Motor cycles are the common mode of transport of the middle class India. When the rider driving on the bumping road circumstances rider has to face problems results in exposure to whole body vibration. Motorcycle pitch is produced due to a sudden acceleration/ sudden deceleration or whenever the vehicle hits the pot hole / bump. The goal of this research was to design of motorcycle suspension system and optimize the pitch using nonlinear controller, modeling and simulation is carried out using MATLAB and the results are compared with existing work. To give the prominent to improve the ride eminence and increase in comfort due to substantially reduced the amplitude of disturbances by presenting nonlinear controllers to decrease the effect of travelling over rough ground.
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IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India
978-1-5090-0774-5/16/$31.00 © 2016 IEEE
1656
Optimization of Motorcycle Pitch with Non Linear
Control
Dankan V Gowda, Kishore D V, Shivashankar, Ramachandra A C, Pandurangappa C
Abstract-Motor cycles are the common mode of transport of the
middle class India. When the rider driving on the bumping road
circumstances rider has to face problems results in exposure to
whole body vibration. Motorcycle pitch is produced due to a
sudden acceleration/ sudden deceleration or whenever the vehicle
hits the pot hole / bump. The goal of this research was to design
of motorcycle suspension system and optimize the pitch using
nonlinear controller, modeling and simulation is carried out
using MATLAB and the results are compared with existing
work. To give the prominent to improve the ride eminence and
increase in comfort due to substantially reduced the amplitude of
disturbances by presenting nonlinear controllers to decrease the
effect of travelling over rough ground.
Keywords-Motorcycle, Nonlinear Control, Suspension system,
Pitch, Bump.
I. INTRODUCTION
In India many enterprises are using motorcycles, these
includes in transportation, courier services, postal delivery,
police etc. vibration in motor cycle riding had out us an
interesting case to concerning for assessment of entire body
vibration.
In any design endeavor with limited time for research and
development, tools that increase productivity or decrease
necessary testing are crucial for success. This gives rise to a
need for development tools such as computer models of
suspension, chassis, and engine systems. Because of schedule
constraints, the suspension design of most automobile two
wheeler is based primarily on steady state analysis [1]. There
are many types of automotive suspension dampers, which are
commonly referred to as shock absorbers. This is misnomer
because the damper does not actually absorb the shock. That is
the function of the suspension springs. As is well known, a
spring/mass system without energy dissipation exhibits
perpetual harmonic motion with the spring and the mass
exchanging potential and kinetic energy, respectively. The
function of the damper is to remove the kinetic energy from
the system and to cover it into thermal energy.
The suspension system in motorcycle is assembled by
springs, shock absorbers and linkages that connected to
vehicle and which intern connects to its wheels. [2]
Dankan V Gowda, Asst. professor, Dept. Of ECE, SVCE, Bangalore,
Karnataka, India (dankanies@gmail.com )
Kishore D V, Asst. professor, Dept. Of ECE, SVCE, Bangalore, Karnataka,
India (kishoredvgowda@gmail.com )
Shivashankar, HOD & Professor, Dept. Of ECE, SVCE, Bangalore,
Karnataka, India (hodece@svcengg.com)
Ramachandra A C, HOD & Professor, Dept. Of ECE, ACE, Bangalore,
Karnataka, India (ramachandra.ace@gmail.com )
Pandurangappa.C, Professor, Dept. Of Mathematics, UBDT, Davanagere,
Karnataka, India,( pandurangappa_c@yahoo.co.in )
If the road is irregular vehicle suspension isolates chassis for
these conditions.
The leading functions of vehicle suspension system are:
providing vertical defiance so the wheel can follow the bumpy
alleyway.
It maintains the steer and camber postures appropriate to
road surface. It gives immediate reaction to control forces
created by the tires and also maintain the tries in contact with
motorway with minimal load variants [3] , [4].
A motorcycle's suspension system consists of a spring
coupled to a viscous damping element, a piston in a cylinder
filled with oil. It assists vehicles handling and braking, if
provides a safety and comforts to the vehicles and passengers
by secluded from road noise, bumps and vibrations.
To reduce the effect of vibration in the motorcycles mainly
we have to use vehicle suspension system [5]. The
conventional passive system is composed of flexible
apparatuses, which is imperiled to many constraints. To make
vehicle activity in good condition and to improve the comfort
stability of vehicle we need to introduce the dynamic
suspensions so that we obtain the dynamic responses to the
road and vehicle condition because its external energy inputs
can produce the subsequent force with peripheral excitations.
The spring and damping parameters are normally fixed in
subservient suspension system which has a capacity to stock
the energy through spring and it dissipate via damper to
achieve level of conciliation between road handling, load
carrying and ride comfort [6]. These parameters in a dynamic
suspension system are having ability to hoard, dispel and
familiarize energy to the system. Depending upon the
operating conditions all these parameters is varied.
II. LITERATURE SURVEY
F. Baronti, [7] presents a system in order to compensate the
load variation which is capable of incessantly correcting the
suspension preload of motorcycle without user intrusion. This
system measures the suspension stroke by the utilization of
electronic system is based on microcontroller and linear
position sensor. To maintain average value of suspension
constant system executes a closed loop control algorithm that
adjust the preload.
F. Baronti, [8] presents the application of electronics to the
control of the rear suspension of motorcycle. The main
objective of the system designed to make the suspension work
around its optimum operating point which intern improves the
safety and comfort of the vehicles. To move the operating
point away from the optimal value, variations has to be taken
in load carried by the vehicle determine a change of
suspension spring compression. A designed electronic system
revels load changes and automatically adjusts the motorcycle
suspension preload in order to compensate the load variation
and keep the suspension to its optimal operating point.
B. Pratheepa,[9] To improve the performance a suspension
system there need to be designed mathematical model and
IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India
1657
simulation of a controller for active and passive suspensions
with Linear Quadratic Regular(LQR) controllers. A controller
is designed for active suspension system and simulated for
passive and active suspension system using MATLAB and
SIMULINK.
It is examined for both active and passive systems using
conventional method and acceleration method. After
simulation the results are represented by graphically for the
various parameters such as passenger displacement and
acceleration. From these graphical simulations got to know
that active suspension system is more proficient than passive
system [11],[12].
III. MATHEMATICAL MODELING
Consider the motorcycle as shown in figure.1To reduces
the ambiances and a force caused by uneven road
environments motorcycle suspension system is designed.
Because of road's apparent asymmetries reason the
motorcycle to move plumb as well as revolve around an axis.
By ignoring the mass of tires, the system comprises of a single
mass (Vehicle frame plus driver) that has plumb motion and
spin. Figure 1shows the system and force balance for
motorcycle suspension.
Fig.1: Motor cycle suspension system [12]
Fig.2: Undeveloped system and force stability for motorcycle suspension
system
Mass M and moment of inertia J is single rigid body can
be considered as the motorcycle structure and driver. Ya and
Yb are the input displacement at each wheel represents the
road conditions. A each axle of suspension system has Spring
and dashpot .Therefore the sum of the damping force (Fa )
(Newton's Law) and the spring force (Fb ) are the total forces
exerted on the motorcycle structure by each wheel.
And
(1)
Each spring Y a and Yb from the reference represents the
instantaneous displacement. The plumb and revolving
displacements of the center of mass, Y (t) and θ (t) are the
plumb displacement and is given by
The terms, θL a and θL b are geometry considerations as
ashown in the figure 3. Let us assume that sinθ ≈ θ for minor
angular displacements, and positive θ is a counter clock wise
rotation.
Fig.3: Geometry contemplations for plumb displacement v/s revolution angle
By combining the equations the negative sign force
expression in (1) and the displacement terms in equation (2)
gives
Fa = (Ca S +ka) [Ya – (Y - θL a)] and
Fb = (Cbs + kb) [Yb – (Y + θL b )]
or defining
Za = (CaS + ka) , Zb = (CbS+ kb) gives
Fa = Za [Ya – (Y - θL a)] and
Fb = Zb [Y b –(Y+θL b )] (3)
Finally, to satisfy Newton's law the sum of the vertical forces
we have
Ms2 Y = Za [Ya – (Y - θL a)] + Zb [Yb – (Y + θLb )]
IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India
1658
and
(Ms2 +Za +Z b)Y – (Za La - Zb Lb )θ = Z a Ya + Zb Y b 6.5)
Y0 =0 and dY/dt/t=0 = 0 gives initially no vertical motion i.e the
force stability for the system with hypothesis that motorcycle
structure and driver.
If we now perform a torque balance
(i.e.
) on the above system with the
center of mass (CM) as the pivot point, one has
and
Again, let assume that initially all conditions are zero (i.e.
t=0
From zero initial conditions finally we can write matrix for the
force and moment balance equations as shown below
For the simplification matrix can be written as
Aij and B ij terms are coefficients of Y and θ and these are
expressed as
IV. SIMULATION
Major sub-systems of the Simulink model are: Road
model and Suspension system. The front-suspension
displacement and rear-suspension displacement information
are obtained from in Longitudinal Dynamic model. The
corresponding info at tire-level is obtained by using the spring
co-efficient. When bump enable signal is received from
graphics model, Road-model is enabled.
In the Road model, front-suspension displacement and
rear-suspension displacements are evaluated based on length
and height of Bump/pot-hole as well as considering the current
vehicle speed. The block also evaluates the precise status of
bump occurrence using Bump Model. This status information
is used to select the input to the suspensionsystem
The suspension system then evaluates the pitch of the
vehicle using the front-suspension displacement and rear-
suspension displacement that are evaluated above.
4.1 Pitch: In a vehicle, during sudden acceleration, the
normal force acting on rear-wheel increases while the normal
force on the front wheel reduces. This results in a positive
pitch.
During sudden deceleration, the normal force acting on
the front wheel increases while the normal force on the rear-
wheel reduces. This results in a negative pitch.
Fig. 5: Motor cycle positive pitch
Fig. 6: Motorcycle negative pitch
IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India
1659
V. RESULTS AND DISCUSSION
The simulation parameters used in motorcycle suspension
system and road model is tabulated in Table I.
TABLE I: PRELOADED PARAMETERS USED IN MOTORCYCLE
SUSPENSION SYSTEM AND ROAD MODEL
Mass of the vehicle + rider
Distance from COG to front wheel
center
Distance from COG to rear wheel
center
Stiffness of rear suspension
Stiffness of front suspension
Damper coefficient rear suspension
Damper coefficient front wheel
Length of the bump/pothole
Height of the bump/pothole
The model simulation results for the cases of Bump and
Pot-hole are shown below. The model simulation results for
the cases of Bump and Pot-hole are shown below.
A. Pitch Due To Bump And Sudden Acceleration
/Deceleration:
Fig.7: Pitch due to bump and sudden acceleration/deceleration
Fig. 4 : Simulink model of Motor cycle Suspension and Road Model
From the fig.7, We can observe that, the vehicle is
moving with constant velocity results a zero pitch at time t=95
sec given sudden throttle due to which results in positive pitch
variation of up to 5 degrees, and at time t=140 sec vehicle
encounter a bump of height and length 1m respectively, results
a oscillatory pitch of range from 20 to 10 degrees. At time
t=185 sec given a sudden deceleration due to which
motorcycle pitch is negative with rage of -5 degrees.
B. Pitch due to Pothole:
From the fig.8,We can observe that, the vehicle is moving
with constant velocity results a zero pitch at time t=100 sec
IEEE International Conference On Recent Trends In Electronics Information Communication Technology, May 20-21, 2016, India
1660
given sudden throttle due to which results in positive pitch
variation up 5 degrees, at time t=185 sec given a sudden
deceleration due to which motorcycle pitch is negative
variation up to -5 degrees. And at time t=230 sec vehicle
encounter a pothole of height and length 1m respectively,
results a oscillatory pith range form 15 to -20 degrees.
Fig.8: Pitch due to pothole and sudden acceleration/deceleration
VI. CONCLUSION
Any automotive industry is concern the Motorcycle pitch
optimization is a thought-provoking task. In this paper
motorcycle modeling of suspension system is done and the
pitch is controlled using a Non-linear controller. Simulation
results matched very closely with the reality. Road
disturbances (bumps/potholes) simulated accurately. The
suspension model when integrated with the other components
in the vehicle model, gave very good results in terms of final
forces and acceleration. Motorcycle pitch without controller is
of range between 25 to 30 degrees. From the above results it
can be concluded that suspension with Non-linear controller,
the motor cycle pitch can be optimized to maximum of 20
degrees. Thus the reduction in pitch results better rider
comfort and road handling. Further research can be done to
measure the motorcycle pitch for random road profiles. To
investigate the consistency and thoughtfulness of the comfort
and vehicle handling indexes to influence parameters.
REFERENCES
[1] T.D. Gillespie, Fundamentals of Vehicle Dynamics, Society of
Automotive Engineers, Warrendale, USA, pp. 237, 1992.
[2] Eshaan Ayyar, Isaac de Souza, Aditya Pravin, Sanket Tambe, Aqleem
Siddiqui & Nitin Gurav, "Slection Modification and Analysis of
Suspension System for an All-Terrain Vehicle" ISSN : 2319 – 3182,
Volume-2,Issue-4, 2013.
[3] Paul Thede and Lee Parks, Motorbooks Race Tech's, Motorcycle
suspension Bible, MBI publishing company, USA, ISBN-13:978-0-
7603-3140-8, chapter1, pp. 6-7, 2010.
[4] Jain K K, Asthana R B. In: Automobile Engineering; London, Tata
McGraw-Hill, pp.293-294, 2002.
[5] Kommalapati. Rameshbabu, Tippa Bhimasankar Rao," Design
Evaluation of a two wheeler suspension system for variable load
conditions" International Journal of Computer Engineering Research,
Vol 03, Issue 4, pp.279-283, 2013.
[6] International Organization for Standardization, ISO 2631-1 (1997),
Mechanical vibration and Shock- Evaluation of Human Exposure to
whole-body vibration- Part 1: General requirements.
[7] F. Baronti.,F. Lenzi., R. Roncella., R. saletti., "Embedded Electronic
Control System for Continuous Self- Tuning of Motorcycle Suspension
[8] Preload"., 2007 Mediterranean Conference on Control and Automation,
July 27 – 29, 2007.
[9] Baronti, F., Lenzi, F., Roncella, R., Saletti, R., Di Tanna, O. "Electronic
control of a motorcycle suspension for preload self-adjustment", IEEE
Trans. On Ind. Electr. 55 , pp. 2832-2837, 2008.
[10] B. Pratheepa., " Modeling and Simulation of Automobile suspension
System", IEEE Trans. On Ind. Electr. 978-1-4244-9082, 2010.
[11] C. Liguori., V. Paciello., A. Paolillo., A. Pietrosanto and P. Sommella.,
" Characterization of Motorcycle Suspension Systems: Comfort and
Handling Performance Evaluation", IEEE Trans. On Ind. Electr. Vol.4
4122-66, 2008.
[12] Dankan V Gowda, Sadashiva V Chakrasali., " Comparative Analysis of
Passive and Semi-Active Suspension System for Quarter Car Model
using PID Controller", Proc. Of Int. Conf. on Recent Trends in Signal
Processing, Image Processing and VLSI, ICrtSIV, DOI:
03.AETS.2014.5.131.
... Application of the Hilbert transform (1D) in seismic signal analysis has been very useful, especially when we represent the signal as the real part of a complex function in time. In general terms, the compensation of the composite wrapping stem from the natural [5] departure of amplitude in sequence beginning point of view information. In a real signal, these are blended in such a way which can be confusing to visual analysis. ...
In the ground of Digital Signal dispensation, the discrete Hilbert Transform has found more and more important. The representation of a signal as the real part of a complex function in time is very much useful in many areas of signal analysis. In this paper, the demonstration of a significant improvement of a real seismic signal in the form of the complex envelope (amplitude and phase ) which may be obtained by using the discrete Hilbert transform techniques. The pulse here considered for the study is similar to the Berlage function that is used to replicate seismic signals. In addition to this, it also presents discussion on the application of Hilbert transform on the spectral factorization which is related to the minimum phase and inverse filters.
... The desired largest function force could be more exactly derived from MF tire model, The greatest friction force will occur [5]at the desired slip x * . Therefore, one can find dy dx = 0 under the condition x=x * . ...
The goal in this research is to develop a brand new ABS set of rules the use of doubtlessly available statistics approximately wheel forces. A novel ABS set of rules that uses both force and wheel slip measurements for manipulate is designed. In this study, a new integrated Nonlinear tracking Control (NTC) is evolved that includes the dynamic evaluation of hydraulic braking systems. A longitudinal dynamic behaviour of vehicle model under straight manoeuvre is simulated, which includes the angular wheel speed, vehicle velocity, wheel slip variation, brake pressure modulation and stopping distance. Mathematical modelling of Vehicle Braking System has been carried out in simulink, which employs a car pitch optimization using nonlinear control, when vehicle undergoes a surprising acceleration/deceleration and for the duration of panic braking scenario.
... The recognition and rectification capacity relies upon the how we pick the estimations of k and m. Exchange off happens in picking these qualities for greatest execution [9], [10]. Consequently, m and k should be carefully changed as per the enlarge review capacity and furthermore lessen the amount of overabundance bits. ...
... In the Later years, time has arrived, here we can connect our desktop with your mobile phone or maybe we can connect your laptop with a mobile phone so that we can control our mobile phones operation [2] from laptop or can control laptop operations from mobile phone right because they are connected each other. ...
The pace of urbanisation has risen tremendously during the last few decades. To provide a higher quality of life, urban dwellers will require a greater variety of improved services and apps. The term "smart city" refers to integrating contemporary digital technology in the setting of a city to improve urban services. There are possibilities to create new services and connect disparate application areas with each other as a result of the use of information and communication technologies in the smart city. However, to make sure the services in an IoT-enabled smart city environment remain running without depleting valuable energy resources, all of the apps have to be maintained using energy resources that are kept at a minimum. IoT can enhance a city's lighting system since it uses more energy than other municipal systems. An intelligent city integrates lighting system sensors and communication channels with enhanced intelligence features for a Smart Lighting System (SLS). To control lighting more efficiently, SLS systems are built to be autonomous and efficient. We cover the SLS and evaluate several IoT-enabled communication protocols in this article. Furthermore, we evaluated several use scenarios for IoT enabled indoor and outdoor SLS and generated a report detailing the energy consumption in different use cases. By using IoT-enabled smart lighting systems, our research has shown that energy savings are possible in both indoor and outdoor settings, which is equivalent to a forty percent reduction in energy usage. Finally, we went through the SLS in the smart city research plans.
Stress is a psychological disorder that affects every aspect of life and diminishes the quality of sleep. The strategy presented in this paper for detecting cognitive stress levels using facial landmarks is successful. The major goal of this system was to employ visual technology to detect stress using a machine learning methodology. The novelty of this work lies in the fact that a stress detection system should be as non-invasive as possible for the user. The user tension and these evidences are modelled using machine learning. The computer vision techniques we utilized to extract visual evidences, the machine learning model we used to forecast stress and related parameters, and the active sensing strategy we used to collect the most valuable evidences for efficient stress inference are all discussed. Our findings show that the stress level identified by our method is accurate is consistent with what psychological theories predict. This presents a stress recognition approach based on facial photos and landmarks utilizing AlexNet architecture in this research. It is vital to have a gadget that can collect the appropriate data. The use of a biological signal or a thermal image to identify stress is currently being investigated. To address this limitation, we devised an algorithm that can detect stress in photos taken with a standard camera. We have created DNN that uses facial positions points as input to take advantage of the fact that when a person is worried their eye, mouth, and head movements differ from what they are used to. The suggested algorithm senses stress more efficiently, according to experimental data.
It has become easier to access agriculture data in recent years as a result of a decline in digital breaches between agricultural producers and IoT technologies. These future technologies can be used to boost productivity by cultivating food more sustainably while also preserving the environment, thanks to improved water use and input and treatment optimization. The Internet of Things (IoT) enables the production of agricultural process-supporting systems. Referred to as remote monitoring systems, decision support tools, automated irrigation systems, frost protection systems, and fertilisation systems, respectively. Farmers and researchers must be provided with a detailed understanding of IoT applications in agriculture as a result of the knowledge described above. This study is about using Internet of Things (IoT) technologies and techniques to enhance agriculture. This article is meant to serve as an introduction to IoT-based applications in agriculture by identifying need for such tools and explaining how they support agriculture.
In this paper the importance of self tuning adaptive PID control scheme for automotive suspension system is explained. The objective of this study is to obtain a mathematical model for the passive and semi-active suspension system for quarter car model. Current automobile suspension system employs springs and damper with fixed coefficient. Vehicle suspension systems are typically rated by their ability to provide good road handling and improve passenger comfort. Passive suspension offers either one of these two conflicting criteria. However, Semi-Active suspension poses the ability to provide both, handling and comfort by directly controlling the suspension force actuators. In this study, the self tuning Proportional Integral Differential Controller (PID) technique is implemented to the semi-active suspension system for a quarter car model. Comparisons between passive and semi-active suspension system are performed for different types of road profiles. The performance of the P, PD, PI and PID – controllers are compared with the passive suspension system.
In this paper the importance of self tuning adaptive PID control scheme for automotive suspension system is explained. The objective of this study is to obtain a mathematical model for the passive and semi-active suspension system for quarter car model. Current automobile suspension system employs springs and damper with fixed coefficient. Vehicle suspension systems are typically rated by their ability to provide good road handling and improve passenger comfort. Passive suspension offers either one of these two conflicting criteria. However, Semi-Active suspension poses the ability to provide both, handling and comfort by directly controlling the suspension force actuators. In this study, the self tuning Proportional Integral Differential Controller (PID) technique is implemented to the semi-active suspension system for a quarter car model. Comparisons between passive and semi-active suspension system are performed for different types of road profiles. The performance of the P, PD, PI and PID – controllers are compared with the passive suspension system.
Comfort and safety of vehicles significantly depends on the behavior of the suspension system. This is particularly true in two-wheel vehicles where the equilibrium is fundamental. Variations of the static load on the vehicle determine a compression of the suspension spring that modifies the static equilibrium point with respect to the optimal value. The system we describe is capable of continuously correcting the suspension preload of a motorcycle without user intervention, in order to compensate the load variations. The electronic system is based on a microcontroller and a linear position sensor that measures the suspension stroke. It executes a closed-loop control algorithm that adjusts the preload and maintains the average value of the suspension stroke constant. The experimental results coming from road tests performed on a scooter are reported and discussed.
In this paper, measurement set-up and data analysis for the characterization of two-wheel vehicles suspension systems with regard to comfort and road holding is proposed. The main aim is the definition of a method for the experimental quantification of the suspension system performance. An application of the method to the verification of both comfort and safety assured by a control strategy for semi active suspensions is reported.
- B. Pratheepa
This paper describes the mathematical model and simulation of controller for active suspension with Linear Quadratic Regulator (LQR) controller and about the improvement in performance. In this work, a controller is designed for active suspension system and simulated for both passive and active suspension system using SIMULINK in MATLAB. Two controller design approaches, namely conventional method (CM) and acceleration dependent method (ADM) have been examined for the active system. Results are graphical representation of various parameters like Passenger displacement and acceleration, RMS acceleration etc which shows active suspension system is more efficient than Passive system. From this simulation, we can say that system has better potential to improve both the ride comfort and road holding.
- Thomas D. Gillespie
This book attempts to find a middle ground by balancing engineering principles and equations of use to every automotive engineer with practical explanations of the mechanics involved, so that those without a formal engineering degree can still comprehend and use most of the principles discussed. Either as an introductory text or a practical professional overview, this book is an ideal reference.
This paper describes the application of electronics to the control of the rear suspension of a motorcycle. The aim of the system is to make the suspension work around its optimal operating point, so that the safety and comfort of the vehicle can be improved. In fact, variations of the load carried by the vehicle determine a change of the suspension spring compression that moves the operating point away from the optimal value. Spring compression can also be changed by varying the suspension preload. The electronic system described here reveals load changes and automatically adjusts the motorcycle suspension preload in order to compensate the load variation and keep the suspension to its optimal operating point. The system is based on a linear position sensor that monitors the actual stroke of the suspension and a microcontroller that executes the control algorithm and drives the preload actuator. Road tests carried out on a motor scooter equipped with the system show its correct functionality and demonstrate the achievement of a better operation of the suspension with simple hardware and cost affordable for the two-wheel market.
Fundamentals of Vehicle Dynamics, Society of Automotive Engineers
- T D Gillespie
T.D. Gillespie, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Warrendale, USA, pp. 237, 1992.
- K K Jain
- R B Asthana
Jain K K, Asthana R B. In: Automobile Engineering; London, Tata McGraw-Hill, pp.293-294, 2002.
Motorbooks Race Tech's, Motorcycle suspension Bible
- Paul Thede
- Lee Parks
Paul Thede and Lee Parks, Motorbooks Race Tech's, Motorcycle suspension Bible, MBI publishing company, USA, ISBN-13:978-0-7603-3140-8, chapter1, pp. 6-7, 2010.
Source: https://www.researchgate.net/publication/306507447_Optimization_of_Motorcycle_Pitch_with_Non_Linear_Control
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