5CCS2ITR

PROJECT ON ROBOT KINEMATIC
ANALYSIS

OF THE FANUC SR-3iA

1. Aim
This project aims to assess students’ knowledge of investigating robots from their schematic
representation, to their position analysis, and kinematics analysis. The project is to work on
FANUC SR-3iA robot with the forward kinematics and inverse kinematics where separate
requirements are presented below with respect to each of the robots.
The forward and inverse kinematics play an essential role in robot analysis and programming.
It is only through the solution of these two problems that the robot manipulator can be
programmed to move through a trajectory, interact with its surroundings and develop the
required task.
In general, the analytical inverse kinematics result should be compared with the differential
inverse kinematics result. In addition, forward kinematics, inverse kinematics and Jacobian
matrix are used for mapping the joint space and the end-effector cartesian space, and
homogenous matrices are used to describe the end-effector position.
2. Report Requirement
• The report should be well written and well presented.
o Very few typos/spelling/grammatical errors.
o Use proper labels and captions in all figures.
o Cite literature used as a basis of report.
o Present your findings in a logical and intelligent way.
• The report should touch on the various aspects listed in each of the three robot
requirements.
• The report should contain 15—20 pages of the main body of the report containing no
more than 10 figures. This page limit does not include title sheet, table of contents,
references or appendices. Additional figures may be presented in Appendices. Please
use Times New Roman, 12 pt. when preparing report, and use 1.5 line spacing

3. Task 1 on the Planar parallel robot (Analytical only)
Fig. 1 gives the sketch of a planar parallel robot. The robot is actuated by a linear actuator in
every leg. A fixed coordinate frame is located with origin at point G, also called frame G,
which is the center of the equilateral triangle O1O2O3. x0 is parallel to rO2/O1. A mobile
coordinate frame E is attached to the mobile platform. This coordinate frame has origin at
point E, which is the centre of the equilateral triangle B1B2B3. x1 is parallel to rB2/B1. The
dimensions of the robot are defined by the lengths of the edges of the equilateral triangles.
The edges of the equilateral triangle O1O2O3 are 300cm, while the edges of the equilateral
triangle B1B2B3 are 100cm. The length of A1B1, A2B2 and A3B3 are 100cm as well.
Write a subsection of this report in which you:
1. Calculate the degrees of freedom (DoF) of the robot.
2. Present the analytical kinematic solution for the inverse kinematics problem, if the
position of point E with respect to frame G is (x,y) and the orientation of frame E with
respect to frame G is Rot (θ, zG). Then the transformation matrix between frame E and
G is:
= [
cos − sin 0
sin cos 0
0 0 1 0
0 0 0 1
]G

You may follow the steps below as guide:
(a) Determine positions of point B1, B2, B3 with respect to frame G.
(b) Determine positions of point O1, O2, O3 with respect to frame G.
(c) Determine positions of point A1, A2, A3 with respect to frame G.
(d) Set up constraint equations based on geometrical analysis and solve the equations.
3. Provide a MATLAB program which is able to solve the inverse kinematics. (Hint: the
input are the position and orientation of the equilateral triangle B1B2B3 and the output
is the position of the prismatic joints, A1, A2, A3)
4. Present the solution for the forward kinematics problem if |11| = q1 = 200cm,
|22| = q2 = 220cm, |33| = q3 = 240cm. (Hint: the output are the position and
orientation of the equilateral triangle B1B2B3)
You may follow similar steps as the guide in Q2. But this time, for forward
kinematics, the unknowns are different apparently.


Figure 1. A Planar Parallel Robot
4. Task 2 on the SCARA robot
A) Background:
In 1979, the first SCARA (Selective Compliant Articulated Robot for Assembly) was
introduced in Japan and then in the United States. The FANUC SR-3iA is one of the three
models of robot manipulators belonging to the FANUC SCARA series and it’s also the
lightest model in the series. The FANUC SR-3iA is the perfect solution for small part
assembly and handling applications. It is a four-axis robot that brings fast speeds and
incredible precision to the production line. Based on its simple and reliable construction, the
FANUC SR-3iA provides accurate and consistent path performance which is necessary for
assembly and handling applications.

Introduction video of the FANUC SR-3iA robot:
https://www.fanucamerica.com/cmsmedia/Videos/Introducing%20the%20FANUC%20SR%20Series%20SCAR
A%20Robots_792_1022.mp4
https://www.fanucamerica.com/cmsmedia/Videos/SR-3iA%20battery%20pack%20assembly_847_1077.mp4

B) Task 2 Generalization
The task is to do the forward and inverse kinematics analysis of the FANUC SR-3iA robot
manipulator. The analytical inverse kinematics result should be compared with the
differential inverse kinematics result. In addition, forward kinematics, inverse kinematics and
Jacobian matrix are used for mapping the joint space and the end-effector Cartesian space.
Time joint position graphs and the corresponding robot path graph will be created. The
dimensions of the robot are provided in Appendix A1.
In the FANUC SR-3iA robot manipulator, the solution of the forward and inverse kinematics
problems is especially simplified since the robot features a decoupled architecture (planar +
z-axis).


Figure 2. Coordinate System of the FANUC SR-3iA

C) The Task
Write a report in which you:
1. Provide a schematic representation of the FANUC SR-3iA robot arm.
2. Calculate the degrees of freedom (DoF) of the FANUC SR-3iA.
3. Present the solution for the forward kinematics problem in symbolic form.
4. Present the analytical kinematic solution for the inverse kinematics problem in
symbolic form.
5. Present the Jacobian matrix of the robot.
6. Provide a MATLAB program which is able to solve the forward kinematics. (Hint: the
inputs are the values of the joint parameters and the output is the position and orientation of the
end effector)
7. Provide a MATLAB program which solves the inverse kinematics (Hint: the input are
the position and orientation of the end-effector; the output are the values for the joint
parameters).
8. Plot the workspace of the FANUC SR-3iA (Position increment: ∆1 = ∆2 = ∆4 =
5°, ∆3 = 10)

Matlab function:
End-effector Workspace graph: plot3(X, Y ,Z, ’.’)

9. Plot the path of the end-effector when the inputs of the joints are the following:


() 0 1 2 3 4 5 6 7 8 9 10
1() -25 -25 -25 0 25 50 50 75 75 50 50
2() 0 40 80 120 80 40 0 -40 -80 -120 -120
3() 0 20 40 60 80 100 120 140 160 180 200
4() 0 0 0 0 0 0 0 0 0 0 0


In your report, include a figure with five subplots (four Time Joint Position graphs
and a robot path graph). Briefly explain your results.

Matlab function:
Time Joint Position graph: plot (Time, Joint)
Robot Path graph: plot3 (X, Y, Z)



10. Plot the Time Joint Position graphs of the four joints when the given trajectory is as
the following:

() 0 1 2 3 4 5
() 276.6 287.2 298.6 304.9 313.5 322.2
() 276.1 254.1 237.5 225.6 211.5 193.6
() -30.0 -30.5 -31.0 -31.5 -32.0 -32.0
() 28 26 23 21 19 16

Figure 3. Given Robot Path Graph

In your report, include a figure with five subplots (four Time Joint Position graphs
and a robot path graph). Briefly explain your results. The initial joint positions of the
robot are 1 = 60°, 2 = −32°, 3 = 30 and 4 = 0°.
(Hint: the joint positions could be obtained by the analytical inverse kinematics solution.)
11. Given that for a small interval of time , the joint velocity ̇ ([1̇ 2̇ 3̇ 4̇]

) and the
end-effector velocity ([ ]
) can be assumed as constant. Following
= ̇, plot the Time Joint Velocity graphs from the Question 10 results.
12. Obtain numerically the end-effector velocity through the robot Jacobian matrix.
(Hint: the robot Jacobian matrix maps the joint velocity to the end-effector velocity: = ()̇
13. Calculate the differential kinematic solution for the inverse kinematics problem.
(Hint: assume = ̇, = and =
−1())
14. Compare the results of the joint velocity ̇ from Question 11 and Question 13.
Provide an error analysis in your report.


Appendix

A1: dimensions of the FANUC SR-3iA robot arm


5. Submission Deadline
Monday, 11 January 2021

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