international journal of mechanical engineering … of robotic manipulato… · international...

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME

125

MODELLING OF ROBOTIC MANIPULATOR ARM

Srushti H. Bhatt1, N. Ravi Prakash

2, S. B. Jadeja

3

1Mechanical Engineering Department, B. H. Gardi, College of Engineering & Technology,

Rajkot, Gujarat, India 2RHRTD Group, Institute for Plasma Research, Gandhinagar, Gujarat, India

3Mechanical Engineering Department, B. H. Gardi, College of Engineering & Technology,

Rajkot, Gujarat, India

ABSTRACT

Kinematic modelling is an important section of robotic technology.The method was

used for three link arm manipulator. The kinematic modelling of the three link arm

manipulator with end effector was carried out. In this paper D-H matrix is used to solve

kinematic equations of robot. The dynamic forces are calculated for the maximum stretch

condition using multi body dynamics analysis. The results validated using the software

analysis andthe mathematical formulation.

Keywords—Forward kinematics, Denavit-Hartenberg (D-H) model, Multi body dynamics

1. INTRODUCTION

Kinematics & dynamics are important section of engineering, related to development

of special application of robots. Kinematicsconcentrates on motion of robots independent of

forces acting on it whereas Dynamics deals with the relationship between motion and the

associated forces and torques.The aim of kinematics is to define position relative to reference

frame & its origin. It is divided into two parts inverse kinematics and forward kinematics.

Forward kinematics deal with finding position and orientation of robot end effector as

function of its joint angle. Inverse kinematics deals with finding appropriate joint angles to

get a certain desired position and orientation of the end effector.

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING

AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)

ISSN 0976 – 6359 (Online)

Volume 4, Issue 3, May - June (2013), pp. 125-129

© IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com

IJMET

© I A E M E

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976

6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May

Simulation work was carried

having 3 degree of freedom.High torque dc motors were

angle was given using the potentiometer and final position

representation of forward kinematic

mutually-interconnected multiple rigid bodies

The work involved mathematical formulation

move as a system and what forces are generated in the

forward dynamic problem yields the motion of a Multibody system over a given time

interval, as a consequence of the applied forces and given initial conditions.

2. MODEL OF ROBOT

The dual arm robotic manipulator as a whole po

manipulator system was created using

The manipulator arm carries payload

for manipulator arm shown in Figure II.

Figure I


6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME

126

Simulation work was carried out for a robotic manipulatorarm withtwo arm each

High torque dc motors were used as actuation system. The joint

angle was given using the potentiometer and final position obtained. Denavi

kinematic was used. In Multibody dynamics analysis,

interconnected multiple rigid bodies is studied.

mathematical formulation &software analysis tofind how

move as a system and what forces are generated in the process with static analysis


interval, as a consequence of the applied forces and given initial conditions.

The dual arm robotic manipulator as a whole possesses nine degree of freedom.

created using 3d cad Catia software as shown in the figure below.

payload 1.2 kg. Analytical forces were calculated at each joint

pulator arm shown in Figure II.

Figure I: 3d Cad Model Of Manipulator

Figure II: Manipulator Arm


June (2013) © IAEME

two arm each

used as actuation system. The joint

Denavit–Hartenberg

Multibody dynamics analysis, dynamics of

find how bodies

with static analysis. The


ssesses nine degree of freedom. The

shown in the figure below.

1.2 kg. Analytical forces were calculated at each joint



127

3. METHODOLOGY

3.1 D-H Parameters The D-H model of representation is very simple way of modelling robot link and

joints that can be used for any robot configuration, regardless of sequence and complexity.

The D-H representation of rigid link is classified into four parameters, two link parameters

(ai, αi) and two joint parameters (di, θi).

• Link Length (ai)

• Link Twist (αi)

• Joint Distance (di)

• Joint Angle (θi)

The arms are symmetric to each other&the results are described using appropriate data.

TABLE I: D-H PARAMETER FOR MANIPULATOR ROBOT

3.2 Forward Kinematic Relationship Between Adjacent Link & Its Solution On establishing D-H parameters on link homogeneous transformation matrix

calculation were done. Four basic parameters for the matrix are rotation about z i-1 by an angle

θi, translation about z i-1 axis by distance di, translation along xi axis by distance ai, and

rotation about xi axis by an angle αi.

Ai = Rot(z, θi)Trans(z, di)Trans(x, ai)Rot(x, αi)

So the resultant T matrix is,

T = Tn = A1*A2*A3*A4:

T=-0.9524 0 0.3048 24.9887

0 1.000 0 0

-0.304 0 -0.9524 -160.061

0 0 0 1.0000

Joint

i θi di (mm) ai (mm) αi

0 θ1 0 0 90°

1 θ2 75 0 90°

2 θ3 0 162 0

3 θ4 0 0 0


6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May

Now calculating the static force acting at each joint of arm.

equations are formulated for finding force acting at each

at each joint is as formulated below in table.

TABLE II: MATHEMATICAL FORMULATION FOR FORCE

Link

1

2

3

Mathematical solutions were

was taken for multi body dynamic analysis

speed, and quality.The analysis was carried out by importing the 3

view and MBD static analysis was carried for the maximum stretch conditi

manipulator arm.The results are displayed here.

Figure III


6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME

128

Now calculating the static force acting at each joint of arm. The mathematical basic

equations are formulated for finding force acting at each joint. The solution of the force value

formulated below in table.

MATHEMATICAL FORMULATION FOR FORCE

Weight

(kg)

Length

(mm)

Force, mg

(N)

1.9 142 18.64

1.1 162 10.79

1 230 9.81

solutions were compared with hyper work. The Motion View

dy dynamic analysis. The software is validated for the robustness,

The analysis was carried out by importing the 3d cad model to the motion

static analysis was carried for the maximum stretch conditi

The results are displayed here.

Figure III: MBD Analysis Using Software


June (2013) © IAEME

The mathematical basic

The solution of the force value

MATHEMATICAL FORMULATION FOR FORCE

Motion View module

validated for the robustness,

model to the motion

static analysis was carried for the maximum stretch condition of the



129

4. RESULTS

TABLE III: FORCE RESULT COMPARISON

SN JOINTS

EXPERIMENTAL

RESULTS FOR

FORCE

SOFTWARE

RESULTS

OF FORCE

1 Joint 1 18.64 18.83

2 Joint 2 10.79 10.37

3 Joint 3 9.81 8.48

5. CONCLUSION

This paper solves and formulates the kinematic problem of the link with base for the

manipulator using D-H notation. Payload characteristic has been analysed using static force

equation & also simulation studies carried out using hyper works software as a proof of

concept. Both results are in good agreement. This result helps to choose proper actuators in

the application of pick and place robot.

6. ACKNOWLEDGMENT

The author acknowledges Institute for Plasma research, NFPfor giving financial

support, infrastructure & necessary guideline which enabled to set up my experimental work.

These supports are gratefully acknowledged.

REFERENCES

[1] Saeed B. Niku, "Introduction to Robotics", Pearson Prentice Hall, 2008, pg. 81-85.

[2] R K Mittal, J Nagrath, "Robotics and Control", Tata McGraw-Hill, 2005, pp. 76-81.

[3] Dr. Anurag Verma and Vivek A. Deshpande. “End-effector Position Analysis of

SCORBOT-ER Vplus Robot”, International Journal of Smart Home Vol. 5, No. 1,

January, 2011.

[4] Mahmoud Gouasmi, Mohammed Ouali, Brahim Fernini and M’hamed Meghatria.

“Kinematic Modelling and Simulation of a 2-R Robot Using SolidWorks and

Verification by MATLAB/Simulink”, International Journal of Advanced Robotic

Systems 26 May 2012.

[5] Peng Song “Modelling, Analysis and Simulation of Multibody systems with contact and

friction” 2002.

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