MNE482/MNE591-02 (Fall 2021) Assignment #4 (Total: 80 points + 20 extra credits) 1) With the DH parameters for each robotic arm with three degrees of freedom shown below, find H10, H21, and H32, then calculate H30, the homogeneous transformation matrix of each robot using the Matlab .mfile given (Assignment4_Fall2021.m). (10 points each) (P-P-P) (R-P-P) (R-R-P) Cartesian Robot Joint # (i) ai αi di θi 1 ( {0} -> {1} ) 0 π/2 d1var 0 2 ( {1} -> {2} ) 0 π/2 d2var π/2 3 ( {2} -> {3} ) 0 0 d3var+ L 0 Find H10, H21, and H32, then calculate H30. Cylindric Robo t Joint # (i) ai αi di θi 1 ( {0} -> {1} ) 0 0 0 θ1var 2 ( {1} -> {2} ) 0 π/2 d2var 0 3 ( {2} -> {3} ) 0 0 d3var + L 0 Find H10, H21, and H32, then calculate H30. Polar Robot Joint # (i) ai αi di θi 1 ( {0} -> {1} ) 0 π/2 H θ1var 2 ( {1} -> {2} ) 0 π/2 0 θ2var + π/2 3 ( {2} -> {3} ) 0 0 d3var + L 0 Find H10, H21, and H32, then calculate H30. Page 1 of 2 MNE482/MNE591-02 (Fall 2021) The figure below represents a schematic of a 5-DoF

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MNE482/MNE591-02 (Fall 2021) Assignment #4 (Total: 80 points + 20 extra credits) 1) With the DH parameters for each robotic arm with three degrees of freedom shown below, find H10, H21, and H32, then calculate H30, the homogeneous transformation matrix of each robot using the Matlab

Mechanical Engineering Oct 26, 2021

MNE482/MNE591-02 (Fall 2021)

Assignment #4 (Total: 80 points + 20 extra credits)

1) With the DH parameters for each robotic arm with three degrees of freedom shown below, find H₁⁰, H₂¹, and H₃², then calculate H₃⁰, the homogeneous transformation matrix of each robot using the Matlab

.mfile given (Assignment4_Fall2021.m). (10 points each)

(P-P-P) (R-P-P) (R-R-P)

	Cartesian Robot
Joint # (i)	a_i	α_i	d_i	θ_i
1 ( {0} -> {1} )	0	π/2	d₁var	0
2 ( {1} -> {2} )	0	π/2	d₂var	π/2
3 ( {2} -> {3} )	0	0	d3var+ L	0

Find H₁⁰, H₂¹, and H₃², then calculate H₃⁰.

	Cylindric Robo		t
Joint # (i)	a_i	α_i	d_i	θ_i
1 ( {0} -> {1} )	0	0	0	θ₁var
2 ( {1} -> {2} )	0	π/2	d₂var	0
3 ( {2} -> {3} )	0	0	d3var + L	0

Find H₁⁰, H₂¹, and H₃², then calculate H₃⁰.

	Polar Robot
Joint # (i)	a_i	α_i	d_i	θ_i
1 ( {0} -> {1} )	0	π/2	H	θ₁var
2 ( {1} -> {2} )	0	π/2	0	θ₂^var + π/2
3 ( {2} -> {3} )	0	0	d3var + L	0

Find H₁⁰, H₂¹, and H₃², then calculate H₃⁰.

Page 1 of 2

MNE482/MNE591-02 (Fall 2021)

The figure below represents a schematic of a 5-DoF LabVolt 5150 robot arm equipped in the robotics lab at SENG107. For the LabVolt 5150, (a) fill the DH parameter table (20 points), (b) find H₁⁰, H₂¹, H₃², H₄³, and H₅⁴, then calculate H₅⁰, the homogeneous transformation matrix using the Matlab .mfile given (Assignment4_Fall2020.m) (10 points), (c) confirm its forward kinematics for the given cases below using the Matlab .mfile given (Assignment4_Fall2021.m) (i.e. fill the forward kinematics table for XYZ Cartesian coordinates obtained by the given joint variable sets) (20 points). (Total: 50 points)

		LabVolt 5150
Joint # (i)	a_i[mm]	α_i[° or radian]	d_i[mm]	θ_i[° or radian]
1 ( {0} -> {1} )
2 ( {1} -> {2} )
3 ( {2} -> {3} )
4 ( {3} -> {4} )
5 ( {4} -> {5} )

Forward Kinematics

			From Measurements at the Labs							Matlab Result
Sets	θ₁	θ₂	θ₃	θ₄	θ₅	X [mm]	Y [mm]	Z [mm]	X [mm]	Y [mm]	Z [mm]
IC	0°	0	0°	0°	0°	380.50	0	140.55
Xmax
Ymax
Zmax
1
2
3

(Optional for extra credit) Choose a robot from Problem 1) and visualize the workspace of the robot using the concept of forward kinematics (Note: This has not been covered by the lectures). Please use Matlab (preferred) or similar computational software and include your code as well as the resultant figures. You can define the range of motions for the joint variables, the structural parameters (i.e. L and

H), or any necessary values as needed. (10 points)

(Extra credit from the lab activities, 5 points from each lab) (10 points)

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