parameterization and real time simulation of an …
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LAPPEENRANTA UNIVERSITY OF TECHNOLOGY
LUT School of Energy Systems
LUT Mechanical Engineering
PARAMETERIZATION AND REAL TIME SIMULATION OF AN EXCAVATOR
Examiners: Professor Aki Mikkola
D. Sc. (Tech.) Kimmo Kerkkänen
ABSTRACT
Lappeenranta University of Technology
LUT School of Energy System
LUT Mechanical Engineering
Manouchehr Mohammadi
Master’s thesis
2017
79 pages, 59 figures, 5 tables and 8 appendices
Examiners: Professor Aki Mikkola
D. Sc. (Tech.) Kimmo Kerkkänen
Keywords: Real-time Simulation, Excavator model, SIM platform, Multibody system,
Model parameterization.
This master’s thesis has been done for simulation, Companies working with real-time
simulation concept, and training target in a way that a vehicle, an excavator, is developed by
parameterization method which obtains a new solution to have a simulated model with a
number of customizable parts, values, and bodies. In other meaning, a user can opt her/his
favorite part/body based on her/his aim.
From the beginning of this project MeVEA software selected as the real-time simulation
software in which all cooperative software should be along MeVEA. The project goal was
create a user-friendly way to present a simulation model with ability of being customized. A
customized model prepares an opportunity for Companies in this field to analyze new models
with a significant spent budget reduction in comparison of previous solutions.
Parameterized simulated model, in this project an excavator, can be used to create a desired
model and simulate it, then its results can be analyzable in order to figure out the optimum
options of the simulated model for each mission and function. At first, it was decided to
create only one way to have a customizable model which was creating an excel file as an
interface that the user could select her/his options among all options, then using a python
code as a bridge between the excel file and MeVEA, however, in the following one other
file created as well.
ACKNOLEDGEMENTS
This thesis has been done at the Laboratory of Machine Design, Department of Mechanical
Engineering at Lappeenranta University of Technology (LUT).
I would like to express my sincere gratitude to my Professor Aki Mikkola for his valuable
guidance, advice and high level of patience. His comprehensive knowledge about the project
in all aspects could help and inspire me to figure out concepts in a best way and overcome
difficulties during this master’s thesis. I had a great opportunity to work with him because
of his permanent presence with extra-ordinary responsibility in every step of this work.
I want to thank my supervisor Kimmo Kerkkänen, as the second supervisor, about the subject
of thesis, appreciable support and constructive feedback which could guide me during my
master’s thesis. I also appreciate help which I had from my colleagues in CoSIM project in
Machine Design Laboratory. Thanks to MeVEA staff cooperation in format of a number of
workshop.
Finally, especial thanks to my dear family who supports me during my life.
Manouchehr Mohammadi
Lappeenranta, June 30, 2017
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TABLE OF CONTENT
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF CONTENT
ABBREVIATION AND SYMBOL LIST
1 INTRODUCTION ..................................................................................................... 10
1.1 SIM Platform – A Glance description ................................................................. 10
1.2 Research Questions .............................................................................................. 12
1.3 Aims and objectives ............................................................................................. 12
1.4 Research Methods ................................................................................................ 13
2 METHODS AND METHODOLOGIES .................................................................. 15
2.1 Literature Review ................................................................................................ 15
2.1.1 Simulation in researches .................................................................................. 15
2.2 Principles of a multibody system and its equations ............................................. 21
2.2.1 Global and local coordinates ............................................................................ 23
2.2.2 Rotational coordinates – Kinematic Constraint Equations .............................. 23
2.2.3 Kinematic Joints Constraints ........................................................................... 24
2.2.4 Equations of Motion ........................................................................................ 26
2.2.5 Integration Methods in Dynamic Analysis ...................................................... 28
2.3 Simulation in practice .......................................................................................... 34
2.3.1 Simulation ........................................................................................................ 34
2.3.2 Simulators ........................................................................................................ 34
2.3.3 Marketing ......................................................................................................... 35
2.3.4 Customizable Model ........................................................................................ 36
2.3.5 Employed Software .......................................................................................... 37
2.3.6 MeVEA ............................................................................................................ 37
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2.3.7 CAD Software – SolidWorks .......................................................................... 39
2.3.8 Blender ............................................................................................................. 39
2.3.9 Python and Excel ............................................................................................. 40
2.4 Four-bar Mechanism ............................................................................................ 41
3 CASE STUDY- THE EXCAVATOR ....................................................................... 46
3.1 Principles of Excavator ........................................................................................ 47
3.2 Simulated industrial vehicle ................................................................................. 48
3.3 Editable Parameters ............................................................................................. 48
3.3.1 Bucket and lifting system ................................................................................ 49
3.3.2 Hydraulic circuit system .................................................................................. 51
3.4 Data Selection ...................................................................................................... 54
3.4.1 Assembly files approach .................................................................................. 54
3.4.2 Coding files approach – User interface ............................................................ 57
3.5 Method – A coupler between Excel and MeVEA Modeller ................................ 58
3.6 Model in MeVEA – Working and Dynamic Simulation Interface ...................... 59
3.7 Results .................................................................................................................. 60
3.7.1 Customization for the Bucket – combination and comparison ........................ 60
3.7.2 Customization for the Hydraulic Circuits – Combination and Comparison .... 63
4 ANALYSIS ................................................................................................................. 67
4.1 Analysis for employment of different Buckets .................................................... 67
4.2 Analysis for employment of different hydraulic circuits ..................................... 71
4.3 Future work .......................................................................................................... 75
4.3.1 Using Software and their connections ............................................................. 76
4.3.2 User-friendlier interface - Gamification .......................................................... 76
4.3.3 Further customizations - Analyze section ........................................................ 77
4.3.4 Visualization of models and environments - Environment customization ...... 77
5 CONCLUSION .......................................................................................................... 78
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LIST OF REFERENCES .................................................................................................. 80
APPENDIX
Appendix 1: Concept of the global coordinate system.
Appendix 2: Rotational coordinates in spatial MBS.
Appendix 3: The revolute joints among bodies and their equations.
Appendix 4: The equation of motion for a constrained system.
Appendix 5: The equations related to a four-bar mechanism.
Appendix 6: Detailed data of Volvo excavators.
Appendix 7: The python script code for making the model customized.
Appendix 8: Results for the medium and big bucket and medium and big cylinder-piston
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SYMBOL AND ABBREVIATION LIST
a - Position vector on a body
A - Rotational transformational matrix
𝐀′- Final rotational matrix
b - Position vector on a body
B - The element of the final rotational transformational matrix
C - Constraint Equations
Cq - Jacobian matrix of the four-bar mechanism
𝐂𝑡 - Velocity matrix of the four-bar mechanism
D - Jacobian matrix
e - Euler parameter
e - Euler vector
E - The element of the final rotational transformational matrix
f - Function
f - Force vector
g - Generalized force
g - Ground acceleration
h - The integration step size
i - Name of a body
𝑖1 - A name of a particle
I - Unit vector
I - Inertia
j - Name of a body
J - Global inertia tensor
l - Length
m - Mass
M - Mass matrix
M1 – Torque applied on a four-bar mechanism
n - Number of coordinates
n1 - Order of a differential equation
𝑛𝑚 - Moments which a body is affected by a force
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O - The element of the final rotational transformational matrix
P - Name of a point on a body
𝑃′- Order of the error equation
pi - Euler parameters in a matrix
p - Euler parameter’s matrix
q - A generalized coordinate vector
r - Vector of position
�̇� - Vector of velocity
�̈� - Vector of acceleration
R - Position
S - Function name
s - Position vector from bodies to their connecting joint
𝐬′- Constant Vector
�̇� - Velocity vector from bodies to their connecting joint
t - Time
T - Kinetic energy
𝐯 – Velocity vector
�̇� - Acceleration vector
V - Potential energy
y - Variable to be integrated
ω - Angular velocity
�̇� - Angular acceleration
𝜑 – Angular variable
ξ - The body-fixed vectors
Φ - Function for kinematic constraints
�̇� - Constraint of the velocity
�̈� - Constraint function of the acceleration
ɣ - Multiplication of Jacobian matrix and acceleration
𝜆 - Lagrange multipliers
α - Positive constant
β - Positive constant
𝜎 - Angular Variable name in a rotational matrix
𝜑 - Angular Variable name
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𝛹 - Angular Variable name in a rotational matrix
θ - Angular Variable name
𝛼′- Angular position for a four-bar mechanism
𝜃′- Angular position for a four-bar mechanism
𝜑′- Angular position for a four-bar mechanism
�̇�′- Angular velocity for a four-bar mechanism
�̇�′- Angular velocity for a four-bar mechanism
�̇�′- Angular velocity for a four-bar mechanism
𝜏 - Torque
ɛ - Truncation error
ɛ𝑔1- Global or total error
ζ - The body-fixed vectors
η - The body-fixed vectors
BEV - Battery electric vehicles
CAD - Computer-aided design
DAE - Differential Algebraic Equations
DES - Discrete event simulation
FEM - Finite Element Method
MBS - Multibody System
MSD - Multibody System Dynamics
LUT - Lappeenranta University of Technology
ODE - Ordinary Differential Equation
RLV - Reusable Launch Vehicles
SD - System Dynamics
SIM - Sustainable product processes through simulation
XML - Extensible Markup Language
3D - Three dimensions
s - Spherical
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1 INTRODUCTION
Simulation can be helpful to create or improve many models which are so expensive to
produce them in reality. In fact simulation is a definition of movements and processes of a
body or bodies through the time. In many cases, modifying and changing in a model is not
cost-effective, however a precise simulation model can catch a set of data for parameters and
gives analysis and results in details. These results can clear that is changing/modifying in
any values in the simulation model leads to improvement of its performance or not.
Moreover, simulation has a couple of economic trends. For instance: (Bangsow, 2010, p. 18)
The variation of a product under simulation will increase.
Because of easy-modifying, the demand to upgrade in quality will increase which
consequences high quality based on customers’ requirements.
Customization and high flexibility in a model can be impressive to increase the
demand of bazaar in order to obtain this approach.
Two striking consequences; life cycle time and also man power will decrease
tremendously.
In manufacturing and design methodologies points of view, using simulation in real job have
many benefits such as shorter lead time, decreasing man power, decreasing in production’s
steps and etcetera. With three major phases, in every simulation model, the questions which
arising for the model can be responded; Planning Phase, the first phase, is a phase to make a
plan to find out all the possibilities and potentials of a model. Implementation phase, the
second one, assists to test the performance and problems of the model during simulation.
Also, the future requirements and limitations of a simulated model can be found in this phase.
Finally, the operational phase which collaborates to test for controlling the alternatives of a
model. Moreover, the level of the model’s quality can somehow be traced. (Bangsow, 2010,
p. 18)
1.1 SIM Platform – A Glance description
To implement the simulation model, after modelling, a platform is needed to test the
capability and movements in a real situation. SIM platform is a capability with a number of
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powerful simulators at Lappeenranta University of Technology (LUT). The concept of the
SIM Platform is to avoid the outdated and time consuming approaches to obtain the results
and trends to the new and practical ways getting aims.
SIM platform has an approach to have a real-time simulation obtaining energy efficient
solutions and Also it looks to extend a design simulation ‘’from a single machine to entire
production systems’’ which leads to a comprehensive analysis about machines performance
in a machines’ complex (LUT, 2016).
Simulators are tools obtaining information from the simulation models. A simulator consists
of two parts which are working together; the hardware part which gives a realistic feedback
with aim of sound and force feedback simultaneously. The second part is the software parts
which for this thesis is the MeVEA software which is a Finnish-based software in
Lappeenranta city (About Mevea, 2017) . Also, there are some simulators at LUT
(Lappeenranta University of Technology) in the electrical and intelligent machine’s
laboratories (Design Laboratory, 2017). Figure 1.1 depicts simulators which are used for
this dissertation work.
Figure 1.1. Simulators at the Lappeenranta University of Technology.
One of the striking aspect of the simulation is being used in many fields. Some of them are
human-centered simulation process and some of them are free of human (Byrski, 2012). A
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simulation is applicable in energy consumption, help to simulate traffic contains BEV
(Battery Electric Vehicles) vehicles and also other kinds of vehicles and roads (Pina, 2013,
p. 13). In addition, the simulation is using in physics and automotive industry to have a great
and new kinds of power transmission for vehicles especially hybrid vehicles (M.Dede, 2014,
pp. 4-21). Game industry uses simulation to increase the quality of its game, graphics and
reality feeling for its users. With using real graphics, many sensors, and feedbacks such as
force feedback, this industry is improving many aspects such as customer’s satisfaction and
its market, as the main goal.
1.2 Research Questions
Research questions frequently appear after encountering with a research problem or issue.
The main problem about this project is: An adjustable customization for a simulation model
always is time consuming and not cost effective. The MeVEA software uses a readable text
file which has all data about a model in it to run a model in its interfaces. There are some
options to have a customizable model such as making some alters in its interface, making
some changes in mentioned readable text file and etcetera. The following questions are the
research questions which come to the mind:
- How can it be possible to get access to all data of the model in a way that it could be
changeable and easy to save?
- What is the suitable method to find out desirable data and select among them and
make a ready model to run?
- Is it possible to have a customized model that a user could select a wide range of
data, instead of only few options, among the sub-assemblies and assemblies and
MeVEA software collects them and makes the model without any concerning about
their adjustment?
- Is the selected configuration made by the user practicable or reasonable?
- Is there any demand to have a wide range of options for model’s parts?
- Which Parameters or parts in the model can be changeable?
1.3 Aims and objectives
In this dissertation work a simulation model in MeVEA software will be developed to be
customizable. At the moment, in simulation point of view, a model has a set of constant
parameters to simulate it and extracts the desirable results and analyzes them. Changing
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adjustable parameters for a model with old ways is time-consuming, thus it is extremely
convenient acquiring a way to create a model which have a capability to change its data or
parameters precisely and quickly.
The main objective of this thesis is to make an adjustable simulation model with user’s
selections. In the other words, there is a simulation model in MeVEA software which collects
data from a user and makes a model, in this case an excavator, according to given data. The
point is, data are coming from some assemblies and sub-assemblies and will use to make the
model and all these assemblies must be well-matched to each other that the user could feel
the effects of her/his selections.
For this dissertation work, the alterable attributes for a simulated excavator model are:
Dimensions of the bucket in visual and collision modes and its mass accordingly.
Dimension of the cylinder and piston for the dipper arm.
The amount of the nominal flow rate going into the dipper arm cylinder.
The parameters which a user will select can cause a simulation model with a capability to do
a task fast in comparison of a normal real model, however with high fuel consumption. On
the contrary, it can be a model with less fuel consumption but slower than before. All
graphics for the environment, customizable parts of the model are adjusted with other fixed
parts.
Future aims is to have more customizations parameters and parts of a model, like the
excavator, with a way to analyze them based on some practical parameters. In the other
words, it will be a model and a way to analyze which model is cost-effective, based on fuel
consumption and working hour time, or which one is more reliable based on wearing,
depreciation, maintenance and easy to work. Future aims will be discussed at the end of this
dissertation work in detail.
1.4 Research Methods
Tools which are used in this dissertation work are the MeVEA software as a real-time
simulation to create a simulation model with other software as its assistants. It should be
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noticed that during creation, other software such as SolidWorks, Blender, Python and Excel
are involved. Afterwards, the simulation model can be run.
In the design section, MeVEA creates an XML file for data of the model and there are some
ways to edit that file in order to have changing capability of the model, however, creating an
XML code with some assemblies in it, (which will be explained in next chapters), and also
writing a python code and run it with a excel code are the most feasible ways to reach to the
bottom line of this dissertation work.
As the Procedure of this thesis, there is a simulation model which has fixed parts and
parameters, and modifiable ones. With the ways noted in design section, the model will be
editable. Simultaneously, the visualization and collision graphics will adapt with assist of
SolidWorks and Blender software and finally the whole model can be run in the MeVEA
platform. Figure 1.2 demonstrates the story line and procedure of this research.
Figure 1.2. The procedure of building and running a simulation model.
As in figure 1.2 has shown, there is an editable model which collects data from the user side
and has interaction with the graphics part and uses appropriate graphics and creates the ready
model. In this dissertation work there are three options for the bucket and also three options
for the hydraulic circuit system.
Gathering
Data / Editing
Tools
Editable
Model
Graphics
Simulate Concluded
Model
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2 METHODS AND METHODOLOGIES
The first part of this chapter is literature review which is about previous researches in real-
time simulation field in order to have a new concept or new idea about customization. Then
principles of a MBS will be discussed. Moreover, simulations and simulators will be under
consideration in being practical point of view. Finally, a four-bar mechanism and its equation
will be explained.
2.1 Literature Review
When a new project and idea comes in mind, it is always logical to have a look and review
to previous researches beforehand to see what researches have already done and what are
their approach to solve a problem. With a literature review previous researches’ results,
analysis can be found and it is possible to have a comparison among them and figure out
their overlapping at work, their idea about the project and title which is under consideration.
Moreover, by a careful literature review it can be possible to find barriers and limitations in
front of previous researches.
In this chapter, previous works in the field of simulation, real-time simulation and earlier
efforts can be discussed, however, because the simulation are very practical in a tremendous
amount of fields, it is rational to have a review in real-time simulation about industrial and
widely-used vehicles, especially in past efforts about parameterization.
2.1.1 Simulation in researches
For the review in previous researches, a practical database have been used which is LUT
FINNA – Wilma. It has covered enormous amount of articles, conferences and books and
has reviewed most scientific databases and journals such as publications in Lappeenranta
University of Technology, Springer, and so on. One of the effort to have done by Steffen
Bangsow in which to aim to the simulation solution, he suggested that steps formulation of
problems and targets, data collection, modelling and running the model, and analyze the
results is a rational chart to solve the simulation problem. (Bangsow, 2010, p. 2). Figure 2.1
shows the steps of Steffen Bangsow, however in his research it did not mentioned a way to
figure out the customization of a simulated model.
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Figure 2.1. Phases of a simulation problem based on Steffen Bangsow research.
Edward Robert Comer and his colleagues have patented an approach in real-time simulation
in training part which all of their system’s parts have interconnection together. As figure 2.2
has demonstrated, there is a data-driven simulation kernel including some sections. In fact
this patent is invented ’’ for training technical skills on equipment, machinery, and software-
based systems’’. In this creation they tried to have a training environment with help of
simulation which is realistic and reliable. (Comer, 2005)
Figure 2.2. Patented application for training with help of simulation (Comer, 2005).
Comer has tried to make connections between the core of simulation training model, such as
XML interface and simulation data, and a simulation client. This aspect which can get access
to some important parts of a model is valuable however the drawback of its system is having
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limitation in order to work with it. In the other words, it cannot emerge from training part
and extend to other parts which can be useable for not-trained user.
Based on previous researches, there are two simulation approaches, discrete-event
simulation and system dynamics, which are called DES and SD simultaneously. Discrete-
event simulation and also system dynamics approaches are based on development
performance of a simulated vehicle through time. Furthermore, they can identify some
improvement for models which can be done in the future of a model. System dynamics
approach is created based on differential equations. (Tako , 2010, p. 784)
J A Ninan has tried to have a customizable model with help of internet. Figure 2.3 illustrates
a chart to obtain a feasible and practical model. In this method data gathers from a user and
creates the CAD model. In this implementation method, it considers two steps to check
feasibility of the model, one of them is after building FE model and analyze it which if it
was feasible it can generate CAD model and extract results. The other consideration is after
creating FEA model and analyze its practicality that if it was not functional, it should be
terminated.
Figure 2.3. Implementation to finalize a CAD model ready to analyze (Ninan, 2006, p. 533).
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A practical attempt to consider customer as an effective option during design is working on
the internet-based framework by J A Ninan. With help of computer-aided design (CAD) and
finite element method (FEM), he tried to allow to customers doing some customization via
internet. (Ninan, 2006, p. 529) He also mentioned that before his research there were some
researchers such as Gilmore and Pine who they have researched about mass customization
and they provided four approaches to make a customizable model; collaborative, adaptive,
cosmetic, and transparent approaches. The research of J A Ninan has some drawbacks such
as being time-consuming in order to analyze in finite element model, though is a kind of
inspiring research about making a model customizable. As figure 2.4 has showed, he have
tried to use FE Analysis and other optimization tools with interaction via internet with
customers to create more appropriate and reliable results which can be modified based on
feedbacks from customers and design sections. (Ninan, 2006, p. 531)
Figure 2.4. Phases in Mass Customization model of Ninan (Ninan, 2006, p. 531).
Having an opportunity to work with a model in a way that more users can have accessibility
to demonstrate their favorite options and specifications is one of the imperative aims for
many kinds of customization and simulation. For instance, Scott Fortmann-Roe have tried
to explain a kind of access to users to present its idea and model, to a client which can display
and simulate the model as well.
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Figure 2.5 depicts this idea schematically. (Fortmann-Roe, 2014, p. 32) Despite of not
exactly customization in simulation model, the aim of this effort could lead a kind of remote
control via internet and share the results of each simulated model.
Figure 2.5. Presence of a client which can simulate and display results based on users model
(Fortmann-Roe, 2014, p. 32)
Moreover other researchers have worked on parameterization issue; Schwarz Bachinger
prepaid and demonstrated a unique way to parameterize ‘’all types of gear transmission
topologies’’ (Schwarz, 2015, p. 1). They have tried to provide a customizable model for a
drivetrain model in its friction elements, clutches, figure 2.6.
Figure 2.6. A block diagram of inputs and outputs of a drivetrain model to parameterize the
friction elements (Schwarz, 2015, p. 1).
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For model shown in figure 2.6, the parameterization is just considered slipping and open
modes for clutches and they have written a Java script as the environment, which means all
specifications needed to model a drivetrain. (Schwarz, 2015, pp. 1-2)
A Kaylani and his colleagues have introduced a NASA approach in producing generic
model. In order to cut cost, NASA has worked on a project named RLV, Reusable Launch
Vehicles, which provides an opportunity to launch more flights per year for shuttles. With
help of a kind of simulation method named DES, discrete event simulation, the functional
performance of a launch vehicle can be analyzed and moreover, it can assess that is a
parameterized parts in a launch vehicle effective to decrease the amount of budget of a flight
or not? After discussion and consideration of model fidelity, generalization in model, and
function ability of the model (means that the model should be easy to customize and
configure), they have shown a story line to attain a generic model in figure 2.7. (Kaylani,
2007)
Figure 2.7. Steps to attain to a generic model in RLV approach (Kaylani, 2007, p. 4)
Ren, Q and D.A.; Morris, worked on design for an EV, electric vehicle, to figure out the
effect of variety kinds of transmission on an electric vehicle performance. At first they tested
an EV with a generic motor with the power of 40 kW in some kinds of power transmission;
single transmission ration, continuously variable gearing mode, and a multispeed gearbox.
They have changed crucial parameters such as total vehicle mass, wheel diameter, rolling
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resistance coefficient et cetera to analyze the effect of these changing in an EV. Employment
of any kinds of power transmission for an electric vehicles has some advantages and
disadvantages in fuel consumption. Figure 2.8 demonstrates a comparison among three kinds
of power transmission in separate driving cycle. It should be noticed that, at this level,
discussing about kinds of driving cycles and their differences is not requirements of this
dissertation work.
Figure 2.8. A comparison among three kinds of power transmission used in an electric
vehicle (Ren, 2016, p. 1264).
Figure 2.8 illustrates comparison among mentioned power transmissions and it shows using
any of power transmission has its benefits. At the moment using a customizable simulation
model with a capability of easy to switch among different kinds of power transmission with
accurate analyze is needed to depict the advantages and drawbacks of usage of each power
transmission.
After a couple of reviewing in other researchers about real-simulation and editable models,
there is a lack of a comprehensive approach to satisfy all vital issues was felt. An approach
which can take care of some major issue such as not being time-consume, easy to use, high
feasibility, and easy to save. Using MeVEA software as a real-time simulation software
interacting with other software creates a customizable model which is reliable and cost-
effective and can be helpful for any companies in design, manufacturing and test sections.
2.2 Principles of a multibody system and its equations
This chapter presents a general point of view of the concepts of multibody System Dynamics
(MSD), global and local coordinates, kinematic constraint equations and equations of
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motion. Many signs from the history of the mechanical engineering root illustrate that
knowledge multibody system dynamics is founded on classic mechanical mechanism,
satellites and robots. ‘’Multibody system dynamics is characterized by algorithms or
formalism, respectively, ready for computer implementation.’’ Precise and practical
interaction with CAD software, parameterization, real-time simulation, joints and
connection among the components, control mechatronic systems and the analysis of the
whole multibody are the main perspectives and concepts of Multibody System Dynamics
(MSD). Moreover, in analysis of MSD’s treatment, there is an interest in using reduction
methods to have a too far precise results of integration codes for ODE, Ordinary Differential
Equations, and DAE, Differential-algebraically equations. (Schiehlen, 1997, p. 149)
The equations which explain a motion for multibody systems are known as Newton-Euler
equations. The principle of equation of motion for MSD will be explained later in this report.
In 1788, Lagrange presented an analysis of the system of mechanical constraints. DAE and
ODE are Lagrange’s equations which explain the total kinetic and potential energy of the
system. In this system, the constraints and generalized coordinates should be taken into
account. (Schiehlen, 1997, pp. 1-2) In a clear way, a multibody system (MBS) has
connections with two groups of vital characters; first, mechanical components which can
illustrate displacements and the second is relations among bodies, constraints, with the
kinematic joints. ‘’ In the other words, a multibody system encompasses a collection of rigid
and/or flexible bodies interconnected by kinematic joints and possibly some force
elements’’. Based on the demands of a MBS, the body for a multibody system can be
described as a rigid or flexible body. With using six generalized coordinates with six degrees
of freedom, DOF, the motion of any rigid body can be demonstrated while 3D space has
defined. (Flores, 2015, p. 1)
After definition and consideration of joints among parts in a MBS system, in a spatial case,
the number of the degree of freedom will reduce. (Flores, 2015, p. 5) Figure 2.9 illustrates
types of coordinates which are common explaining the MBS. (Flores, 2015, p. 7)
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Figure 2.9. Frequently used coordinates in MBS (Flores, 2015, p. 7).
2.2.1 Global and local coordinates
Three variables which are independent from each other can describe the displacement of a
free moving particle ‘’i1’’ in 3D space and the vector ‘’r’’, vector of position, is (Flores,
2015, p. 11):
𝐫𝑖1 = {𝑥𝑖1 𝑦𝑖1 𝑧𝑖1}𝑇 (2.1)
With the same way, above definition can be used for a rigid body and its location. Also its
orientation can be explained with respect of a reference system. (Flores, 2015, p. 12) In
appendix 1, the concept of global coordinate system can be found.
2.2.2 Rotational coordinates – Kinematic Constraint Equations
There are some approaches to explain rotational coordinates in 3D MBS which are Euler
Angles, Bryant Angles and Euler Parameters. With aid of six coordinates, three translational
and three rotational ones, the location of any rigid body can be discovered. In appendix 2,
all the steps for rotational coordinates in spatial MBS can be found.
A constraint always embeds a kind of limitation or restriction in the degree of freedom for
one or more bodies. With assistance of the concept of generalized coordinates, the location
and orientation of bodies can be defined and now it will be known with a vector,𝐪 =
{𝐪1, 𝐪2, 𝐪3, … , 𝐪𝑛}𝑇 that n is the number of coordinates. In this report, Φ depicts the
constraint with a denoted parameter and a number. The parameter illustrates the type of
24
constraint and the number is the number of equation. For instance, 𝚽(s,2) shows that there is
a spherical constraint with two equations. (Flores, 2015, p. 31) The kinematic equation based
on the vector of body-coordinates can be shown as (Flores, 2015, p. 33)
𝚽 ≡ 𝚽(𝐪) = 0 (2.2)
Where q shows the vector 𝐪𝑖 = {𝐫𝑖 𝐩𝑖}𝑇 which has ri, which includes three translational
coordinates,𝐫𝑖 = {𝑥𝑖 𝑦𝑖 𝑧𝑖}𝑇, pi is Euler parameters, and i is a body name. With a derivation
of Φ, the velocity constraints will appear (Flores, 2015, p. 33)
𝚽 = 𝐃𝐯 = 0̇ (2.3)
D is the Jacobian matrix. v is the below equation (Flores, 2015, p. 28)
𝐯𝑖 = {𝐫�̇�
𝛚𝑖} (2.4)
While the omega is the angular velocities vector (Flores, 2015, p. 28)
𝛚𝑖 = {𝛚𝑥 𝛚𝑦 𝛚𝑧}𝑖𝑇 (2.5)
The second derivative of Φ is (Flores, 2015, p. 33)
�̈� ≡ 𝐃�̇�+�̇�𝐯=0 (2.6)
Derivative of the velocity is the derivative of the equation a2.1 in appendix 2. Term 𝐃�̇� is
denoted as ɣ. (Flores, 2015, p. 33)
2.2.3 Kinematic Joints Constraints
With three kinematic joints, the spherical, revolute and spherical-spherical joints, a
tremendous amount of 3D MBS can be studied in real simulation point of view. For a
spherical joint, figure 2.10, it allows three relative rotations. ‘’Therefore, the center of the
spherical joints has constant coordinates with respect to any of the local coordinates systems
25
of the connected bodies, i.e., a spherical joint is defined by the condition that the point Pi on
body i coincides with the point Pj on body j. This condition is simply the spherical constraint,
which can be written in a scalar form as”: (Flores, 2015, p. 43)
𝚽(s,3) ≡ 𝐫𝑗𝑃 − 𝐫𝑖
𝑃 = 𝐫𝑗 + 𝐬𝑗𝑃 − 𝐫𝑖 − 𝐬𝑖
𝑃 = 0 (2.7)
Figure 2.10. Spherical joint between two bodies, i and j (Flores, 2015, p. 44).
The first derivative of the Eq. 2.7 describes the equation of the velocity constraint (Flores,
2015, p. 44):
�̇�(s,3) = �̇�𝑗 + �̇�𝑗𝑃 − �̇�𝑖 − �̇�𝑖
𝑃 = 0 (2.8)
The second derivative of the Eq. 2.7 illustrates the equation of the acceleration constraint
(Flores, 2015, p. 44):
�⃗⃗⃗� ̈(s,3) = �̈�𝑗 − �̃̇�𝑗𝑃𝛚𝑗 − �̃̇�𝑗
𝑃�̇�𝑗 − �̈�𝑖 + �̃̇�𝑖𝑃𝛚𝑖 + �̃�𝑖
𝑃�̇�𝑖 = 0 (2.9)
The revolute joints between two bodies and their equations, can be found in appendix 3.
26
2.2.4 Equations of Motion
Before the inception of this section it should be mentioned that in appendix 4, the equation
of motion for constrained system can be found. In this part, a main process for dynamic
analysis of MBS will explain. This process is based on the standard Lagrange multipliers
method. At first, the equation of motion for a constrained MBS based on Newton-Euler
concepts are written as below which g is the generalized force vector. (Flores, 2015, p. 61)
𝐌�̇� − 𝐃𝑇𝜆 = 𝐠 (2.10)
With consideration of constraint equations at the acceleration level with the differential
equations at the same time, the dynamic analysis can be accomplished. Hence, 𝐃�̇� can be
written as (Flores, 2015, p. 61)
𝐃�̇� = ɣ (2.11)
‘’ Equation 2.10 can be appended to Eq. 2.11, yielding a system of differential algebraic
equation (DAE). This system of equations is solved for accelerations vector,�̇� and Lagrange
multipliers, λ. Then, in each integration time step, the accelerations vector,�̇�, together with
velocity is integrated in order to obtain the system velocities and positions for the next time
step.’’ (Flores, 2015, p. 61) For launching any dynamic simulation a set of initial conditions,
such as velocity or position is needed. Equations 2.10 and 2.11 can be written such below in
a matrix form (Flores, 2015, p. 62);
[𝐌 𝐃𝑇
𝐃 0] {
�̇�𝜆} = {
𝐠𝜆} (2.12)
For this level, the equation of motions can be analytically considered and solved. In order to
do that, the equations 2.10 can be written as below in which the acceleration vector is put
(Flores, 2015, p. 62).
�̇� = 𝐌−1(𝐠 + 𝐃𝑇𝜆) (2.13)
27
In order to have the inverse matrix for M, it is supposed that there is no null inertia (or mass)
in the MBS matrix (Flores, 2015, p. 62).
𝜆 = [𝐃𝐌−1𝐃𝑇]−1(ɣ − 𝐃𝐌−1𝐠) (2.14)
If equation 2.14 is used in the equation 2.13, then the below equation can be obtained (Flores,
2015, p. 62):
�̇� = 𝐌−1𝐠 + 𝐌−1𝐃𝑇{[𝐃𝐌−1𝐃𝑇]−1(ɣ − 𝐃𝐌−1𝐠)} (2.15)
Figure 2.11 illustrates a flowchart which obtains the algorithm of a standard solution of the
equation of motion. The following steps explain the algorithm:
- 𝑡0, 𝐪0 𝑎𝑛𝑑 𝐯0 are initial values.
- The mass matrix, M, should be assembled. The Jacobian matrix should be evaluated.
The constraint equations should be constructed. Ɣ, the right-hand side of the
accelerations, should be determined and the force vector g, should be calculated.
- To obtain values for 𝐯 ̇ and λ, the linear set of equations of motion for a constrained
MBS should be solved.
Figure 2.11. The flowchart for dynamic analysis of MBS base on the standard Lagrange
multipliers method (Flores, 2015, p. 63).
28
In simulations, the main equations of the constraint begin to be broken because of integration
process. In order to solve this problem and keep the constraint break under control, a method
called the Baumgarte stabilization method can be helpful. The main goal of this method is
substitute differential equations which have been used up to now with following equation.
Figure 2.9 illustrates open and close loop of control systems (Flores, 2015, p. 64).
Figure 2.9. Open and closed loop for control systems (Flores, 2015, p. 64).
�̈� + 2𝛼�̇� + 𝛽2𝛗 = 0 (1.61)
Alpha and Beta are constant, positive constant. ‘’ The principle of the method is based on
the damping of acceleration of constraint violation by feeding back the position and velocity
of constraint violations, as illustrated in figure 12’’. (Flores, 2015, p. 64) In close loop
system, φ and its differential do not move toward zero, it means that the system is not stable.
By using the Baumgarte method (Flores, 2015, p. 64):
[𝐌 𝐃𝑇
𝐃 0] {
�̇�𝜆} = {
𝐠
ɣ − 2𝛼�̇� − 𝛽2𝛗} (1.62)
2.2.5 Integration Methods in Dynamic Analysis
This section explains the utilization of some practical integration algorithms in the resolving
in the equation of motion. ‘’ Particular emphasis is paid to the Euler method, Runge-Kutta
approach and Adam Predictor-corrector method that allows for the use of variable time steps
29
during the integration process.’’ (Flores, 2015, p. 67). In regular, the equations of motion for
MBS is based on two main methods which are Newton-Euler method and the augmentation
one. Translational and rotational motions are interpreted by Newton-Euler method, while to
link the constraint equation of MBS, the augmentation method have been used. Using
numerical integration algorithms is considerably beneficial to solve ODE, hence, in this
dissertation work the DAE are changed to ODE. The number of n1 second-order differential
equations can be converted to 2n1 first-order equations can be seen as below (Flores, 2015,
p. 68):
�̈�1 = 𝑓(𝑦1, �̇�1, 𝑡) (2.16)
�̇�1 = 𝑦2 (2.17)
�̇�2 = 𝑓(𝑦1, 𝑦2, 𝑡) (2.18)
Methods Euler, Rung-Kutta and Adams predictor-corrector are mostly used numerical
integration methods. Although these methods have been used for many years, more than 100
years about Rung-Kutta, availability of computers helped enormously to understand a
tremendous amount of ways to utilize them. ‘’ The discrete points may have either constant
or variable spacing as ℎ𝑖1 = 𝑡𝑖1+1 − 𝑡𝑖1, where ℎ𝑖1 is ‘’the integration step size’’ for any
discrete 𝑡𝑖1 . At each 𝑡𝑖1 , the solution y (𝑡𝑖1) is approximated by a number 𝑦𝑖1 . Since no
numerical method is capable of finding y (𝑡𝑖1) exactly, the below quantity, Eq. (2.19),
represents the global or total error at t=𝑡𝑖1’’. (Flores, 2015, p. 68)
ɛ𝑔1
𝑖1 = |𝑦(𝑡𝑖1) − 𝑦𝑖1| (2.19)
The occurred errors has two different components, first one is a kind of truncation error and
other one is the round-off error. The truncation error which is a kind of inherent error,
happens because this error is related to nature of numerical algorithms while analyzing 𝑦𝑖1.
Finite word length in a computer can cause the round-off error. There is a method called
single step methods which is a type of method for progressing to solve an equation of motion
for a MBS which needs data from problem to solve it. For this dissertation work, in this
30
thesis, the solution method for the equation of motion is Runge-Kutta method which is a
single step method. The algorithm for the single step methods, called multistep methods
which is Adams predictor-corrector method. A crucial point about the numerical integration
method is it require some function evaluation. For instance, for 4-order Runge-Kutta method,
4 function evaluation are needed. The numerical task has a relation with an initial value’s
integration which can be seen as below equation (Flores, 2015, p. 68):
�̇�1 = 𝑓(𝑦, 𝑡) (2.20)
Initial condition for the Eq. 2.20 is: 𝑦(𝑡0) = 𝑦0 where ‘’y is the variable to be integrated and
function f (t, y) is defined by the computational sequence of the selected algorithm’’. (Flores,
2015, p. 69)
Euler approach is one of the best and also simple approach integrators. Euler method can
solve the differential equations in one single step (Flores, 2015, p. 69):
𝑦𝑖1+1 = 𝑦𝑖1 + ℎ𝑓(𝑦𝑖1 , 𝑡) (2.21)
‘’ Where variable h is the integration step size h=𝑡𝑖1+1 − 𝑡𝑖1, for i which is a non-negative
integer.’’ (Flores, 2015, p. 69). Figure 2.12 illustrates the Euler method in a basic type. Curve
y=y (t) is the solution of the Eq. (2.20) which can be seen that it passes through the point P.
The height RQ, value of y1=y0+Δy should be found. There is no data or information about
the curve’s points, however the slope of the curve is equal to f (t,y) and it means the
differential equation based on the geometric interpretation. So the equation �̇�0 = 𝑓(𝑡0, 𝑦0)
is the slope of the tangent at point P. Length PS does not have a big deviation from the curve
PQ if h is not big. So, 𝑅𝑆 ≅ 𝑅𝑄. RS is equal to ℎ�̇�0.
31
Figure 2.12. ‘’Geometric interpretation of the Euler integration method’’ (Flores, 2015, p.
70).
With help of the Taylor series about t=𝑡𝑖1, y (t) can be expanded at t=𝑡𝑖1+1 (Flores, 2015, p.
70).
𝑦(𝑡𝑖1+1) = 𝑦(𝑡𝑖1) + ℎ𝑓(𝑡𝑖1 , 𝑦𝑖1) + 𝑂(ℎ2) (2.22)
The truncation error is in this equation is given by (Flores, 2015, p. 70)
ɛ𝑙 = 𝑂(ℎ2) (2.23)
The accuracy of the method is related to the order of that method and can explain the
truncation error. So in a scalar equation (Flores, 2015, p. 70):
ɛ𝑙 = 𝑂(ℎ𝑃′+1) (2.24)
The order for this equation is 𝑃′th order. The Euler method is a first order method. If h is too
big, the accuracy while computing will decrease and in order to very high amount of
oscillation in motion, there will be very fast changes in the derivatives of the function.
(Flores, 2015, p. 70)
32
The difference between y (𝑡𝑖1) and 𝑦𝑖1 can assist to find the whole (global) truncation error.
It should be noticed that this calculation is in the absence of other error, round-off error
(Flores, 2015, p. 70).
ɛ𝑔1
𝑖1 = |𝑦(𝑡𝑖1) − 𝑦𝑖1| (2.25)
If the precise express is needed, then the Runge-Kutta method, which is a second-order
algorithm, can help (Flores, 2015, p. 70),
𝑦𝑖1+1 = 𝑦𝑖1 +ℎ
2(𝑓1 + 𝑓2) (2.26)
The function, 𝑓1 , (Flores, 2015, p. 70)
𝑓1 = 𝑓(𝑡𝑖1 + 𝑦𝑖1) (2.27)
𝑓2 = 𝑓(𝑡𝑖1 + ℎ, 𝑦𝑖1 + ℎ𝑓1) (2.28)
For this approach, in any time step, two function evaluations are needed. The Rung-Kutta
method can be interpreted as figure 2.13 geometrically.
Figure 2.13. Runge-Kutta method in geometric interpretation (Flores, 2015, p. 71).
33
𝑓1 does not depend on 𝑓2 and on 𝑦𝑖1+1. It should be noticed that for more accuracy in bigger
time steps, the fourth-order of Runge-Kutta method can be used. (Flores, 2015, p. 71)
𝑦𝑖1+1 = 𝑦𝑖1 + ℎ𝑓5 (2.29)
Where
𝑓5 =1
6(𝑓1 + 2𝑓2 + 2𝑓3 + 𝑓4) (2.30)
𝑓1 = 𝑓(𝑡𝑖1 , 𝑦𝑖1) (2.31)
𝑓2 = 𝑓(𝑡𝑖1 +ℎ
2, 𝑦𝑖1 +
ℎ
2𝑓1) (2.32)
𝑓3 = 𝑓(𝑡𝑖1 +ℎ
2, 𝑦𝑖1 +
ℎ
2𝑓2) (2.33)
𝑓4 = 𝑓(𝑡𝑖1 + ℎ, 𝑦𝑖1 + ℎ𝑓3) (2.34)
Figure 2.14 illustrates the interpretation of fourth-order Runge-Kutta method geometrically.
‘’ The local error of this method is of order ℎ5, which is relatively small even for larger time
steps. The major disadvantage of this method is that the function f (t, y) needs to be evaluated
four time at each time step.’’ (Flores, 2015, p. 72)
Figure 2.14. ‘’Geometric interpretation of the fourth-order Runge-Kutta method’’ (Flores,
2015, p. 72).
34
2.3 Simulation in practice
In addition of scientific targets, simulation has to be functional in other areas such as
marketing. To reach to this objective, a comprehensive simulated model is required which
can satisfy requested expectations. This chapter introduces simulation and simulators, then
simulation will be discussed from marketing aspect. Then, customizable models and
employed software will be discussed. Finally, design and results for a four-bar mechanism
will be presented.
2.3.1 Simulation
Real time simulation is a functional tool which prepares a vast angle about behaviors of
variety vehicles and responses of their parts in diverse situations. Based on real inputs and
data for all components, with a detailed and correct design in simulation, real output can be
achievable and useable. Another striking benefit of real-time simulation is being cost
effective. To design and build a real machine for obtaining results, a significant amount of
budgets have to be costed, however, with real simulation, this aim can be achievable.
Moreover, there is a considerable chance to modify and make parameterization for a
simulated vehicle.
A drawback of simulation is that for some parameters and situations there are always some
estimation data which can distance from obtaining real results. The number of assumptions
and simplifications should be minimal in order to decrease the errors in result data.
2.3.2 Simulators
Simulators play a crucial role to provide real feeling to user (customer) while using them.
With help of accurate software and hardware which are working simultaneously, simulator’s
output is enough accurate. For this master’s thesis a kind of simulator, illustrated in figure
2.15, have been used. The software installed on it is MeVEA. Moreover, with a motion
platform which has employed four hydraulic cylinder-pistons, the feeling of movement can
be transferred to the user.
35
Figure 2.15. SIM STUDIO with motion platform in order to obtain real feeling to users.
This motion platform has two joysticks and also a steering wheel, which obtains real feeling
about moving, lifting sands, et cetera. Also, this simulator has sound effect beside real
movements.
2.3.3 Marketing
Simulations and simulators have a tremendous amount of possibilities in markets. There are
considerable number of companies which can utilize simulators and achieve its benefits. In
order to decrease testing budget, a company can use a simulator which is appropriate to its
research and extract results without spending significant amount of money. One of the most
remarkable point of simulation for marketing is parameterization. It means the amount of
spending money can be raised if the company wants to change some parts of a machine and
figures out new results. With a parameterized simulation model, any type of changing are
unchallenging. Not only simulating of a machine in simulator is cheaper than manufacture
it, but also substituting some parts in simulation has no more charge. That is why more and
more companies are figuring on the advantages of simulations and simulators.
36
2.3.4 Customizable Model
Preventing of wasting time and budget are the main purposes of producing a generic model
in simulation. There are noticeable number of possibilities for a user, based on the concept
of parameterization, to build a simulation model and extract it results. Suppose a simulation
model with many assemblies such as engine assembly, hydraulic assembly, power
transmission assembly, et cetera, which can be selected by a user. Each of these assemblies
has their own sub-assemblies. Based on user’s options, there are a large number of
combinations for assemblies and sub-assemblies which will present different results and
analysis. Figure 2.16 depicts a schematic of a simulation model with its assemblies and sub-
assemblies. As the figure 2.16 shows, there are many options and combinations for building
one model which every single changing in sub-assemblies will affect to other parts and data,
so when a user finishes his/her selections, a new model is created which are totally different
from other models.
Figure 2.16. Simulation model made by assemblies and sub-assemblies
Each sub-assembly has its own code, based on a software which has been used to write the
code. Then, all assemblies will gather and the real-simulation model will be ready to run.
37
2.3.5 Employed Software
In this dissertation work as it mentioned before, all real-time simulation issues is handled
in MeVEA software. In addition, for other aspects, such as graphics, other software are
used. Blender, Python, SolidWorks, and Excel. The duty of each software will be
explained in next chapters.
2.3.6 MeVEA
MeVEA does the real-time simulation task with some rational simplifications. There is no
graphics while modelling in MeVEA. Objects in MeVEA do not have any shape so their
collision graphics and graphics, connections and environments must be defined in other
software. In order to reach faster and easier analysis during simulation, these simplifications
are very important. MeVEA has two interfaces, one is to create a simulation model and other
one is to run the model and get all results. Figures 2.17 and 2.18 show the work interface
and dynamic simulation one, respectively.
Figure 2.17. Working interface in MeVEA software to create a model, like excavator.
38
Figure 2.18. Dynamic simulation interface in MeVEA software.
As it is shown in figure 2.17 in MeVEA, the bodies, constraints among them, all graphics of
bodies and environment, data related to movements, hydraulic model, inputs and outputs,
virtual sensors, and other data can be modeled and implemented.
In dynamic simulation interface, a user can run the simulation model and see does it work
properly or not and extract desired results and plots. Because of simplification, graphics in
working interface do not have all details, on the other hand in dynamic simulation interface,
graphics are different and with details.
User can run the model and control it with joysticks and a steering wheel, if needed, or with
keyboard, figure 2.19. As figure below depicts, user can have plotting diagrams while
simulating. These plots demonstrate behavior of each element during running a simulation
model. In the other words, plots are the main section of final results in MeVEA. In plot tab
in the dynamic simulation interface, user can opt specifications which she/he wants to see
its behavior at the end of simulation.
39
Figure 2.19. Running situation with the keyboard control and a plot.
2.3.7 CAD Software – SolidWorks
To model some parts of the graphics in my case study, an excavator, SolidWorks played a
crucial role because of its precision in 3D assemblies. With a user-friendly environment,
SolidWorks is the first option for designing. In graphics point of view, MeVEA can read .stl
files format, however 3ds file format is more compatible with MeVEA. So beside
SolidWorks, presence of another software for other graphics is needed.
2.3.8 Blender
With blender all environment graphics, collision graphics and some vehicle’s parts can be
modeled and it is a strong software for making visualization extremely professional.
Moreover, Blender is an open-source software which can be utilized easily and has some
striking features such as fast modeling, photorealistic rendering, and preparing real feeling
about materials (Blender, 2017). The output file of the Blender can be 3ds format which is
readable in MeVEA software. In MeVEA two types of graphics are needed, one of them is
visualization graphic and the other one is collision graphic. File format for Collision graphics
in MeVEA is only .3ds (Mevea, 2017). Clearly, visualization graphic is to see the model and
the environment and the collision graphic is for parts of a model which must have collision
with other parts of body and also environment. For instance, in the excavator model, the
40
bucket should dig the sand, so it must have collision graphics beside its visualization one. In
blender the collision and visualization graphics can be seen and modified simultaneously in
order to have a realistic actions during running a simulation model.
Figure 2.20-a, illustrates a visualization graphic of a bucket and in figure 2.20-b the
visualization and collision graphics can be seen simultaneously. Moreover, scales, colors
and textures can be set and manipulated in blender.
Figure 2.20. a) Visualization graphic, b) Visualization and collision graphics in blender.
2.3.9 Python and Excel
With Python and excel software, parameterization target can be reachable. Python is a coding
software which can be used as an open-source software with a practical database (Python,
2017).
With an Excel file as an interface file, a user can choose an option among available options
for a model for instance, and can create the vehicle based on his/her customization.
To implement this customization, a code-based software is needed to play as a bridge. With
writing a script in Python software, all selected options can be readable in MeVEA and after
running the simulated vehicle, the desired options in the vehicle can be seen in the MeVEA
environment. Creating Python code and excel file will be explained in the case study chapter.
41
2.4 Four-bar Mechanism
To evaluate and figure out the real-simulation mechanism, there is a four-linked model is
considered, figure 2.21. In order to find out behavior of a mechanism, position analysis, the
velocity analysis, the Lagrangian formulation and the equation of motion will be explained.
Figure 2.21. Four-Bar Mechanism
For the four-bar mechanism, position analysis, equations of the close loop for the
mechanism’s dimensions, figure 2.22, can be written as below.
Figure 2.22. 4-bar mechanism for analysis
42
Table 2.1 demonstrates the dimensions for 4-bar mechanism, shown in figure 2.22. It should
be noticed that values in the table are considered in center to center way.
Table 2.1. Values for parameters shown in figure 2.22.
Parameter 𝑙0 𝑙1 𝑙2 𝑙3 𝜃0′ 𝛼0
′ 𝜑0′ 𝑚1 𝑚2 𝑚3
Value
(unit)
117.9
cm
50
cm
100
cm
80
cm
90°
15.68°
106.1°
5
kg
10
kg
8
kg
−𝑙1 cos 𝜃′ − 𝑙2 cos 𝛼′ + 𝑙0 + 𝑙3 cos𝜑′ = 0 (3.1)
−𝑙1 sin 𝜃′ − 𝑙2 sin 𝛼′ + 𝑙3 sin 𝜑′ = 0 (3.2)
The final equation for position:
𝛼′(𝜃′, 𝜑′) = 𝑡𝑎𝑛−12(−𝑙1 sin 𝜃′ + 𝑙3 sin 𝜃′ , 𝑙0 − 𝑙1 cos 𝜃′ + 𝑙3 cos 𝜑′) (3.6)
The equation of the velocity,
[�̇�′
�̇�′] = [𝑆1(𝜃
′, 𝛼′, 𝜑′)
𝑆2(𝜃′, 𝛼′, 𝜑′)
] �̇�′ (3.10)
Kinetic energy:
𝑇 =1
2(𝑚1𝑙𝑐1
2 (�̇�′)2 + 𝐼1(�̇�′)2) +
1
2(𝑚2𝑙1
2(�̇�′)2 + 𝑙𝑐22 (�̇�′)2 + 2𝑙1𝑙𝑐2 cos(𝜃′ − 𝛼′) �̇�′�̇�′ +
𝐼2(�̇�′)2) +
1
2(𝑚3𝑙𝑐3
2 (�̇�′)2 + 𝐼3(�̇�′)2) (3.11)
Where T is the kinematic energy, m is the mass, I is inertia and 𝑙𝑐 is l/2.
Potential energy:
V𝑚1𝑔𝑙𝑐1 sin 𝜃′ + 𝑚2𝑔𝑙1 sin 𝜃′ + 𝑙𝑐2 sin 𝛼′ + 𝑚3𝑔𝑙𝑐3 sin𝜑′ (3.12)
43
V is the potential energy and g is the ground acceleration.
The final equation of motion:
𝐌(𝜃′)(�̈�′)2 + 𝑉(𝜃′, �̇�′) = 𝜏𝜃 (3.21)
The constraint equations, Jacobian matrix, Newton difference for position analysis and
velocity analysis for the four-bar mechanism can be found in appendix 5.
Results of 4-bar-mechanis:
After modelling in MeVEA, figure 2.23, the result of simulation can be found below;
Figure 2.23. Dynamic simulation for 4-bar mechanism
Figure 2.24 depicts the total torque versus time in this mechanism while there is a torque on
the revolute joint between stand1 and left. Link.
44
Figure 2.24. Total torque for 4-bar-mechanism.
Clearly, figure 2.24 shows the torque is increased through the time with a fluctuation.
Figure 2.25 illustrates the angular velocity in y and z direction for the middle link in x while
simulating.
Figure 2.25. The angular velocity in y and z direction for the Middle-link.
45
As figure 2.25 illustrates, the angular velocity in z direction is 1.03e3 deg/s in its maximum
position while in y direction is 1.03e-11 simultaneously and they are repeating these data
through the time because of the constant torque applying to the system. In figure 2.26, the
local joint force for the left-link body on the constraint between left-link and the middle-link
is shown. In this figure, the Fxl force is increasing through the time, however, the Fyl force
is almost is repeated.
Figure 2.26. The local joint force in joint between the left-link and the middle-link.
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3 CASE STUDY- THE EXCAVATOR
With assistance of parameterization, implementing some feasible alternatives in the
excavator model, figure 3.1, can be done. The excavator model can have some modification
in some parts such as hydraulic circuit and bucket.
Figure 3.1. The excavator model with one of its pair of customizations.
The excavators employ to dig and lift up any kind of particles which usually are sand,
construction waste et cetera. The driver uses six main cylinder-pistons to move the main-
boom, dipper-arm (shown in figure 3.1), bucket. Due to the working principle of the many
kinds of excavators, there is no need to move and drive very fast with high acceleration. So
there in no gear index in this specific excavator and with customization in hydraulic circuits,
some variable speeds in order to lift the main-boom or the dipper-arm are achievable.
47
In this thesis, the focus is worked to customize in two main parts, the bucket and the
hydraulic circuit. For this moment there are three kinds of buckets and three kinds of
cylinder-piston moving the dipper-arm.
3.1 Principles of Excavator
Excavators, as an industrial and heavy work vehicle, are employed to work in rough terrains
and sometimes in dire situations. They do not need to have fast speed, because they are
always transport particles, sand, soil, construction wastes to another movable vehicle like
camion, however there are some models of excavators which have the on-road travel speed
up to 35 km/h and off-road travel speed up to 8.9 km/h (Volvo, 2012). Caterpillar, Komatsu,
Volvo, Hitachi and Liebherr are some of the prominent companies which are producing
construction equipment including excavator. Moreover, excavators can carry out a variety
tasks; digging, ripper application, foundation drilling, material handling, high demolition,
long reach, and et cetera (Volvo, 2012), figure 3.2. Also, there is a company, named Sandvik,
which is also produces various products and equipment, such as mining products,
exploration drill rigs, et cetera which the simulation model of this project has the same
principle with products of Sandvik (Sandvik, 2017)
Manufacturers of excavators are always attempting to improve their products considering
some parameters which in many cases are intertwined. Power of engine, weight, swing
mechanism, drive’s options, hydraulic system, electrical system, brake system, travel speed,
digging reach, the amount of dug particles, et cetera are some of substantial parameters in
design point of view. (Caterpillar, 2017) In this dissertation work size of bucket which is
directly related to the amount of dug particles in each time and also the hydraulic system are
discussed. Also, in appendix 6, some data and information about excavators which are
producing in a pioneer company, Volvo Company, can be seen. In order to have an excavator
with high maneuver speed in its booms, the amount of oil going into the cylinders and the
flow rate should increase. Simultaneously, if the size of the bucket is big, it can be expected
a reduction in work cycle time significantly. However, two important points should be
considered; First, in fuel-consumption point of view, this situation can boost fuel
consumption as well. Secondly, with utilizing a more powerful valve in a part of hydraulic
circuit, and/or employment a big bucket, another parameters in hydraulic circuits, should be
considered. Put differently, because selected parameters for a vehicle in most cases are
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intertwined together, by changing a parameter, other parameters have to be changed or at
least checked.
Figure 3.2. Typical types of the excavator’s applications (Caterpillar, 2017).
3.2 Simulated industrial vehicle
A customized model largely uses to indicate the capability of an especial vehicle in different
situations. It means that with a customizable simulation model the ability of a vehicle can be
figured out. Moreover, it allows to make a practical comparison among a model with
different options, data and parts and prepares an outlook to find optimize options of the
model for each specific situation.
This concept obtains a giant opportunity in marketing point of view such that a customer can
have many options in front of herself/himself and select the best kind of assembly which is
appropriate for her/his target.
3.3 Editable Parameters
MeVEA creates four XML (Extensible Markup Language) format files while saving which
the executable file, MVS file, reads them to run a model. One of the created XML is a file
49
which has the main data about the model in it. Another XML files are material library file,
commentary file and world file. For instance in world file, settings about lights and cameras
save. In order to have an editable simulation model, at first of all parts and parameters of the
excavator should be recognized. Each part of the excavator has its own specification which
have to be considered carefully. There are some classifications to put all parts of a vehicle
to attain an absolute model. As an example for a classification, parts of a vehicle can be
considered as a classification. In this case, parts of the excavator are under carriage, upper
carriage, main boom, dipper arm, bucket and its attachments.
Another classification for a vehicle can be its systems and interactions. For example, in the
excavator, there are some systems such as the hydraulic system, engine and force system
and parts system. Each system has its own sub-systems and all of them are interacting
together. In this dissertation work, two main parts and systems have considered to be
customizable to select and operate for a user. As figure 3.2 has shown, the head of the
excavator demonstrates its main function and one of them is digging. Another momentous
system is hydraulic system which is acting through the excavator and it is the source of
power for any movement of the excavator. Making a whole hydraulic system customizable,
is a tough function and in some cases is not so feasible and reliable, however, some parts of
it can be editable and allows to have a model with diverse options in the movement velocity,
potent arms to lift or dig. In next chapters these two systems will study.
3.3.1 Bucket and lifting system
Clearly the main aim for an excavator in its bucket type, is to dig and transfer any particles.
In some cases of an excavator working time, the most serious aim is to save time, or working
in a place which has many narrow spots, therefore having an opportunity to utilize a few
kinds of buckets seems practical and convenient. In this case there are three kinds of buckets
with variety dimensions and weights, figure 3.3.
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Figure 3.3. Types of the bucket which are used for the customization.
In MEVEA Modeller the bucket has in bodies’ sub-tree which has some parameters to set it.
Each part has Visualization Graphics, Collision Graphics which have interaction with
bodies’ graphics in Graphics sub-tree. Moreover, each part has some parameters such as
position or mass that have to be defined. Figure 3.4 depicts the MeVEA Modeller interface
which includes Model Tree, Objective View, Body Preview Window and Preview Window.
Figure 3.4. Sections of the MeVEA Modeller interface.
Model Tree
Objective View
Preview Window
Body Preview
Window
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As it mentioned, each body and particle have two kinds of graphics. Visualization Graphic
is to show the body to the user and Collision Graphics are for any collision among the parts
and the environment. For instance, according to MeVEA definitions for collisions of
particles (such as sands or gravel) and collisions of the bucket, the function digging happens.
Table 3.1 depicts parameters which have to change to obtain a customizable bucket. It should
be noticed data about the bucket is set in Objective View window, shown in figure 3.4, and
its graphics are selected based on existing graphics in the Graphics sub-tree which should be
designed and defined beforehand.
Table 3.1. Parameters which have to define for each three types of the bucket.
The BUCKET of the EXCAVATOR
Parameters (unit)
Visualization Graphics -
Collision Graphics -
Position m
Orientation rad
Mass kg
Moments and products of inertia kg.m2
Centre of Mass m
All parameters define in an XML file which usually has the same name of the executable
file. To have an appropriate visualization and collision graphics, the modelling configurator
changes parameters in table 3.1 through accessing in sub-trees ‘bodies’ and ‘graphics’.
3.3.2 Hydraulic circuit system
To have a reliable precise excavator, working in different situations, hydraulic part plays a
vital role to preserve a vehicle powerful and sustainable. There are six main cylinders and
pistons in the studied excavator, which do the hydraulic functions. Figure 3.5 shows the
hydraulic schematic of the excavator in details.
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Figure 3.5. A comprehensive hydraulic schematic of the excavator.
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Table 3.2 demonstrates the explanation of each number that mentioned in figure 3.5.
Table 3.2. Explanations of numbers of hydraulic circuits mentioned in figure 3.5.
No Name of the part No Name of the part No Name of the part
1 Volume_DriveLeftA 14 DV63_MainBoom2 27 PRV_BuckRot_B
2 PRV_DriveLeft_AB 15 CBV_LiftCylinderA 28 Vol_BuckRot_B
3 Volume_DriveLeftB 16 Vol_BoomLiftCylA 29 Vol_BuckRot_A
4 PRV_DriveLeft_BA 17 CBV_LiftCyl_B 30 PRV_BuckRot_A
5 Volume_CabinSlewA 18 Vol_BoomLiftCylB 31 DV63_TravelRight
6 PRV_CabinSlew_AB 19 DV63_BucketTilt 32 Vol_DriveRight_B
7 Volume_CabineSlewB 20 PRV_BucketTiltB 33 PRV_DriveRightAB
8 PRV_CabinSlew_BA 21 PRV_BucketTiltA 34 Vol_DriveRight_A
9 Throttle_PumpCtrl2Tank 22 Vol_BucketLiftCylB 35 PRV_DriveRightBA
10 PRV_Branch2 23 Vol_BucketLiftCylA 36 Vol.i.BuckTi.Bo.Li
11 Pump_Main 24 DV63_BucketBank 37 Vol.i.BuckRo.BuBa
12 Pump_Idle 25 Vol_BucketTiltCylA 38 Vol.i.BuRo.BuBank
13 Voume_Pump 26 DV_63BucketRotator 39 Vol.i.Dri.R_BuRo
In this project, the hydraulic cylinder-piston which has the responsibility to carry out
movement and velocity of the Dipper Arm is selected to be customized. The reason behind
this choiceness is the velocity and reaction of the Dipper Arm have significant effects on the
working cycle time and final working time. To do so, some specifications in this part of the
hydraulic circuits have to be editable. These changing will occur in the flow rate going in to
a directional valve and a cylinder. It should be noticed that in the definition of the MeVEA
Modeller the design of some specification such as a cylinder or behavior of a valve is based
on interpretation of splines. Table 3.2 depicts the parameters have to be modified in the
hydraulic circuit.
With setting mentioned in the table 3.3, an arbitrary section in the hydraulic circuit can be
created, however, it is not feasible to have a tremendous amount of changing in a vast area.
Otherwise stated, to have plenty of options for the hydraulic circuit system, numerous revises
and modifications in other parts of hydraulic circuit systems and also other parts of designed
model is needed simultaneously which is not the target of this dissertation work.
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Table 3.3. Specifications of hydraulic circuits to have a customizable cylinder-piston for the
Dipper Arm.
The HYDRAULIC CIRCUITS for the DIPPER ARM
Parameters
(unit)
Cylinder piston diameter m
Cylinder piston rod diameter m
Nominal flow rate l/min
Collision Graphics -
Position for cylinder-piston m
Splines – for the valve and friction of the dipper arm cylinder -
Visualization Graphics -
3.4 Data Selection
There are three approaches to get access to the options for the selectable data which one of
them is in its beta version. The first way is making MVA and XML files for existing options
and using them in MeVEA Modeller and the second one is designing an excel file which
gives the access to the user in order to select her/his favorite option for each customizable
part. It should be noticed that because of simplicity and using a kind of interface, the second
approach, using an excel file, is employed as the user interface.
Third approaches is to employ the MeVEA launcher which is compatible with MeVEA
software, however at the moment it is in its testing mode. In following sections, mentioned
approaches will discuss.
3.4.1 Assembly files approach
Based on number of options (at the moment three), a certain MVA and XML files should be
created for each option. On the other hand, in the main XML file (an XML file with the same
name with the executable file) some assembly folders must be created due to reading those
MVA files. MVA files are a type of readable files which are used to have separated options.
For this level, six MVA files and three more XML file must be created; three MVA files for
three options of buckets, three MVA files for three options for hydraulic circuits, three XML
files for the interaction between particles and the bucket. Collision between particles (sands)
and the bucket in any type of options is different, that is why three more XML files are
55
needed. Figure 3.6(a) depicts created all XML, MVA and MVS files and figure 3.6(b)
represents the main XML files and assembly folders inside it.
Figure 3.6. (a) Created MVS, XML and MVA files for the excavator. (b) Expanded main
XML file, excavator.xml.
As figure 3.6(b) shows, in each time which a user intends to create a model, she/he should
select three files among the files which is showed in figure 3.6(a), two MVA files for the
bucket and hydraulic circuit and one XML file as particle file. A point should be considered
that the selected XML file, for particles, must be according to selection of the bucket,
because these two files are intertwined together and choosing different files for the bucket
and particles causes an impractical simulation model. With XML editor, all kinds of editing
purposes can be done in an easy way. (XML editor, 2017)
It is important to mention that MeVEA has a launcher which can use assembly approach in
a more attractive way. In SIM platform (SIM STUDIO), there is another kind of interface
(launcher) which has an ability to collects data from user and use it. The difference between
this approach and assembly approach is that in assembly approach, user have to select three
files from mentioned file and write their names in the main XML file, however, while using
launcher the user just should select favorite options in a simplest form by clicking on their
images. As it mentioned already, this approach is at its beta version, so despite of being easy
56
to select specifications, it could not be the first option to be a user-interface. Figure 3.7 and
3.8 demonstrate the environments of the MeVEA launcher.
Figure 3.7. a. the first page of the MeVEA launcher, course selection. b. The number of
available users. c. The number of available vehicles.
Figure 3.8a demonstrates the first page in launcher which shows the available courses for
the specific number of defined users. In figure 3.8b, the number of users which have defined
to work with simulated machines have shown. Each user has their own username and
password. Figure 3.8c shows prepared available simulated vehicles which the user can opt
one of them and work with it.
Afterwards, in the next page of the launcher, the user should select an organized exercise
among defined exercises, at the moment one exercise is available, figure 3.8a. Then she/he
can select her/his favorite specification among present specifications in an easiest way.
Figures 3.8b and 3.8c demonstrate available options for the bucket and the hydraulic circuit
of the excavator respectively.
57
Figure 3.8. a. The available exercise for selected vehicle to run. b. Selection page for an
option among options, here are buckets of the excavator. c. Selection page for an option
among options, here are hydraulic circuits of the excavator.
3.4.2 Coding files approach – User interface
In order to provide an access for users to pick out among the options, there is an excel file is
designed, figure 3.9. In this excel file a user has three options to pick one of them out for
each part or definition and then save it. Next, the MeVEA software, with help of a Python
code, can collect and place all data together and make the simulation model ready.
Figure 3.9. The interface which a user can select her/his favorite value for each part.
58
As figure 3.9 illustrates all values have three options which by clicking on their cells, the
options can be viewed. It should be noticed that options for the main motor can be a part of
future work. After selecting data by user, the story and issue is a way to make a connection
between selected data in the excel file and reading them in the MeVEA software. In MeVEA
software, each part has its own branch, for instance body or dummy branch, which is written
in the main XML file (Reference of Mevea, 2017). Next chapter will explain about the
method to create mentioned connection.
3.5 Method – A coupler between Excel and MeVEA Modeller
To implement user desired data from the excel file to the MeVEA Modeller, a code written
in Python language software is in charge. Figure 3.10 depicts a part of the used python code.
The python code collects selected data and options from the excel sheet, then it exports them
into the MeVEA Modeller in a way that it gets data from the excel file and substitutes them
in the XMLs files in their right places. The python script code can be found in appendix 7.
To use of this script code, after selecting and saving the desired data in the excel file by user,
she/he just needs to run the script file.
Figure 3.10. A part of the python script code as a bridge between the excel file and the
excavator model in MeVEA Modeller.
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3.6 Model in MeVEA – Working and Dynamic Simulation Interface
As it has already explained in MeVEA section, MeVEA has two user interfaces which in
working user interface all data can be seen. After modelling, the model can be run in the
dynamic simulation interface. In the dynamic simulation interface (simulator), each model
has some inputs and outputs which all inputs can control either with keyboard or joysticks.
(Mevea, 2016, p. 7). Figure 3.11(a) depicts joysticks and keyboard control which has
eighteen inputs for the excavator such as slew input, or boom tilt input to move and rotate
the main boom and et cetera.
As figure 3.11(b) illustrates, this user interface includes three main parts; menu bar, toolbar
and simulation control (Mevea, 2016, p. 13). In part simulation controls, the model can be
started to run, stop running and based on number of defined cameras, the main camera can
be selected. Moreover, based on the type of running model, the number of gear and the
situation of the model in what gear is using in a certain time and also time and time steps
can be viewed. It should be noted that when the keyboard control has run, the joysticks will
not work.
Figure 3.11. a. Dynamic simulation interface with two kinds of controller, keyboard controls
and joysticks. b. parts of the dynamic simulation interface.
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3.7 Results
After customization for the excavator model, it can run in the dynamic simulation interface
and it is prepared to a comparison among types of customized models. A user may select
her/his favorite parameters and start to run. The process to run the model is as below;
At first, based on coding file approach for instance, the user selects her/his favorite bucket
and hydraulic circuits in the excel file and then save them. Afterwards, the python code, as
the connection bridge between the excel file and MeVEA, have to be run. Then, in the
dynamic simulation interface the model can be run and extract results by plotting. In
following chapters, plots and results of choices of buckets and also the selections of
hydraulic circuits will be discussed. The excavator has an initial model with a bucket and a
hydraulic circuits which are designed together, however, in this research it is attempted to
generate other combinations to see results during these changings and figure out how a
simulated model can be a more optimized.
3.7.1 Customization for the Bucket – combination and comparison
There are three kinds of buckets with three sets of parameters which have been under tests.
The volume of the bucket and its weight effect of its functions, working cycle time and fuel
consumption. Specifications of buckets are shown in table 3.4.
Table 3.4. Specifications of buckets.
Parameters / unit Small Bucket Medium Bucket Big Bucket
Position / m (-0.31,-0.13.0) (-0.3,-0.13,0) (-0.3.-0.13,0)
Orientation / rad 0,0,0 (0,0,0) (0,0,0)
Mass / kg 315 450 750
Moments and products of
inertia (Ixx,Iyy,Izz) / kg.m2 (185,228.1,168,1) (187,228.1,168.1) (180,221,165.1)
Centre of Mass / m (0.2,-0.7,0) (0.2,-0.7,0) (0.2,-0.7,0)
Volume / 𝑚3 0.318 0.512 22.55
In following figures the most remarkable specifications during customization of buckets will
be shown and discussed. Four specifications will be measured and discussed when the
61
changing of buckets are the main aim. A same test is repeated for three times for three
different buckets and the results and plots will discuss in following paragraphs.
The first item under consideration is the total cycle time and global Y Position for all three
buckets. Figure 3.12 demonstrates the result for the small bucket. It should be mentioned
that all result graphs for the medium bucket and also big bucket can be found in appendix 8.
Figure 3.12. Total time and positions of the small bucket in global y direction.
As it is clear in figure 3.12, for the small bucket, total time to accomplish the test is 17.36
seconds. Next specification is the angular velocity in global y direction for the dipper arm
cylinder during the test. As figure 3.13 shows, the amount of the angular velocity for the
small bucket has a small-scale of oscillation around a certain value.
62
Figure 3.13. The angular velocity in global y direction for the dipper arm cylinder using the
small bucket.
Power transmission of the main motor of the excavator is the next specification which is
traced during the test. Figure 3.14 depicts results while using the small bucket. The
maximum value of power is 1.124e2 kW at 1.21s.
Figure 3.14. Power for the main motor of the excavator using small bucket.
63
Finally, one of the most crucial factor, fuel consumption, has been traced during the test.
Figure 3.15 illustrates the graph of fuel consumption while using the small bucket for the
excavator. As it is clear, the final value as the most crucial specification for the fuel
consumption, is 4.86e-2.
Figure 3.15. Fuel consumption for the excavator using the small bucket.
3.7.2 Customization for the Hydraulic Circuits – Combination and Comparison
In this chapter, results for three kinds of hydraulic circuits for a same test can be seen. There
are too many options and specifications can be traced during this test, however, some of
them have selected which are effected during hydraulic circuit changing. The results for total
time for each test, the angular velocity for the dipper arm cylinder, the amount of force
implemented to employ the dipper arm cylinder, velocity of the dipper arm cylinder, and
finally the fuel consumption has been studied. Figures below will demonstrate result graphs
while using small hydraulic circuit. It should be noticed that graphs demonstrating results
for the medium and big buckets can be seen in appendix 8. Specifications of different
cylinder-piston of the dipper arm are shown in table 3.5.
64
Table 3.5. Specifications of cylinder-piston of the dipper arm.
Parameters / unit Small type Medium type Big type
Mass / kg 8 10 12
Cylinder piston diameter/mm 120 140 160
Piston rod length/ mm 1630 1650 1670
Figure 3.16 demonstrates angular velocity and total time for the cylinder of the dipper arm.
Figure 3.16. Angular velocity values for the dipper arm cylinder in the global Y direction
and also total working cycle time while employing the small hydraulic circuits.
The amount of torque generated by the dipper arm cylinder-piston while using the small
hydraulic circuit is shown in figure 3.17. According to figure 3.17, the mean value of the
torque is 3479.5 Nm in lifting function and 3674 in lowering function.
65
Figure 3.17. Torque values for the dipper arm cylinder-piston using small hydraulic circuit.
Figure 3.18 depicts values for velocity of dipper arm cylinder for the small hydraulic circuit.
Figure 3.18. Velocity of the cylinder-piston for the small hydraulic circuits.
66
Figure 3.19 shows fuel consumption behavior for the excavator when it has used the small
hydraulic circuits. As it is shown, the rate of the fuel consumption for all functions, lifting,
swinging and lowering is almost the same and its final value is 4.89e-2.
Figure 3.19. The amount of fuel consumption for the excavator while using the small
hydraulic circuit.
There are many other factors of the excavator can be traced during the test, however in this
dissertation work a few of them, which were highly important, have been under
consideration. In the next chapter, mentioned results specifications which have been shown
in this section and appendix 8 will analyze.
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4 ANALYSIS
In this chapter results which are collected in the previous chapter will be analyzed.
Afterward, from future-work aspect, the parameterization project and its concepts will be
discussed.
4.1 Analysis for employment of different Buckets
In this section, the extracted results from tests with three types of bucket for the excavator
will be analyzed. In some situations, working cycle time is one of the most critical aspect
which manufacturing companies and their customers pay attention about it. Figure 4.1
illustrates a comparison among three kinds of bucket when they have been used in the similar
tests which has been mentioned in chapter three.
Figure 4.1. Graphs for employing three kinds of bucket in a same test.
In figure 4.1, final time to accomplish the test is shown for small, medium and big buckets.
During using medium bucket, the excavators needs time more 11.5 percent than using small
68
bucket. Moreover, to employ big bucket, the excavator needs time more 40 percent than
using medium bucket.
When the bucket size changes, the amount of forces apply on the dipper arm will change, so
the specification ‘angular velocity’ can be able to demonstrate that are these effects
noticeable or not. Figure 4.2 depicts plots for three types of bucket and the angular velocity
has not changed during bucket substitutions significantly.
Figure 4.2. Plots for the angular velocity for dipper arm.
The behavior of the main motor is the next specification which should be under consideration
during bucket changing. Figure 4.3 demonstrates a comparison for the main motor function
of the excavator among three types of bucket. As it shows, in the first maximum spot, there
is no difference among using different buckets because the maximum number is 112.5 kW
for all of them. However, the maximum spot in the next steps for each type of bucket is
different. On the other hand, there is no big discrepancy between employing small bucket
and medium bucket on their maximum amount of power in each cycle. Furthermore when
the big bucket is used, the second crucial local maximum for it is 113.2 kW which is around
13-15 percent more than analogous spot for small and medium bucket.
69
Figure 4.3. Motor power of the excavator when three buckets have been used one by one.
Finally, the last but not the least, fuel consumption is the factor which have been analyzed.
As figure 4.4 displays, the final value of fuel consumption for the medium bucket is 5.52e-
2 which is 13 percent more than this value for the small bucket. On the other hand, fuel
consumption for the big bucket is 7.77 that is 40.7 percent more than the value for the
medium bucket.
Figure 4.4. Fuel consumption for three tests with three types of bucket.
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In comparison point of view in a glimpse, utilizing big bucket provides an opportunity to lift
up particles in each cycle more than employing medium and small buckets for the excavator.
The volume of the big bucket is 4.4 times bigger than the medium bucket and 7 times bigger
than the small bucket. Figure 4.5 illustrates three factors, total cycles time, the maximum
amount of particles which can be lifted in each attempt, and the fuel consumption, for three
bucket types.
Figure 4.5. Comparison three specifications for three kinds of buckets of an excavator.
According to figure 4.5, although using big bucket preparers a chance to transfer more
particles, total cycle time and fuel consumption value will increase considerably as well. On
the other hand, capacity of the medium bucket is around 59 percent more than the small
bucket and fuel consumption while using it is just 13 percent more than utilizing the small
bucket. Moreover, total time to accomplish the mission for the medium bucket is 11 percent
greater than the small one. It should be noticed that opting among buckets for the excavator
is highly depend on customers’ demands. For instance, in some condition when the amount
of transferring particles are notably important, employing the big bucket can be feasibly
practical.
17.36
3.24.86
19.35
5.1 5.52
27.24
22.5
7.72
0
5
10
15
20
25
30
Total Cycle Time (S) Capacity (m3e2) Fuel Consumption
Small Bucket Medium Bucket Big Bucket
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4.2 Analysis for employment of different hydraulic circuits
In this chapter four major specifications about the excavator will be analyzed in order to
figure out the behavior of the vehicle while employing each type of the hydraulic circuit.
Figure 4.6 illustrates angular velocities of the dipper arm piston for three types of cylinder-
piston. Also consumed time for each test can be viewed.
Figure 4.6. Angular velocity for three types of cylinder-piston for the excavator.
As figure 4.6 shows, as expected, spent time for test when the medium cylinder-piston have
been used is almost 27 percent more than using the small one. Also, to accomplish the test
with the big cylinder-piston, the excavator needs 23 percent time more than with the medium
one. As it is obvious, angular velocity for the small cylinder-piston is more than the medium
one, 24 percent, and also big one, 69 percent in its maximum spot. The average value for the
small cylinder-piston is 0.2137 deg/s which is 27 percent bigger than the angular velocity of
the medium cylinder-piston and 77 percent more than the big one. The average velocity for
medium and big cylinder pistons are 0.1671 deg/s and 0.1204 deg/s respectively.
72
Next factor is torque generated by the hydro-motor of the excavator. Figure 4.7 depicts
torque values for three types of cylinder-piston for the dipper arm.
Figure 4.7. Torque generated by dipper arm cylinder-piston with its three types.
With help of MATLAB software it can be found that the average value of the needed torque
for the small cylinder-piston is 31 percent more than the medium bucket and 57 percent more
than the big cylinder-piston. Moreover, the maximum value for the small cylinder-piston is
13 percent in lifting function more than the medium bucket.
Along substitution cylinder-pistons of the dipper arm, the actuator velocity will change,
therefore the working time in each cycle and also the generated force will change
accordingly. Figure 4.8 illustrates actuator velocities for the dipper arm in three types of
cylinder-piston of dipper arm. Maximum values, local maximum values in both cycle sides
confirm that the actuator velocity for small cylinder-piston is more than others.
73
Figure 4.8. The actuator velocity of the dipper arm cylinder-piston for three types of it.
The cylinder diameter of the dipper arm in the small case is 16 percent lower than the
medium case and the local maximum value of the actuator velocity in the small case is 18
percent more than the medium case. Furthermore, with the value 0.24 m/s as the local
maximum spot of the actuator velocity in case of small cylinder-piston, it is around 56
percent bigger than its big cylinder-piston case. This difference is happened while the
diameter in the big case is 33 percent bigger than the small case.
Another crucial specification is the generated force by the cylinder-piston in three types of
it. As figure below, figure 4.9, shows the maximum and maximum local values for the big
cylinder-piston is bigger than the medium and small cases. For instance the maximum value
for the big cylinder-piston is 26.7 percent more than the medium cylinder-piston and 51.8
percent more than the small case.
74
Figure 4.9. Generated force by three types of cylinder-piston of the dipper arm.
As same as the previous section, section 4.3, the last specification is fuel consumption.
Figure 4.10 demonstrates a comparison among three kinds of cylinder-piston.
Figure 4.10. Fuel consumption for three types of cylinder-piston of the dipper arm.
According to figure 4.10, fuel consumption in big cylinder-piston case is 6.1 percent more
than the medium cylinder-piston and 8.4 percent more than the small case. Unlike changing
75
buckets caused a significant differences in fuel consumption, changing cylinder-piston size
does not have a noticeable difference in theirs fuel consumption.
To end up analysis for different hydraulic circuit of the excavator, figure 4.11 can provide a
convenient summary. This figure includes total time which each of the hydraulic circuit
required to carry out the test, the average value of needed torque, the volume of each type of
cylinder, maximum generated force, and finally fuel consumption.
Figure 4.11. A comparison among crucial specifications during tests utilizing three types of
cylinder-piston for the dipper arm of the excavator.
There are a tremendous amount of factors for each part of the excavator which could consider
and analyze, therefore in the next section, one of the discussed option that can be
accomplished in future is plot for parameterized vehicles. By the way, results and plots for
each vehicles and each function are entirely different with another vehicle or function of that
vehicle.
4.3 Future work
In many researches and projects, there is always a point of view about the future and what
will improve, change, and modify in next steps. The improvement for this research, from
some angles can be considered which are feasible. Modification in software and interactions
among them, involving other software, producing a real model based on the simulation as
12.71
36.3
7.1
2.34.8
16.14
27.63
9.67
2.844.9
19.92
23.65
12.6
3.65.2
0
5
10
15
20
25
30
35
40
Total Time (S) Needed Torque(Nme2)
Volume ofCylinder(m3e2)
Maximum Force(Ne5)
Fuel Consumption
Small Cylinder-Piston Medium Cylinder-Piston Big Cylinder-Piston
76
marketing point of view, etcetera. In this chapter some of the most feasible future work will
be discussed.
4.3.1 Using Software and their connections
To design a simulation model, in this case, some software such as SolidWorks, MeVEA,
Blender, and Python have been used. To create visualization graphics, two software, Blender
and SolidWorks have been used, however, sometimes communications between them and
MeVEA have some problems. Undoubtedly, SolidWorks is helpful to design bodies in
details and their assemblies in a proper way. On the other hand, Blender is a strong software
to create real graphics especially for the environment. The drawback to use both software is
a lack of an appropriate united file format to save created files and implement them in
MeVEA. MeVEA can read 3ds and Osgt file formats and SolidWorks cannot create them.
Also Blender is not be able to create Osgt file format. Moreover, all parts create in
SolidWorks should be colorless because Blender cannot recognize colors coming from
SolidWorks.
At the moment the optimized way to create graphics is to generate bodies in SolidWorks and
export them to Blender and produce them ready and add the environment graphics and apply
them in MeVEA. This steps takes time and sometimes it is not without adversity. Two
solutions may come to mind; one of them is to design bodies in a third software which can
do all graphics in itself, and second solution is to write a code such as a Python or a Matlab
code to act as a bridge between three software and create a unique file format which is
readable in MeVEA with all details.
4.3.2 User-friendlier interface - Gamification
At the moment there are three kinds of interfaces which users can customized their model
before running. As in chapter 3.4 is explained, a user can either use assembly file approach
or coding files approach. Moreover there is a third way to have an eye-catching interface
and it is using MeVEA launcher. In this very way some gamification aspects can be added
too. This means that in a launcher, a simple mission also can be considered with some meters
such as fuel-meter, velocity-meter et cetera. With using MeVEA launcher, the interface will
be friendlier than before. A kind of user-interface with outstanding graphics can be designed
that user can run a simulation model in format of a game and also she/he can trace the
77
progress of simulating model in a way that for instance how much pressure is applying to
the motor or other specified parts, how much time is spent, how much fuel is consumed et
cetera. In addition, in gamification point of view, a competition can be designed in order to
rank users based on their performances. Another striking idea is to have a model in variety
environments to create more games and test the model.
4.3.3 Further customizations - Analyze section
With assistance of coding and assembly approaches many other feasible and reasonable
parameterizations can be done to figure out the optimum combinations. This idea provides
a right set of circumstances to customers in order to analyze some important specifications
of a vehicle. It means that this circumstances will be able to answer to some major questions
such as, what will happen about abrasion of bodies of the vehicle, fuel consumption, forces
and torques applied to the vehicle, the amount of time needed to do a mission and so on.
Furthermore, a company can classified its products based on market and customer’s
demands. For instance, in some situation, time is the most important factor, however in other
situation the most serious factor can be fuel consumption, or life-time of the vehicle, so the
company can provide and offer wider range of its products to market.
Moreover, a simulation model can possesses three sections. A user customizes a model based
on her/his needs. Afterwards, she/he runs it in the simulation environment and can have
gamification and see options explained in section 5.2. Finally, she/he can see some diagrams,
plots, and comparison tables to figure out her/his performance and also the performance of
the vehicle as well. It should be noticed that this diagrams and plots also can be customized
in which the user select them among other diagrams and tables before simulation.
4.3.4 Visualization of models and environments - Environment customization
The concept of improvement of visualization is to have different graphics for different parts
while customization. For instance, for a bucket of the excavator, some visualization graphics
can be set for each type of the bucket. Also an idea is to have a customization for
environment, not only in gamification point of view but also to test and extract results of a
simulation model in some different environment which have their situations and figure out
how a vehicle, for example an excavator, will represent its performance and reliability in
various environments.
78
5 CONCLUSION
The main objective for this master’s thesis is to create and design innovative ways to obtain
a real-time simulation model which can be customized. This target can be achievable with
help of MeVEA software, Python, SolidWorks, and Blender software. MeVEA software is
selected as the real-time simulation software.
With a Python code all desirable parameters for a simulation model can be customized. All
collision and visualization graphics for a vehicle and the environment are done with
SolidWorks and Blender. Development idea and process commenced from studying on
previous attempts and researches about real-time simulation models and efforts to customize
them. In this observations and after a comprehensive study on simulation concepts and steps
(literature review), a lack of a practical model that can be customized in a functional and
simple way felt. Despite of some limitations and difficulties, acquiring to this type of
simulation model has wealthy benefits and this aim can be reachable with a logical and
feasible steps.
To put the issue in a nutshell, the concept is to collect data which are selected with a user
and combine them with other data and make the simulation model ready to run. Then the
model will be run and required information and data can be extracted. At first in a user-
friendly environment, an Excel file, a user selects her/his favorite data. Then with a Python
code, as a bridge between the Excel file and MeVEA software, this data can add to the
generic model in MeVEA and the model is ready to simulate.
With a parameterized model, the amount of time need to change and analyze a simulation
model will decrease tremendously. In addition, these types of modifications is not cost-
effective without parameterized models. A parameterized model can reduce the amount of
money from two aspects; in general it can prevent the amount of budget which should spend
to manufacture a real model. Moreover, it can decrease total number of hours spending to
design some models which cost a significant amount of money and obtains an interesting
interface to change parameters and work with the model in an enjoyable environment and
extract precise analysis.
79
Parameterized simulated model accomplished all targets and demands which were discussed
as its benefits and functions at the commencement of this master’s thesis. Having a
customized simulation model provides an opportunity to build a model in a noticeable short
time with obtaining accurate analysis in comparison of previous concepts. With a customized
model the speed of creating simulation models and present those to market will increase
significantly and it is a brilliant way to conquer the real-simulation market.
80
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APPENDICES
Appendix 1
Figure A1.1 shows a spatial body. (Flores, 2015, p. 12)
Figure A1.1. Body i without constraint and its location in 3D (Flores, 2015, p. 12).
𝐫𝑃𝑖 = 𝐫𝑖 + 𝐬𝑃
𝑖 (a1.1)
ξi2ηi2ζi2: the body-fixed coordinate system which is body’s coordinate system.
𝐬𝑖 𝑃 = 𝐀′
𝑖 𝐬𝑖′ 𝑃 (a1.2)
𝐀′𝑖 : Rotation matrix and 𝐬𝑖
′ 𝑝 is a constant vector for the mentioned rigid body.
Appendix 2
Spatial MBS showing its translation and rotation concept, figure A2.1. (Flores, 2015, p. 16)
Figure A2.1. Translation and rotation (Flores, 2015, p. 16).
Figure A2.2. Rotation vectors without presence of translation (Flores, 2015, p. 16).
The elements of A, rotational transformation matrix:
𝐎 = [cos𝛹 − sin𝛹 0sin𝛹 cos𝛹 0
0 0 1] , 𝐄 = [
1 0 00 cos 𝜃 − sin 𝜃0 sin 𝜃 𝑐𝑜𝑠𝜃
] , 𝐁 = [cos 𝜎 −𝑠𝑖𝑛𝜎 0−𝑠𝑖𝑛𝜎 cos 𝜎 0
0 0 1]
(a2.1)
Then,
𝐀 = [𝑐𝑜𝑠𝛹𝑐𝑜𝑠𝜎 − 𝑠𝑖𝑛𝛹𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜎 −𝑐𝑜𝑠𝛹𝑠𝑖𝑛𝜎 − 𝑠𝑖𝑛𝛹𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜎 𝑠𝑖𝑛𝛹𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝛹𝑐𝑜𝑠𝜎 + 𝑐𝑜𝑠𝛹𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜎 −𝑠𝑖𝑛𝛹𝑠𝑖𝑛𝜎 + 𝑐𝑜𝑠𝛹𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜎 −𝑐𝑜𝑠𝛹𝑠𝑖𝑛𝜃
𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜎 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜎 𝑐𝑜𝑠𝜃] (a2.2)
θ=0 then,
𝐀 = [𝑐𝑜𝑠(𝛹 + 𝜎) 𝑠𝑖𝑛(𝛹 + 𝜎) 0𝑠𝑖𝑛(𝛹 + 𝜎) −𝑐𝑜𝑠(𝛹 + 𝜎) 0
0 0 1
] (a2.3)
The Bryant angles can help to overcome to singularity issue. (Flores, 2015, p. 16).
Figure A2.3. Steps of rotation for Bryant angles, a) main global system coordinates; b and
c and d) First, second and third rotation respectively (Flores, 2015, p. 17).
𝐎 = [1 0 00 𝑐𝑜𝑠𝜑1 −𝑠𝑖𝑛𝜑1
0 𝑠𝑖𝑛𝜑1 𝑐𝑜𝑠𝜑1
],𝐄 = [𝑐𝑜𝑠𝜑2 0 𝑠𝑖𝑛𝜑2
0 1 0−𝑠𝑖𝑛𝜑2 0 𝑐𝑜𝑠𝜑2
], 𝐁 = [𝑐𝑜𝑠𝜑3 −𝑠𝑖𝑛𝜑3 0𝑠𝑖𝑛𝜑3 𝑐𝑜𝑠𝜑3 0
0 0 1
]
(a2.4)
The transformation matrix, A is A=O*E*B,
𝐀
= [𝑐𝑜𝑠𝜑2𝑐𝑜𝑠𝜑3 −𝑐𝑜𝑠𝜑2𝑠𝑖𝑛𝜑3 𝑠𝑖𝑛𝜑2
𝑐𝑜𝑠𝜑1𝑠𝑖𝑛𝜑3 + 𝑠𝑖𝑛𝜑1𝑠𝑖𝑛𝜑2𝑐𝑜𝑠𝜑3 𝑐𝑜𝑠𝜑1𝑐𝑜𝑠𝜑3 − 𝑠𝑖𝑛𝜑1𝑠𝑖𝑛𝜑2𝑠𝑖𝑛𝜑3 −𝑠𝑖𝑛𝜑1𝑐𝑜𝑠𝜑2
𝑠𝑖𝑛𝜑1𝑠𝑖𝑛𝜑3 − 𝑐𝑜𝑠𝜑1𝑠𝑖𝑛𝜑2𝑐𝑜𝑠𝜑3 𝑠𝑖𝑛𝜑1𝑐𝑜𝑠𝜑3 + 𝑐𝑜𝑠𝜑1𝑠𝑖𝑛𝜑2𝑠𝑖𝑛𝜑3 𝑐𝑜𝑠𝜑1𝑐𝑜𝑠𝜑2
]
(a2.5)
The steps of Euler parameters’ utilization:
𝑒0 = 𝑐𝑜𝑠𝜑
2 (a2.6)
𝐞 = {𝑒1 𝑒2 𝑒3}𝑇 = 𝐫 𝑠𝑖𝑛
𝜑
2 (a2.7)
e0, e1, e2 and e3 are Euler parameters.
Figure A2.4. Euler Parameters (Flores, 2015, p. 20)
𝑒02 + 𝑒𝑇𝑒 = 𝑒0
2 + 𝑒12 + 𝑒2
2 + 𝑒32 = 1 (𝑎2.8)
(a2.9)
𝐩𝑇𝐩 = 1 (a2.10)
𝐀 = 2
[ 𝑒0
2 + 𝑒12 −
1
2𝑒1𝑒2 − 𝑒0𝑒3 𝑒1𝑒3 + 𝑒0𝑒2
𝑒1𝑒2 + 𝑒0𝑒3 𝑒02 + 𝑒2
2 −1
2𝑒2𝑒3 − 𝑒0𝑒1
𝑒1𝑒3 − 𝑒0𝑒2 𝑒2𝑒3 + 𝑒0𝑒1 𝑒02 + 𝑒3
2 −1
2]
(a2.11)
Figure A2.5. Types of orientation of a body-fixed frame which clarify the resolution of the
Euler parameters a ξηζ || xyz; b ξ || x; c η || y; d ζ || z (Flores, 2015, p. 21).
So, if case A6.a
𝐩 = {1 0 0 0}𝑇 (a2.12)
In cases of figure A6.b, figure A6.c, and figure A6.d:
𝐩 = {𝑐𝑜𝑠𝜑
2 𝑠𝑖𝑛
𝜑
2 0 0 }
𝑇
(a2.13)
𝐩 = {𝑐𝑜𝑠𝜑
2 0 𝑠𝑖𝑛
𝜑
2 0 }
𝑇
(a2.14)
𝐩 = {𝑐𝑜𝑠𝜑
2 0 0 𝑠𝑖𝑛
𝜑
2 }
𝑇
(a2.15)
Appendix 3
In figure A7, vectors aj and bj are perpendicular to each other and to the joint axis.
The constraint equations (Flores, 2015, p. 45)
𝛗(s,3) ≡ {
𝛗(s,3) = 𝐫𝑗 + 𝐬𝑗𝑃 − 𝐫𝑖 − 𝐬𝑖
𝑃 = 0
𝛗(𝑛1,1) ≡ 𝐬𝑖𝑇𝐚𝑗 = 0
𝛗(𝑛1,1) ≡ 𝐬𝑖𝑇𝐛𝑗 = 0
(a3.1)
Figure A3.1. Revolute joint between two bodies, i and j (Flores, 2015, p. 45).
�̇�(𝑛1,1) = 𝐛𝑗𝑇�̇�𝑖 + 𝐬𝑖
𝑇�̇�𝑗 = 0 (a3.2)
�̈�(𝑛1,1) = 𝐬𝑖𝑇�̈�𝑖 + 𝐛𝑗
𝑇�̈�𝑗 + 2�̇�𝑗𝑇�̇�𝑖 = 0 (a3.3)
Figure A3.2. Body i and j connected with a spherical-spherical joint (Flores, 2015, p. 47).
Appendix 4 (Flores, 2015, pp. 49-52)
Equations of Motion for the Constrained Systems and Translational equations of motion
(without being constrained).
𝑚�̈� = 𝐟 (a4.1)
m is the mass, �̈� is the acceleration of the COM, and f is the force
Rotational equations:
𝐽�̇� + �̃�𝐽𝛚 = 𝑛𝑚 (a4.2)
J is the global inertia tensor, �̇� is the global angular acceleration, ω is the global angular
velocity, and nm is the all moments effecting on the body.
[𝑚𝐈 00 𝐽
] {�̈��̇�
} + {0
�̃�𝐽𝛚} = {
𝐟𝑛𝑚
} (a4.3)
[𝑚𝐈 00 𝐽
] {�̈��̇�
} = {𝐟
𝑛𝑚 − �̃�𝐽𝛚} (a4.4)
𝐌𝑖 = [𝑚𝐈 00 𝐽
], �̇�𝑖 = {�̈��̇�
}, 𝐠𝑖 = {𝐟
𝑛𝑚 − �̃�𝐽𝛚} (a4.5)
So,
𝐌𝑖�̇�𝑖 = 𝐠𝑖 (a4.6)
𝐌�̇� = 𝐠 + 𝐠(𝑐) (a4.7)
𝐠(𝑐) = 𝐃𝑇𝜆 (a4.8)
The dynamic equations of motion for a constrained multibody system
𝐌�̇� − 𝐃𝑇𝜆 = 𝐠 (a4.9)
Appendix 5
The constraint equations, Jacobian matrix, Newton difference for position analysis and
velocity analysis can be seen as below;
Figure A5.1. 4-bar mechanism for solving the constraint equation
𝛼′- 𝜃′𝜑′ �̇�′ �̇�′ �̇�′
Joint-p
[𝐫𝑥,𝐴
𝐫𝑦,𝐴] = [
𝑅𝑥,𝐴
𝑅𝑦,𝐴] + [
𝐶𝑜𝑠 𝜃′ −𝑆𝑖𝑛 𝜃′
𝑆𝑖𝑛 𝜃′ 𝐶𝑜𝑠 𝜃′ ] [−(𝑙
2)𝐴
0
] = [00]
𝐂1: 𝑅𝑥,𝐴 − (𝑙
2)𝐴
𝐶𝑜𝑠 𝜃′ = 0
𝐂2: 𝑅𝑦,𝐴 − (𝑙
2)𝐴𝑆𝑖𝑛 𝜃′ = 0
Joint-e
[𝑅𝑥,𝐴
𝑅𝑦,𝐴] + [
𝐶𝑜𝑠 𝜃′ −𝑆𝑖𝑛 𝜃′
𝑆𝑖𝑛 𝜃′ 𝐶𝑜𝑠 𝜃′ ] [(𝑙
2)𝐴
0
] = [𝑅𝑥,𝐵
𝑅𝑦,𝐵] + [
𝐶𝑜𝑠 𝛼′ −𝑆𝑖𝑛 𝛼′
𝑆𝑖𝑛 𝛼′ 𝐶𝑜𝑠 𝛼′ ] [−(𝑙
2)𝐵
0
]
𝐂3: 𝑅𝑥,𝐴 + (𝑙
2)𝐴𝐶𝑜𝑠 𝜃′ − 𝑅𝑥,𝐵 + (
𝑙
2)𝐵
𝐶𝑜𝑠 𝛼′ = 0
𝐂4: 𝑅𝑦,𝐴 + (𝑙
2)𝐴𝑆𝑖𝑛 𝜃′ − 𝑅𝑦,𝐵 + (
𝑙
2)
𝐵𝑆𝑖𝑛 𝛼′ = 0
Joint-f
[𝑅𝑥,𝐵
𝑅𝑦,𝐵] + [
𝐶𝑜𝑠 𝛼′ −𝑆𝑖𝑛 𝛼′
𝑆𝑖𝑛 𝛼′ 𝐶𝑜𝑠 𝛼′ ] [(𝑙
2)
𝐵
0
] = [𝑅𝑥,𝐶
𝑅𝑦,𝐶] + [
𝐶𝑜𝑠 𝜑′ −𝑆𝑖𝑛 𝜑′
𝑆𝑖𝑛 𝜑′ 𝐶𝑜𝑠 𝜑′ ] [−(𝑙
2)𝐶
0
]
𝐂5: 𝑅𝑥,𝐵 + (𝑙
2)𝐵
𝐶𝑜𝑠 𝛼′ − 𝑅𝑥,𝐶 + (𝑙
2)𝐶𝐶𝑜𝑠 𝜑′ = 0
𝐂6: 𝑅𝑦,𝐵 + (𝑙
2)
𝐵𝑆𝑖𝑛 𝛼′ − 𝑅𝑦,𝐶 + (
𝑙
2)𝐶𝑆𝑖𝑛 𝜑′ = 0
Joint-g
[𝐫𝑥,𝐶
𝐫𝑦,𝐶] = [
𝑅𝑥,𝐶
𝑅𝑦,𝐶] + [
𝐶𝑜𝑠 𝜑′ −𝑆𝑖𝑛 𝜑′
𝑆𝑖𝑛 𝜑′ 𝐶𝑜𝑠 𝜑′ ] [(𝑙
2)𝐶
0
] = [00]
𝐂7: 𝑅𝑥,𝐶 + (𝑙
2)
𝐶𝐶𝑜𝑠 𝜑′ = 0
𝐂8: 𝑅𝑦,𝐶 + (𝑙
2)
𝐶𝑆𝑖𝑛 𝜑′ = 0
As the last constraint equation, there is a torque,𝑀1 is implementing at the joint p.
𝐂9: 𝑀1 − 𝜃′
The function of this torque is a constant number.
Jacobian Matrix
𝐪 = [𝑅𝑥,𝐴 𝑅𝑦,𝐴 𝜃′ 𝑅𝑥,𝐵 𝑅𝑦,𝐵 𝛼′ 𝑅𝑥,𝐶 𝑅𝑦,𝐶 𝜑′]
𝐂𝐪 =
[ 𝜕𝐂1
𝜕𝐪1⋯
𝜕𝐂1
𝜕𝐪𝑛
⋮ ⋱ ⋮𝜕𝐂𝑛
𝜕𝐪1⋯
𝜕𝐂𝑛
𝜕𝐪𝑛]
𝐂𝐪 =
[ 1 0 (
𝑙
2)𝐴𝑆𝑖𝑛𝜃′ 0 0 0 0 0 0
0 1 −(𝑙
2)𝐴
𝐶𝑜𝑠𝜃′ 0 0 0 0 0 0
1 0 − (𝑙
2)𝐴𝑆𝑖𝑛𝜃′ −1 0 −(
𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ 0 0 0
0 1 (𝑙
2)𝐴𝐶𝑜𝑠𝜃′ 0 −1 (
𝑙
2)
𝐵𝐶𝑜𝑠𝛼′ 0 0 0
0 0 0 1 0 −(𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ −1 0 −(𝑙
2)
𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 1 (𝑙
2)
𝐵𝐶𝑜𝑠𝜃′ 0 −1 (
𝑙
2)𝐶𝐶𝑜𝑠𝜑′
0 0 0 0 0 0 1 0 −(𝑙
2)
𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 0 0 0 1 (𝑙
2)𝐶𝐶𝑜𝑠𝜑′
0 0 −1 0 0 0 0 0 0 ]
Newton difference for position analysis:
Δq= −𝐂𝐪−1𝐂
𝛥𝐪 = −
[ 1 0 (
𝑙
2)𝐴𝑆𝑖𝑛𝜃′ 0 0 0 0 0 0
0 1 −(𝑙
2)𝐴𝐶𝑜𝑠𝜃′ 0 0 0 0 0 0
1 0 −(𝑙
2)𝐴𝑆𝑖𝑛𝜃′ −1 0 −(
𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ 0 0 0
0 1 (𝑙
2)𝐴𝐶𝑜𝑠𝜃′ 0 −1 (
𝑙
2)𝐵
𝐶𝑜𝑠𝛼′ 0 0 0
0 0 0 1 0 −(𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ −1 0 − (𝑙
2)𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 1 (𝑙
2)𝐵
𝐶𝑜𝑠𝜃′ 0 −1 (𝑙
2)
𝐶𝐶𝑜𝑠𝜑′
0 0 0 0 0 0 1 0 − (𝑙
2)𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 0 0 0 1 (𝑙
2)
𝐶𝐶𝑜𝑠𝜑′
0 0 −1 0 0 0 0 0 0 ] −1
×
[ 𝐑𝑥,𝐴 − (
𝑙
2)𝐴𝐶𝑜𝑠 𝜃′
𝐑𝑦,𝐴 − (𝑙
2)𝐴𝑆𝑖𝑛 𝜃′
𝐑𝑥,𝐴 + (𝑙
2)𝐴𝐶𝑜𝑠 𝜃′ − 𝐑𝑥,𝐵 + (
𝑙
2)𝐵
𝐶𝑜𝑠 𝛼′
𝐑𝑦,𝐴 + (𝑙
2)𝐴𝑆𝑖𝑛 𝜃′ − 𝐑𝑦,𝐵 + (
𝑙
2)𝐵
𝑆𝑖𝑛 𝛼′
𝐑𝑥,𝐵 + (𝑙
2)𝐵
𝐶𝑜𝑠 𝛼′ − 𝐑𝑥,𝐶 + (𝑙
2)𝐶𝐶𝑜𝑠 𝜑′
𝐑𝑦,𝐵 + (𝑙
2)
𝐵𝑆𝑖𝑛 𝛼′ − 𝐑𝑦,𝐶 + (
𝑙
2)𝐶𝑆𝑖𝑛 𝜑′
𝐑𝑥,𝐶 + (𝑙
2)
𝐶𝐶𝑜𝑠 𝜑′
𝐑𝑦,𝐶 + (𝑙
2)𝐶𝑆𝑖𝑛 𝜑′
𝑀1 − 𝜃′ ]
Velocity Analysis:
�̇� = 𝐂𝐪−1[−𝐂𝑡]
𝐂𝑡 =
[ 00000000�̇�1]
[ �̇�𝑥,𝐴
�̇�𝑦,𝐴
�̇�′
�̇�𝑥,𝐵
�̇�𝑦,𝐵
�̇�′
�̇�𝑥,𝐶
�̇�𝑦,𝐶
�̇�′ ]
=
[ 1 0 (
𝑙
2)𝐴𝑆𝑖𝑛𝜃′ 0 0 0 0 0 0
0 1 −(𝑙
2)𝐴𝐶𝑜𝑠𝜃′ 0 0 0 0 0 0
1 0 −(𝑙
2)𝐴
𝑆𝑖𝑛𝜃′ −1 0 −(𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ 0 0 0
0 1 (𝑙
2)𝐴𝐶𝑜𝑠𝜃′ 0 −1 (
𝑙
2)𝐵
𝐶𝑜𝑠𝛼′ 0 0 0
0 0 0 1 0 −(𝑙
2)𝐵
𝑆𝑖𝑛𝛼′ −1 0 − (𝑙
2)𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 1 (𝑙
2)𝐵
𝐶𝑜𝑠𝜃′ 0 −1 (𝑙
2)
𝐶𝐶𝑜𝑠 𝜑′
0 0 0 0 0 0 1 0 − (𝑙
2)𝐶𝑆𝑖𝑛𝜑′
0 0 0 0 0 0 0 1 (𝑙
2)
𝐶𝐶𝑜𝑠𝜑′
0 0 −1 0 0 0 0 0 0 ] −1
×
[ 00000000�̇�1]
Appendix 6
Some detail information about three types of excavators of Volvo Company. In figures
below, the data about EW160D, EW180D, and EW210D can be found (Volvo, 2012).
Appendix 7
Python code as a bridge between the excel file, user-interface, and MeVEA software.
Appendix 8
Results for the Medium Bucket:
Bodies/Bucket: Global Position of LOC (y direction)
Figure A8.1. Total time and positions of the medium bucket in global y direction.
Total time: 19.35 s
Dummies- DipperArmCylinder_Dummey wy
Figure A8.2. The angular velocity in global y direction for the dipper arm cylinder using the
medium bucket.
Power Transmission: Motor Power (P)
Figure A8.3. Power for the main motor of the excavator using medium bucket.
Max: 1.124 e2 kW at 1.21s
Min: 2.5e-2 kW at 4.33
Output: AO_Fuel Consumption:
Figure A8.4. Fuel consumption for the excavator using the small bucket.
Max: 5.524e-2
Big Bucket
Results for the big bucket:
Figure A8.5. Total time and positions of the big bucket in global y direction.
Total time: 27.24 s
Dummies- DipperArmCylinder_Dummey wy:
Figure A8.6. The angular velocity in global y direction for the dipper arm cylinder using the
big bucket
Power Transmission: Motor Power (P)
Figure A8.7. Power for the main motor of the excavator using big bucket.
Max: 1.132e2 kW at 14.3s and Min: 1.55e-3 kW at 5.81s
Output: AO_Fuel Consumption:
Figure A8.8. Fuel consumption for the excavator using the big bucket.
Maximum value: 7.77e-2