkel, E.V., Jicharev, D.N., Lensky, A.V., Sativsky, K.V. andTchesalin, L.S., ”Control of Autonomous Motion of Two-Wheel Bicycle with Gyroscopic Stabilization”,Proceedings of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium, May 1998, pp. 2670-2675. 7. Samoilescu, G. and Radu, S., ”Stabilizers and Stabilizing Systems for Ships”, Constantin Brancusi University 8th International Conference, Targu Jiu, May 24-26, 2002. 8. Nukulwuthiopas, W., Laowattana, S. and Maneewarn, T., ”Dynamic Modeling of a One- Wheel Robot using Kane’s Method”, Proceedings of the IEEE ICIT 2002 Conference, Bangkok, Thailand, pp. 524-529. 9. Ahmed, J., Miller, R.H., Hoopman, E.H., Coppola, V.T., Bernstein, D.S., Andrusiak, T. and Acton, D., ”An Actively Controlled Moment Gyro/Gyro Pendulum Testbed ”, Proceedings of the 1997 IEEE International Conference on Control Applications, Hartford, CT, October 5-7, 1997, pp. 250-252 10. P. Alexander M.E. , T. Sudha M.E. , M. Omamageswari M.E., “Automatic Gear Transmission In Two Wheelers Using Embedded System” International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 164 - 175, ISSN Print: 0976-6480, ISSN Online: 0976-6499. 11. Rahul M. Sherekar and Anand N.Pawar, “A Review: Rapid Prototyping Techniques For Designing And Manufacturing of Customized Anatomical Implants” International Journal of Mechanical Engineering & Technology (IJMET), Volume 5, Issue 3, 2014, pp. 77 - 90, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359.