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
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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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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
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.
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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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
forward dynamic problem yields the motion of a Multibody system over a given time
ssesses nine degree of freedom. The
shown in the figure below.
1.2 kg. Analytical forces were calculated at each joint
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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.