ECE 5463 Fall 2013
Homework 1
Solution
1.
Introduce angles which are between links and the horizontal axis, which will make the
deriving simpler.
r
3
10o
160
220
Nest
2
Nest
(x, y, z)
(x, y, z)
y
250
y
r
z
1
z
x
x
Nest
150o
From nest:
12000 a1 0
5200 a2
ECE 5463
Homework 1  Fall 2014
Due Wednesday, September 10, 2014
1. For the Mitsubishi RM501 robot, express the Cartesian coordinates of the wrist joint (x, y,
z) as the function of the joints (a1, a2, a3) for the waist, shoulder, and elbow, respectivel
ECE 5463
Homework 5
Due October 14, 2013
You should make use of HW4solution for this problem.
It is assumed that the homogeneous transformation relating the tool coordinate system
(fixed to the end effector) [ X T , YT , Z T ] to the workstation coordinat
g 3x
y s gux 9t s 9ts 9ts
ee d byw s vux Gts Gt s Gt s x
gx
g
ntn l wwp l mii l (nn k wwp k (k nj 7ww jp ij nn h pww h ii h rq x q
i
ee d ml ml (k 3ik nj ij h h ee d q rq
y wvGHD u
q
q xgwy gy cfw_
y
 jn w ji cfw_  n h w i h cfw_ I3hk e%
y
ECE 763
Homework 7
Due November 21, 2011
1. The noload speed at the output of a DC motor and gear unit (n=50) is 7.5 RPM for an
input voltage of 3 volts. When the motor is stalled with a 3 volt input, it draws 1.0 amp
of current and exerts a torque (at t
ECE 763
Homework #4
Due October 31, 2011
The purpose of this homework is to:
(a) Assign coordinate frames to the MITSUBISHI RM501 robot,
(b) Determine its link parameters, and
(c) Derive its kinematic equations.
The basic dimensions and movement range of
ECE 5463 Fall 2014
Homework 1
Solution
1.
Introduce angles which are between links and the horizontal axis, which will make the
deriving simpler.
r
3
10o
160
220
Nest
2
Nest
(x, y, z)
(x, y, z)
y
250
y
r
z
1
z
x
x
Nest
150o
From nest:
12000 a1 0
5200 a2
ECE 5463
Homework 7
Due October 28, 2013
1. Calculate the response of the U12M4T motor (that is, an equation for the output
velocity as a function of time) for a 3 volt step of input voltage with (a) L=0
and (b) L=100 h, respectively. For both parts, assu
ECE 5463 Fall 2013
Homework 2
Due Wednesday, September 11, 2013
Write a program for the Mitsubishi robot to pick up 2 parts from an indexing conveyor in
succession, and place each on an output conveyor. The task makes use of 5 basic positions:
(1) Positio
ECE 5463
Homework 6
Due October 21, 2013
1. Complete the process for obtaining the dynamic equation of the threelink robot
which we discussed in the class. Your equation should be in the format as below
and in details with the length and mass of each lin
ECE 5463 Midterm II  Solutions
FA 2016
1.
Mark X or fill the spaces with correct answers in the following statements (20 points):
a. In a DC motor, explain why we can assume that K and Kb are numerically the same? (6
points)
Motor and generator are physi
ECE 5463
Homework 1
Solution
1. Introduce angles which are between links and the horizontal axis, which will make the
deriving simpler.
r
3
10o
(x, y, z)
160
220
Nest
2
Nest
(x, y, z)
y
r
250
z
1
z
y
x
Nest
x
120o
From nest:
12000 a1 0
5200 a2 0
0 a3 36
ECE 5463
Homework #4 Solution
(a) The coordinate frames should be attached as shown, and the zero configuration will be straight out to the
right with the end effector directed upward. Then the rest of the problems can be resolved accordingly as
follows.
ECE 5463
Homework 10
Due November 28, 2016
1. The U12M4T motor is used to drive a robot joint, derive the transfer function when the proportional,
integral and derivative (PID) feedback control scheme is used. Assume the feedback gains are Kp,
5.7
.
KI, a
ECE 5463
Homework #4 Solution
(a) The coordinate frames should be attached as shown, and the zero configuration will be straight out to the
right with the end effector directed upward. Then the rest of the problems can be resolved accordingly as
follows.
ECE 5463 Midterm II  Solution
FA 2015
Name _
1. Answer the following two questions (10 points)

What components compose the knee of the robotic brace you saw in the class?
What is the function each component plays?
A DC motor and a Harmonic Drive speed
ECE 5463
Homework 9
Due November 9, 2016
1. Use PWM circuit to drive the U12M4T motor with the voltage supply of 12 volts.
The period of the pulse is T = 50s.
Answer the following questions:
a. If the number of the bits used to control the width is 12 bit
ECE 5463
Homework 11
Due December 5, 2016
1. The repeatability error of the Mitsubushi RM501 is 0.5 mm. Assume that the
maximum error which occurs when the arm is stretched out to 500 mm. What
should be the resolution of the increment encoder at the joint
ECE 5463 Midterm I Solutions
Fall 2016
1.
Using the DH convention, attached a frame to each link, and then obtain the H.T. between the
frames:
Z2
X
2
1
X2
X1
Z
1
10
10
20
s
15
Z0
X0
Xs
Then you have:
S
X T = S T0 T1 T2 X T
1
0
2
c(90 o ) s(90 o )
s(90 o
ECE 5463
Homework 7
Due October 26, 2016
1. This problem is for you to complete the dynamic equation of the robot which we
started in the class. The robot is a threelink system as shown in the end of this
problem. Your equation should be in the format as
ECE 5463 Midterm I  Solutions
Fall 2015
Name _
1. In the RM501 robot, use the PS and other comments to set a position such that the waist,
shoulder, and elbow joints are each 60 degrees away from the Nest position. You should
set the Home position first
ECE 5463
Homework 8
Due November 2, 2016
1. The noload speed at the output of a DC motorgear unit (n=50) is 6.0 RPM for an
input voltage of 3 volts. When the motor is stalled with a 3 volt input, it draws
1.0 amp of current and exerts a torque of 2.5 nt
ECE 5463
Homework 1  Fall 2016
Due Wednesday, September 7, 2016
1. For the Mitsubishi RM501 robot, express the Cartesian coordinates of the wrist joint (x, y,
z) as the function of the joints (a1, a2, a3) for the waist, shoulder, and elbow, respectively
ECE 5463
Homework 3
Solution
1.
Starting from the A coordinate system, rotate about z for . You can obtain the rotational matrix. The
position vector is [7, 4, 0]T. So we obtain:
c
s
A
TB =
0
0
s
c
0
0
0
0
1
0
7
4
0
1
For B going to C, there is no vari