Engineering Research About The Kinematic Analysis Of Robots (Essay Sample)

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Exercise 1
*
First, we create a dh table that lists all the parameters. In the table, we list the parameters below.
θ,α,a and d.
θ is the angle through which the xn-1 axis rotates through to be mapped onto xn (Corke, 2015).
α is the angle that you rotate zn-1 axis to map it onto zn axis (Corke, 2015).
a is the distance between the centers of the coordinates of two joints in the direction of the xn axis (Corke, 2015)
d is the distance between the centers of the coordinates of two joints in the direction of the zn-1 axis (Corke, 2015).
After analyzing the robot, we obtain the parameters and table them in a dh table.
Joint

θ

α,

a

d

1

0

90

1

0

2

0

0

1

0

3

0

0

1

0

* We use the Peter corke robotic toolbox to depict the robot on the MATLAB platform.
We create a variable L and include the dh parameters in it in the order: theta, d, a and alpha
L (1) =Link ([0 0 0 1.571]);
L (2) =Link ([0 0 1 0]);
L (3) =Link ([0 0 1 0]);
We employ the Serial Link toolbox function to generate a robot object and to store it into the workspace variable rob (Corke, 2015).
Rob=SerialLink(L);
According to (Corke, 2015), use the function Rob.name to name our robot.
Rob.name='question 1';
We apply the function Rob. Plot to produce a plot of the robot after
specifying the values of q in radians (Corke, 2015).
Rob.plot([0,0,0,]);
The robotic toolbox then produces the plot of the robot.
* The homogenous transformation matrix.
Typing rob in the workspace produces a dh table which lists all the essential parameters of the mechanism.
Rob =
We finally apply the function rob. fkine to carry out the forward kinematic evaluation of the robot and to yield a homogenous transformation matrix. From the homogenous matrix we can establish the rotation matrix of the end effector and its position (Corke, 2015).
Rob.fkine([0 0 0])
ans =
1 0 0 2
0 -0.0002 -1.0000 0
0 1.0000 -0.0002 0
0 0 0 1
Exercise 2
After examining the robot, we find the parameters and table them in a dh table.
Joint

θ

α,

a

d

1

0

-90

0

2

2

0

90

0

3

3

0

0

0

4

4

-90

90

0

2

5

90

90

0

2

6

-90

0

0

3

In the instance of prismatic joints, we take the sum of the length of the joint (2) and the displacement due to the prismatic joint.
b)We utilize the Peter corke robotic toolbox to describe the robot with the aid of the MATLAB platform.
We create a variable L that contains the dh parameters in the order of: theta, d, a and alpha for all links in the mechanism (Corke, 2015).
L(1)=Link([0 2 0 -1.571]);
L(2)=Link([0 3 0 1.571]);
L(3)=Link([0 4 0 0]);
L(4)=Link([-1.571 2 0 1.571]);
L(5)=Link([1.571 2 0 1.571]);
L(6)=Link([-1.571 3 0 0]);
We exploit the Serial Link toolbox function to form a robot object and to keep it into the workspace variable rob (Corke, 2015).
Rob=SerialLink(L);
We employ the function Rob.name to label the robot (Corke, 2015).
Rob.name='question 2';
We apply the function Rob. Plot to construct a plot of the machine after
stating the values of q in radians (Corke, 2015).
Rob.plot([0,0,0,0,0,0]);
c)The homogenous transformation matrix.
Typing rob in the workspace produces a dh table which lists all the essential parameters of the mechanism.
Rob =
We finally apply the function rob. fkine to perform the forward kinematic analysis of the robot and to produce a homogenous transformation matrix. From the homogenous matrix we can establish the rotation matrix of the end effector and its position (Corke, 2015).
Rob.fkine([0,0,0,0,0,0])
ans =
1 0 0 0
0 -1.0000 0.0004 1.001
0 -0.0004 -1.0000 4.999
0 0 0 1
Exercise 3
After analyzing the robot, we obtain the parameters and table them in a dh table.
Joint

θ