welding robot

1. Dr. Anurag Verma et. al. / International Journal of Engineering Science and Technology
Vol. 2(9), 2010, 4682-4686
FORWARD KINEMATICS ANALYSIS
OF 6-DOF ARC WELDING ROBOT
DR. ANURAG VERMA1
, MEHUL GOR2
1,2
Mechanical Engineering Department, G. H. Patel College of Engineering & Technology,
Bakrol Road,V.V.Nagar-388120, Gujarat, India
Abstract:
The forward kinematics problem is concerned with the relationship between the individual joints of the robot
manipulator and the position and orientation of the tool or end-effector. Stated more formally, the forward
kinematics problem is to determine the position and orientation of the end-effector, given the values for the joint
variables of the robot. Present work is an attempt to develop kinematic model of a 6 DOF robot which is used
for arc welding operation. Developed model will determine position and orientation of the end-effector with
respect to various joint variables. The said analysis is carried out in Matlab.
Keywords: Forward kinematics, Position & Orientation of End-effector.
1. Introduction
Kinematic is the science of motion which treats motion without regard to the forces that cause it [1]. Within
the science of kinematics one studies the position, velocity, acceleration and all higher order derivatives of the
position variables (with respect to time and other variable(s).
A mechanical manipulator can be modeled as an open-loop articulated chain with several rigid bodies(links)
connected in series by either revolute or prismatic joints driven by actuators[2]. One end of the chain is attached
to a supporting base while the other end is free and attached with a tool (the end-effector).
A robotic manipulator is designed to perform a task in the 3-D space. The tool or end-effector is to follow a
planned trajectory to manipulate objects or carry out the task in the workspace. This requires control of position
of each link and joint of the manipulator to control both the position and orientation of the tool. To program the
tool motion and joint link motions, a mathematical model of the manipulator is required to refer to all
geometrical and/or time-based properties of the motion. Kinematic model describes the spatial position of joints
and links, and position and orientation of the end-effector [3,4,5].
2. Problem Statement
To perform desired work robot’s end effector has to follow the specific trajectory. To do so all the joints must be
operated with respect to time. The joints can either be very simple, such as a revolute joint or a prismatic joint.
The objective of forward kinematic analysis is to determine the cumulative effect of the entire set of joint
variables.
3. Methodology
3.1. Technical Specification of Robot
Collect technical specification of robot. 6-DOF arc welding robot has
 Degree of Freedom = 6
 Type of Joint = All rotary
 Payload = 20 kg
 Repeatability = ± 0.08 mm
 Mechanical Unit Mass = 220 kg
ISSN: 0975-5462 4682

2. Dr. Anurag Verma et. al. / International Journal of Engineering Science and Technology
Vol. 2(9), 2010, 4682-4686
3.2. Frame Assignment
The Denavit-Hartenberg method is used for systematically establishing a coordinate system (body attached
frame) to each link of an articulated chain. Once these link attached coordinate frames are assigned,
transformations between adjacent coordinate frames can then be represented by a single standard 4x4
homogeneous coordinate transformation matrix.
Using the link frame assignment algorithm [3] first of all the Zi-axis of the entire joint is fixed in the direction of
rotation as followed by the right-handed rule for rotation. The index number for the Z-axis of joint n in each
case is n-1. That means, joint 1 rotation axis is denoted as Z0. Here the rotation about the Z-axis will be the joint
variable. Then Xi axis is fixed considering Zi-1 and Zi axes. And finally Yi axis is fixed to completes the right
handed orthonormal coordinate frame {i}. Thus frame assignment of 6-DOF robot will be completed as shown
in Fig. 1
Fig.1 Frame Assignment
3.3. DH Parameter
The four DH parameters –two link parameters (ai, αi) and two joint parameters (di, θi) are defined as:
(1) Link length (ai) – Distance measured along xi axis from the point of intersection of xi axis with zi-1 axis to
the origin of frame {i}.
(2) Link twist (αi) – angle between zi-1 and zi axes measured about xi- axis in the right hand sense.
(3) Joint distance (di) – distance measured along zi-1 axis from the origin of frame {i-1} to the intersection of
xi-axis with zi-1 axis.
(4) Joint angle (θi) – angle between xi-1 and xi axes measured about the zi-1 axis in the right-hand sense.
3.4. Kinematic Model
The position and orientation of the tool frame relative to the base frame can be found by considering the n
consecutive link transformation matrices relating frames fixed to adjacent links. The tool frame, frame {n}, can
also be considered as a translated and rotated frame with respect to base frame {0}. The transformation between
these two frames is denoted by end-effector transformation matrix T, in terms of tool frame orientation (n,o,a)
and its displacement (d) from the base frame {0}.
T = 0
Tn = 0
T1
1
T2 … n-1
Tn (1)
θ6
θ5
θ4
θ3
θ1
θ2
X
Z
Y
X
Y
Z
Y2
X
Z
Z
X
Y
X
Z
Y
Z
Y
X
Z
Y
X
0.30
0.77
0.15
0.1
0.7
0.05
0.30
3
4
5
6
0.15
2
1
0
0.1
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3. Dr. Anurag Verma et. al. / International Journal of Engineering Science and Technology
Vol. 2(9), 2010, 4682-4686
This equation is known as the kinematic model of the n-DOF manipulator.
To find the transformation matrix relating two frames attached to the adjacent links, consider frame {i-1} and
frame {i}. The transformations of frame {i-1} to frame {i} consists of four basic transformations.
(1) A rotation about zi-1 axis by an angle i;
(2) Translations along zi-1 axis by distance di;
(3) Translation by distance ai along xi axis and
(4) Rotation by an angle i about xi axis
Using the spatial coordinate transformation, the composite transformation, Which describes frame {i} with
respect to frame {i-1}, is obtained using equation
i-1
Ti = Tz(i)Tz(di)Tx(ai)Tx(i) (2)
i-1
Ti =
















































 
1000
00
00
0001
1000
0100
0010
001
1000
100
0010
0001
1000
0100
00
00
ii
ii
i
i
ii
ii
CS
SC
a
d
CS
SC



i-1
Ti =














1000
0 iii
iiiiiii
iiiiiii
dCS
SaSCCCS
CaSSCSC



(3)
where Ci = cosi, Si = sini, Ci = cosi, and Si = sini
4. Results
Kinematic model is developed using above methodology in Matlab for 6-DOF arc welding robot. Frame
assignment of 6-DOF robot will be as per fig. 1 and DH parameter of robot will be as per table 1.
Table 1 DH Parameter
A
(M)

(DEG)
D
(M)

(DEG)
0.150 -90 0.300 1
0.770 0 0 90+2
0.100 -90 0.150 3
0 90 0.740 4
0.050 -90 0 5
0 0 0.300 6
Developed model is used to determine position and orientation of end effector. For values of θ1 = 68.06°, θ2 =
99.39°, θ3 = -58.56°, θ4 = -30.29°, θ5 = -51.06° & θ6 = 6.38°, results obtained is shown below.
Transformation matrix for link 1 is
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4. Dr. Anurag Verma et. al. / International Journal of Engineering Science and Technology
Vol. 2(9), 2010, 4682-4686
0
T1 =
(4)
Transformation matrix for link 2 is
1
T2 =
(5)
Transformation matrix for link 3 is
2
T3 =
(6)
Transformation matrix for link 4 is
3
T4 =
(7)
Transformation matrix for link 5 is
4
T5 =
(8)
Transformation matrix for link 6 is
5
T6 =
(9)
The homogeneous matrix 0
T6 which specifies the location of the 6th
coordinate frame with respect to the base
coordinate system will be
0
T6=0
T1 x 1
T2 x 2
T3 x 3
T4 x 4
T5 x 5
T6
0
T6 =
(10)
0.3736 0 -0.9276 0.0560
0.9276 0 0.3736 0.1391
0 -1.000 0 0.3000
0 0 0 1.0000
-0.1632 -0.9866 0 -0.1256
0.9866 -0.1632 0 0.7597
0 0 1.0000 0
0 0 0 1.0000
0.5216 0 0.8532 0.0522
-0.8532 0 0.5216 -0.0853
0 -1.000 0 -0.1500
0 0 0 1.0000
0.8635 0 -0.5044 0
-0.5044 0 -0.8635 0
0 1.0000 0 0.7400
0 0 0 1.0000
0.6285 0 0.7778 0.0314
-0.7778 0 0.6285 -0.0389
0 -1.000 0 0
0 0 0 1.0000
0.9938 -0.1111 0 0
0.1111 0.9938 0 0
0 0 1 0.3000
0 0 0 1.0000
0.1539 0.9322 -0.3276 -0.1001
0.9685 -0.0767 0.2368 -0.2924
0.1956 -0.3537 -0.9147 -1.3477
0 0 0 1.0000
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5. Dr. Anurag Verma et. al. / International Journal of Engineering Science and Technology
Vol. 2(9), 2010, 4682-4686
5. Conclusion
From our analysis of the forward kinematic for the joint variable values of θ1 = 68.06°, θ2 = 99.39°, θ3 = -58.56°,
θ4 = -30.29°, θ5 = -51.06° & θ6 = 6.38°, the position of the end effector obtained as (-0.1001, -0.2924, -1.3477)
in spatial co-ordinate system with assuming origin at the base of the robot. Thus the developed model is capable
to determine position of end-effector for given input values of joint variable. Entire position and orientation of
end-effector are as shown in equation(10).
References
[1] Craig Jhon J.(1986), Introduction to Robotics, Mechanics & Control, Pearson Education, pp 68-102
[2] Fu K.S., Gonzaleza R.C. & Lee C.S.G., (1987) Robotics – Control, Sensing, Vision & Intelligence, First Edition, McGraw-Hill Book
Company, pp 12-51
[3] Mittal R.K. & Nagrath I.J.(2006) , Robotics & Control, First Edition, Tata McGraw-Hill Publishing Co. Ltd., pp 70-107
[4] Niku Saeed B.(2003), Introduction to Robotics – Analysis, Systems & Applications, First Edition, Pearson Education Pvt. Ltd.
[5] Schiling Robert J (1996), Fundamentals of Robotics, Prentice-Hall of India Pvt. Lid, pp 25-76
[6] Yoshikawa Tsuneo (1990), Foundations of Robotics – Analysis & Control, First Edition, Prentice Hall of India Pvt. Ltd, pp 31-45
[7] Palm William J. III (1995), Introduction to MATLAB for Engineers, First Edition, McGraw-Hill International Edition. Singapore
ISSN: 0975-5462 4686