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Ft-Me3015-22 23 01

This document contains a 3 question exam on robot kinematics. Question 1 involves determining the transformation matrices between different reference frames after performing two rotations on a unit cube. Question 2 involves determining the Denavit-Hartenberg parameters, forward kinematics, and inverse kinematics constraints for a 3 degree of freedom spatial robot arm. Question 3 involves completing the description of an RRP spatial robot, deriving its Jacobian matrix, plotting its configuration for a given set of joint values, and using the Jacobian to determine joint torques required to balance an external load.

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Thao Phuong
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94 views3 pages

Ft-Me3015-22 23 01

This document contains a 3 question exam on robot kinematics. Question 1 involves determining the transformation matrices between different reference frames after performing two rotations on a unit cube. Question 2 involves determining the Denavit-Hartenberg parameters, forward kinematics, and inverse kinematics constraints for a 3 degree of freedom spatial robot arm. Question 3 involves completing the description of an RRP spatial robot, deriving its Jacobian matrix, plotting its configuration for a given set of joint values, and using the Jacobian to determine joint torques required to balance an external load.

Uploaded by

Thao Phuong
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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FL051.

1
Giảng viên ra đề: 22 / 12 / 2022 Người phê duyệt: 22 / 12 / 2022

Phạm Công Bằng Nguyễn Quốc Chí

Học kỳ/năm học 1 2022-2023


THI CUỐI KỲ Ngày thi 27 / 12 / 2022
Môn học Kỹ thuật robot
TRƯỜNG ĐH BÁCH KHOA – ĐHQG-HCM Mã môn học ME3015
KHOA CƠ KHÍ Thời lượng 120 phút Mã đề
Ghi chú: - Hình thức thi là tự luận
- Được sử dụng tài liệu

Question 1 (2.0 marks) (L.O. 1)


In a fixed reference frame {R} as shown in Fig. 1, there is a unit cube A that its frame {A} is initially
coincident with {R}. Point P is attached to the cube given by Ap = [1, 1, 1]T. In addition, there is another
frame {B} determined by:
1 0 0 3
0 1 0 6 
BT 
R 
0 0 1  1
 
0 0 0 1

ZR
{R}
ZA
Fig. 1
P
A
YA YR ZB

XA {B}
XR
YB

XB

Implement two rotations of the cube: a rotation of -900 about YR-axis, then followed by 900 about ZR-axis.
Do the followings:
a. Determine 𝑅𝐴𝐓.
b. Determine 𝐵𝐴𝐓.
c. Determine Bp – coordinates of point P in {B}.

MSSV: .................................. Họ và tên SV: ................................................................................... Trang 1/3


Question 2 (4.0 marks) (L.O. 2)
An RPP spatial robot with known frames is used to manipulate a gripper at point D as shown in Fig. 2.

Fig. 2 X2 X3

Z2
D

Z3

X1
Z0  Z1

X0
With this manipulator, do the followings:

a. Determine three sets of D-H parameters corresponding to the three joints.


b. Derive the neighboring homogeneous transformation matrices: 0T1, 1T2, and 2T3.
c. Derive the forward-pose kinematics solution, i.e. 0xD, 0yD, and 0zD, as a function of joint variables
(dd3
d. Derive the constraint of 0xD, 0yD, and 0zD in which solutions of the inverse kinematic problem exist.
Assume that:
 there are no joint limits of 
 d2 = [0, d2max] and d3 = [0, d3max]

Question 3 (4.0 marks) (L.O. 2)


An RRP spatial robot is designed to manipulate a gripper at point D as seen in Fig. 3. Frames {0}, {1}, {2}
and {3}, which are assigned to link 0, link 1, link 2 and link 3 respectively.

a. Complete frame components at (1), (2), (3), (4), (5), và (6).


b. Fill in the table missing D-H parameters.
i ai i di i
1 1
2 2
3 d3

Trang 2/3
X3
Fig. 3 {3}
(6)
Z3
D
(5)

(4)
(2)
(3)

l1
Y0

{0}
(1)

c. Derive the Jacobian matrix 0J() for this manipulator where 0𝐕𝑫 = 0𝐉(𝜃)𝛉̇. Note that:
 𝛉̇ is a velocity vector of joint angles (𝜃̇1 , 𝜃̇2 , 𝑑̇3 ).
 The coordinates of point D in the base frame {0} are known as:
0
xD = cos(𝜃1 )[𝑑3 sin(𝜃2 ) + 𝑙2 cos(𝜃2 )]
0
{ yD = sin(𝜃1 )[𝑑3 sin(𝜃2 ) + 𝑙2 cos(𝜃2 )]
0
zD = 𝑙1 + 𝑙2 sin(𝜃2 ) − 𝑑3 cos(𝜃2 )

d. When joint values are given as 1 = 2 = 00, and d3 = l1.


 Plot the posture of the robot
 Use positional expressions in part c to verify the position of point D

e. With the posture in part d, using the Jacobian matrix in part c to compute the required joint torques 1,
2, and 3 that balance the robot with all following assumptions:
 The links are massless and there is an external point mass of 1 kg at D,
 The robot is affected by the downward gravitational acceleration of 9.81 m/s2.

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