Project Design Of Mechanical System Topic Calculations For Industrial Robot Control.pdf

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HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGYSCHOOL OF MECHANICAL ENGINEERING

Hanoi, August, 2022

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TABLE OF CONTENTS

CHAPTER I. FUNDAMENTAL KNOWLEDGE OF INDUSTRIAL ROBOTS...1

1.1 History of industrial robots development...1

1.2. Definition and classification...1

1.2.1. Definition...1

1.2.2. Classification...2

1.3 Application of Industrial Robot...3

CHAPTER II. KINEMATICS PROBLEM...4

2.1. Survey of forward kinematics...4

2.1.1. Setting coordinate system for robot...4

2.1.2. Setting the Denavit-Hatenberg parameters...4

2.1.3. Coordinate transformation matrix...5

2.2. Forward kinematics problem...6

CHAPTER IV. MANIPULATOR DYNAMICS...18

4.1. The iterative Newton-Euler dynamics algorithm...18

*** Calculation:...18

CHAPTER V. CONCLUSION...21

REFERENCES...22

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LIST OF FIGURES AND GRAPHS

Figure 1. Link-frame attachment...4

Figure 2. A three-link planar arm...6

Figure 3a. Calculation of forward kinematics in MATLAB...7

Figure 3b. Tranformation matrix 0T and 0HT in MATLAB...8

Figure 4a. 0T and 0HT after subsituting given data of problem 2.2A...8

Figure 4b. Frame assignment of problem 2.2A...9

Figure 5a. 0T and 0HT after subsituting given data of problem 2.2B...9

Figure 5b. Frame assignment of problem 2.2B...10

Figure 6a. 0T and 0HT after subsituting given data of problem 2.2C...10

Figure 6b. Frame assignment of problem 2.2C...11

Figure 7. The two inverse kinematics solutions for the 3R manipulator:“elbow-up” configuration



 1



and the “elbow-down” configuration



 1



...12

Figure 8a. Frame assignment of problem 2.3A...13

Figure 8b. Frame assignment of problem 2.3B...13

Figure 9. Resolved-Rate-Algorithm block diagram...14

Figure 10. The force balance, including inertial forces, for a single manipulator link...18

Figure 11a&b. Calculation of dynamics in MATLAB...19

Graphs:Graph 1. Joint rates...15

Graph 2. Joint angles...15

Graph 3. { }T



Xx y m m rad versus time...16

Graph 4. Determinant of Jacobian matrix versus time...16

Graph 5. Joint torque T{ }  123T versus time...17

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CHAPTER I.

FUNDAMENTAL KNOWLEDGE OF INDUSTRIAL ROBOTS

1.1 History of industrial robots development

The world’s first industrial robot was brought to life in the United States in 1962. The idea ofthe industrial robot was born from American engineer, George Charles Devol, Jr. in 1954. Devol met Joseph Frederick Engelberger, an entrepreneur and the man who would come to be known as "the father of robotics", and convinced him of the potential of his idea. And in 1961, the two Americans established Unimation Inc., a venture company specializing in industrial robot development. In the following year, they succeeded in the trial production of the world’s first industrial robot, the Unimate. US car manufacturers already working on factory automation at the time showed interest in the Unimate, and with the deployment of the robot in the General Motors Company (GM)’s die-casting factory, the practical use of industrial robots commenced.

Unimate – The First Industrial Robot

1.2. Definition and classification1.2.1. Definition

An industrial robot is one that has been developed to automate intensive production tasks such as those required by a constantly moving assembly line. As large, heavy robots, they are placed in fixed positions within an industrial plant and all other worker tasks and processes revolve around them.

According to the international standard ISO 8373:2012, the industrial robot definition is ‘a multifunctional, reprogrammable, automatically controlled manipulator, programmable in three or more axes that can be fixed in one area or mobile for use in industrial automation applications’.Industrial robots are not usually humanoid in form, although they are capable of reproducing human movements and behaviors but with the strength, precision and speed of a machine.

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Based on mechanical configuration, industrial robots can be classified into six major types namely: Articulated Robots

 Cartesian Robots SCARA Robots

 Delta Robot Polar Robots  Cylindrical Robots

Apart from mechanical configuration, industrial robots can also be categorized based on motion control, power supply control and physical characteristics.

SCARA Robot Articulated Robot

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 By applications: industry, aviation universe, medical, military,… .

1.3 Application of Industrial Robot

Typical applications of robots include:  Welding

 Painting

 Assembly, Disassembly

 Pick and Place for printed circuit boards

 Packaging and Labeling  Palletizing

 Product inspection  Testing

All accomplished with high endurance, speed, and precision. They can assist in material handling.

Robot arc welding cell

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CHAPTER II. KINEMATICS PROBLEM

2.1. Survey of forward kinematics

2.1.1. Setting coordinate system for robot

Figure 1. Link-frame attachment

* Link-frame attachment procedure:

1. Identify the joint axes and imagine (or draw) infinite lines along them. For steps 2 through 5 below, consider two of these neighboring lines (at axes i and i ).1

2. Identify the common perpendicular between them, or point of intersection. At the point of intersection, or at the point where the common perpendicular meets the ith axis, assign the link-frame origin.

3. Assign the Zˆi

axis pointing along the ith joint axis.

4. Assign the Xˆi axis pointing along the common perpendicular, or, if the axes intersect,

assign Xˆi to be normal to the plane containing the two axes.

5. Assign the Yˆi axis to complete a right-hand coordinate system.

6. Assign {0} to match {1} when the first joint variable is zero. For {N}, choose an

origin location and XˆN direction freely, but generally so as to cause as

linkage parameters as possible to become zero.

2.1.2. Setting the Denavit-Hatenberg parameters

- Use Denavit-Hartenberg (D-H) method to solve the forward kinematics problem.

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- D-H Table:

Joint i1 ai1 di i

1 0 a0 d1 12 1 a1 d2 2

i i1 ai1 di iwhere: a = the distance from i Zˆi to Zˆi1

1, 2 and 3 are joint variables.

2.1.3. Coordinate transformation matrix

- Transformation that transforms vectors defined in

 

0012211. . . ... .23i1.iiT T T T i T Ti

- The general form of this transformation:

0 0 0 1

R R R PR R R PT

R R RR R R RR R R

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iPPx Py Pz : is the postion vector.

2.2. Forward kinematics problem

cos sin 0sin cos 0 0

0 0 0 1aT

cos sin 0sin cos 0 0

0 0 0 1aT

cos sin 0sin cos 0 0

0 0 0 1aT

1 0 00 1 0 00 0 1 00 0 0 1

0012T1T T.2

cos sin 0 cossin cos 0 sin

aaT

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+ Joint 3:

0012023T 1T T T. .23 2T T.3

HT T T T TH T TH

0, , ;cos ,cos ,cos ;sin ,sin ,sin ;cos c ,sin ;

c s 0 cs c 0 s s

L L cL LT

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Figure 3a. Calculation of forward kinematics in MATLAB

Figure 3b. Tranformation matrix 0T and 0

HT in MATLAB

*** Calculation:a. Problem 2.2A

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0 1 0 01 0 0 5.50 0 1 00 0 0 1T

HT after subsituting given data of problem 2.2A

Figure 4b. Frame assignment of problem 2.2A

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0 1 0 4.791 0 0 2.320 0 1 00 0 0 1T

Figure 5a. 0T and 0

HT after subsituting given data of problem 2.2B

Figure 5b. Frame assignment of problem 2.2B

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Figure 6a. 0T and 0

HT after subsituting given data of problem 2.2C

Figure 6b. Frame assignment of problem 2.2C

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- Assume

is given that:

c 00 0 1 00 0 0 1

1 12 1231231 12 123 123

c ,,

c ,s .c

s s

x L c L c Ly L s L s L

    Find 1, 2 and 3.

- Sovle the inverse kinematics problem+ We have 3 equations:

   

1 12 1231231 12 123 123123

c 1s 2 3x L c L c L

y L s L s L   

      

+ Substituting

 

3 into

 

and

 

, we have two equations:

  

31 12 1231 12 12

4 5x L c L c L c

y L s L s L s

  

  

cos R , 1P Q      

+ Substituting any one of these solutions back into

 

4 and

 

gives us:

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1 112

2 1 1 1 1

' 'Atan2 ,'

x L cc

L y L s x L c

 

+ Finally, 3 can be determined from

 

: 3   1 2.

- Conlcusion: From the inverse kinematics soltion for the 3-R manipulator, for a given end-effectorposition and orientation, there are two different ways of reaching it, each corresponding to a different value of . These different cofigurations are shown as below:

Figure 7. The two inverse kinematics solutions for the 3R manipulator:“elbow-up” configuration



 1



and the “elbow-down” configuration



 1



+ For  : 1 1210.510Unsatisfied.+ For  : 1 190 ,02180 ,033600.

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* Given: 0

  

4.445, 4.664, 90 , 3.5 2 1.5x y    L L L m* Result:

+ For  : 1 1319.090Unsatisfied.+ For  : 1 000

1 30 , 2 45 , 3 15      .

Figure 8a. Frame assignment of problem 2.3A

Figure 8b. Frame assignment of problem 2.3B

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CHAPTER III. STATICS

*** Calculation:

* Given:

+ Initial joint angles:



000123T 15 30 45 T    

+ End-effector velocity: 0

  

0, 2 0,3 0, 2

X x y     .+ Static force: 0

  

T



1 2 3

 

T , ,



W f f m  N N Nm.* Solutions:

Figure 9. Resolved-Rate-Algorithm block diagram

+ Use MATLAB to program and simulate Resolved-rate-control algorithm (simulate in 5 seconds, 0.1s for each step).

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+ Graph 1. Joint rates (m/s)

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+ Graph 2. Joint angles (rad)

+ Graph 3. X{ x y}T



m m rad



versus time

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+ Graph 4. Determinant of Jacobian matrix versus time

+ Graph 5. Joint torque T{ }  123T (Nm) versus time

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CHAPTER IV. MANIPULATOR DYNAMICS

4.1. The iterative Newton-Euler dynamics algorithm

+ Outward iterations: : 0i 2

+ Inward iterations: : 3i 1

Figure 10. The force balance, including inertial forces, for a single manipulator link

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- Use MATLAB to calculate

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Figure 11a&b. Calculation of dynamics in MATLAB*Given:

+ Weight of each link: m1 20, m2 15, m3 10

 

+ Moment of inertia of each link:



2



1 0.5, 2 0.2, 3 0.1

I  I  I  kgm+ Joint angles:



000

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CHAPTER V. CONCLUSION

"Calculating and designing control problems for industrial robots" is a highly practical topic, whenthe industry is growing, competition is constantly demanding, productivity and quality must be improved thanks to modern machinery lines replacing manual labor of humans.

Thus, in the module "Designing a mechanical system - Robot", I learned how to calculate and design a control system for a robot. Specific work completed includes the following:

 SCARA robot overview.

 Calculating the forward kinematics, inverse kinematics. Calculating velocity, static forces.

 Find out the dynamic problem of robot.

Through the above topic, I have learned how to apply professional knowledge trained at Hanoi University of Science and Technology in the past time into real life, especially with industry. I also learned a lot such as teamwork skills, problem solving, finding documents, writing reports... very useful for later. Once again, I would like to thank Dr. Tran Dinh Long helped me complete this thesis.

Due to the limitation of time and knowledge in this project, I only solved some fundamental problems in the design of a robot. In addition, there are many problems need to be solved to have a complete robot product such as mechanical design, equipment selection, algorithms, software programming, .... Therefore, I hope that other teachers and you will give me your comments to improve this topic.

Sincere thanks to all of you!

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