فهما رزقني و علما زدني ربMy Lord! Advance me in Knowledge and true understanding .

Dec. 12, 2012, IIUM, Malaysia.

ROBOTICSMCT 4215

Tutorial Question Set 1

فهما رزقني و علما زدني ربMy Lord! Advance me in Knowledge and true understanding .

ROBOTICSMCT 4215

Tutorial Question Set 1

TutorMd. Akhtaruzzamanakhter900@yahoo.com

LecturerAssoc. Prof. Dr. Amir A. Shafie

Department of Mechatronics Engineering, Kulliyyah of Engineering,International Islamic University Malaysia (IIUM)

53100 Kuala Lumpur, Malaysia

Write down the steps to assign x axis to a frame attached with robot joint.

3Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Ans:1. Assign the Z-axis to each joint.

a) Revolute joint: Z-axis is the axis of rotation (using right hand rules).

b) Prismatic joint: Z-axis is along the direction of movement.

c) End effector: Z-axis always points away from the end effector.

2. X-axis for each joint.a) X-axis is in the direction of the common normal

between the previous Z-axis, and the current Z-axis.

Q.3.

Write down the steps to assign x axis to a frame attached with robot joint.

4Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Ans (Con.) :

1. Exceptions

1. Z-axes are parallel: There exists infinite number common normals. X-axis is co-linear with the common normal of the previous joint.

2. Z-axes are intersecting: X-axis is perpendicular to the plane made by the Z-axes (perpendicular to both Z-axes).

Q.3.

Simple Analysis

5Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.3.

(n-1)(n)

(n+1)

Assign the frames to any of the robots shown below and tabulate the D-H parameters. (Assume suitable link parameter).

6Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Pre analysis: (Four Steps; Ө, d, a, α)1. Rotate an angle of Ө(n+1) about Zn axis so that Xn

comes at the parallel of X(n+1).

2. Translate with the distance of d(n+1) along the Zn axis so that the Xn and X(n+1) becomes collinear.

3. Translate with the distance of a(n+1) along the Xn axis so that both the origins of the Xn and X(n+1) comes on the Z(n+1) axis.

4. Rotate an angle of α(n+1) about X(n+1) axis to align the Zn axis with the Z(n+1) axis.

Q.1.

Pre Analysis

7Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.1.

85/18/2011

Assign the frames to any of the robots shown below and tabulate the D-H parameters. (Assume suitable link parameter).

Assign the frames to any of the robots shown below and tabulate the D-H parameters. (Assume suitable link parameter).

9Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.1.

Ans (a):

x0

Z0

x1

x2

x3

x4

Z1Z2

Z3

Z4

Ө d a α1.2.3.4.

0 d1 0 0Ө2 0 a2 0

Ө3 0 a3 180

0 d4 0 0

Ө1

Ө2

Ө3d4

Assign the frames to any of the robots shown below and tabulate the D-H parameters. (Assume suitable link parameter).

10Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.1.

Ans (b):

# d a

1 Ө1 0 a1 0

2 Ө2 0 a2 0

3 0 -d3 0 180

4 Ө4 d4 0 0

x0

x1

x2

x3

Z0Z1

Z2

Z3

Ө1 Ө2

Ө4

d3

x4

Z4

Assign the frames to any of the robots shown below and tabulate the D-H parameters. (Assume suitable link parameter).

11Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.1.

Ans (c):

# d a

1 Ө1 0 a1 0

2 Ө2 0 a2 0

3 0 -d3 0 180

4 Ө4 0 0 0

x0

Z0

Ө1

x1

Z1

Ө2

x2

Z2

d3

x3

Z3

Ө4 x4

Z4

Obtain the individual link transformation matrices (A-matrices).

12Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.2.Ans.: (Analysis)

Obtain the individual link transformation matrices (A-matrices).

13Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.2.Ans. (a):

Ө d a α1.2.3.4.

0 d1 0 0Ө2 0 a2 0

Ө3 0 a3 180

0 d4 0 0

Obtain the individual link transformation matrices (A-matrices).

14Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.2.Ans. (b):

# d a

1 Ө1 0 a1 0

2 Ө2 0 a2 0

3 0 -d3 0 180

4 Ө4 d4 0 0

The robot in Fig. 1 is a three-link articulated robot arm with three rotary joint.

15Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.4.

# d a

1 Ө1 d 0 90

2 Ө2 0 e 0

3 Ө3 0 f -90

4 -90 0 0 -90

x0

Z0

x1Z1

x2Z2

x3

Z3

x4

Z4

(a) Assign coordinates frames to the robot arm using the D-H algorithm.(b) Fill out the parameters table of the robot arm.

The robot shown in Fig. 2 has 3-DOF, and the transformation matrix is given in symbolic form, as well as in numerical form for a specific location. The length of each link L1,L2 and L3 are 1, 2 and 1.5 ft respectively.

16Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.5.

(a) Derive the inverse kinematic equations for 1,2and3 in symbolic form.(b) Calculate the values of 1, 2and 3 for the given location.Ans:

100077.20422.0906.0023.1866.453.0211.0772.15.0785.0366.0

10000

)()(

222332323

2223311231231

2223311231231

0

SLSLCSCLCLSCSSCSCLCLCSSCCC

TH

1000paonpaonpaon

zzzz

yyyy

xxxx

The robot shown in Fig. 2 has 3-DOF, and the transformation matrix is given in symbolic form, as well as in numerical form for a specific location. The length of each link L1,L2 and L3 are 1, 2 and 1.5 ft respectively.

17Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia

Q.5.

(a) Derive the inverse kinematic equations for 1,2and3 in symbolic form.(b) Calculate the values of 1, 2and 3 for the given location.Ans: (Con.)

100010000

)()(

222332323

2223311231231

2223311231231

0

paonpaonpaon

zzzz

yyyy

xxxx

H SLSLCSCLCLSCSSCSCLCLCSSCCC

T

S1 = ax & C1 = -aySo, tan(1) = -(ax/ay) 1 = tan-1(-ax/ay) = atan2(-ax , ay)

1 = tan-1(-0.5/-0.866) = 30.000732 = 69.5373733 = -123.33325

Thank You&

Terima Kasih

18Dec. 12, 2012, Kulliyyah of Engineering, IIUM, Malaysia