Figurel shows a photo of the Stanford Manipulator. The manipulator has five revolute joints and one...

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Figurel shows a photo of the Stanford Manipulator. The manipulator has five revolute joints and one prismatic joint as shown in Figure 2. 1. Assign the appropriate frame of each joint on Figure 3 based on DH-convention. 2. Assign the appropriate DH- parameters and label them on the figure. 3. Fill in the DH-table. 4. Write a Matlab function called DHmatrix.m that can generate the general DH-matrix using the DH-parameters a,,d,,a, and 0. The general DH-matrix is given by: HT=tran, (0, 0, d) rotz(0) tran (a,0,0) rotx(a) Note: Use the functions created in Problem 1. 5. Write another m-file that calculates the position and orientation of the end-effector of the manipulator. Check your program when the robot is at the configuration shown in Figure 3. Select your own numerical values for the parameters. P R 820 R Figure 1: Stanford Manipulator Figure 2: RRPRRR Stanford Manipulator R R R Figure 3: Stanford Configuration **UNIUM * 100 pm Write m-files using Matlab that define the following functions for calculating 4x4 Homogeneous transformation matrices [T]: function [I]=rotx (angle) function [T]=roty (angle) function [T]=rotz (angle) function [T]-tran (x, y, z) Each function is to return a 4x4 Homogeneous transformation matrix [T]. The argument (i.e. the input) of each function is either an angle for a rotation (Remember all angles are in radians) or the three components of the position vector for translation. Use the above functions to calculate expressions for the following transformations: T = rotx() tran(0.2, 4,0) rotz(-) T = roty(0.5) rotx(-0.3) tran(-0.1,0.4.1) function created in question 1: CODE: clc;clear all; T1=rotx(pi/4)*tran(0.2,4,0)*rotz(-pi/3); T2=roty(0.5)*rotx(-0.3)*tran(-0.1,0.4,1); disp('T1='); disp(T1) disp('T2='); disp(T2) function T=rotx(x) T=[1 0 0 0; 0 cos(x) -sin(x) 0; O sin(x) cos(x) 0;0 0 0 1]; end Output: Homogeneous transform for rotation about x-axis Homogeneous transform for rotation about y-axis Homogeneous transform for rotation about z-axis Translation by vector x,y,z function T=roty(y) T=[cos(y) 0 sin(y) 0; 0 1 0 0; -sin(y) 0 cos(y) 0:0 0 0 1]; end function T=rotz(z) T=[cos(z) -sin(z) 0 0; sin(z) cos(z) 0 0; 0 0 1 0;0 0 0 1]; end function T-tran(p,q,r) T= [1 0 0 0;0 1 0 0;0 0 1 0;p q r 1]; end T1= 0.5000 0.8660 0 0 -0.6124 0.3536 -0.7071 0 -0.6124 0.3536 0.7071 0 -3.3641 2.1732 0 1.0000 T2= 0.8776 -0.1417 0.4580 0 O 0.9553 0.2955 0 -0.4794 -0.2593 0.8384 0 -0.1000 0.4000 1.0000 1.0000 Figurel shows a photo of the Stanford Manipulator. The manipulator has five revolute joints and one prismatic joint as shown in Figure 2. 1. Assign the appropriate frame of each joint on Figure 3 based on DH-convention. 2. Assign the appropriate DH- parameters and label them on the figure. 3. Fill in the DH-table. 4. Write a Matlab function called DHmatrix.m that can generate the general DH-matrix using the DH-parameters a,,d,,a, and 0. The general DH-matrix is given by: HT=tran, (0, 0, d) rotz(0) tran (a,0,0) rotx(a) Note: Use the functions created in Problem 1. 5. Write another m-file that calculates the position and orientation of the end-effector of the manipulator. Check your program when the robot is at the configuration shown in Figure 3. Select your own numerical values for the parameters. P R 820 R Figure 1: Stanford Manipulator Figure 2: RRPRRR Stanford Manipulator R R R Figure 3: Stanford Configuration **UNIUM * 100 pm Write m-files using Matlab that define the following functions for calculating 4x4 Homogeneous transformation matrices [T]: function [I]=rotx (angle) function [T]=roty (angle) function [T]=rotz (angle) function [T]-tran (x, y, z) Each function is to return a 4x4 Homogeneous transformation matrix [T]. The argument (i.e. the input) of each function is either an angle for a rotation (Remember all angles are in radians) or the three components of the position vector for translation. Use the above functions to calculate expressions for the following transformations: T = rotx() tran(0.2, 4,0) rotz(-) T = roty(0.5) rotx(-0.3) tran(-0.1,0.4.1) function created in question 1: CODE: clc;clear all; T1=rotx(pi/4)*tran(0.2,4,0)*rotz(-pi/3); T2=roty(0.5)*rotx(-0.3)*tran(-0.1,0.4,1); disp('T1='); disp(T1) disp('T2='); disp(T2) function T=rotx(x) T=[1 0 0 0; 0 cos(x) -sin(x) 0; O sin(x) cos(x) 0;0 0 0 1]; end Output: Homogeneous transform for rotation about x-axis Homogeneous transform for rotation about y-axis Homogeneous transform for rotation about z-axis Translation by vector x,y,z function T=roty(y) T=[cos(y) 0 sin(y) 0; 0 1 0 0; -sin(y) 0 cos(y) 0:0 0 0 1]; end function T=rotz(z) T=[cos(z) -sin(z) 0 0; sin(z) cos(z) 0 0; 0 0 1 0;0 0 0 1]; end function T-tran(p,q,r) T= [1 0 0 0;0 1 0 0;0 0 1 0;p q r 1]; end T1= 0.5000 0.8660 0 0 -0.6124 0.3536 -0.7071 0 -0.6124 0.3536 0.7071 0 -3.3641 2.1732 0 1.0000 T2= 0.8776 -0.1417 0.4580 0 O 0.9553 0.2955 0 -0.4794 -0.2593 0.8384 0 -0.1000 0.4000 1.0000 1.0000