Consider the diagram shown below. A robot base is set up 2π‘š from a table. A frame {π‘­πŸŽ} is attached to the base of the robot such that the 𝑦0 passes through the two legs of the table. The tabletop is 2π‘š high and 2π‘š square. A frame {π‘­πŸ} is fixed to the edge of the table. A cube measuring 25 π‘π‘š on each side is placed at the center of the table and a frame {π‘­πŸ} is defined at the center of the cube. A camera is situated directly above the center of th

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4. Consider the diagram shown below. A robot base is set up 2π‘š from a table. A frame {π‘­πŸŽ} is attached to the base of the robot such that the 𝑦0 passes through the two legs of the table. The tabletop is 2π‘š high and 2π‘š square. A frame {π‘­πŸ} is fixed to the edge of the table. A cube measuring 25 π‘π‘š on each side is placed at the center of the table and a frame {π‘­πŸ} is defined at the center of the cube. A camera is situated directly above the center of the cube (4π‘š) above the tabletop and a frame {π‘­πŸ‘} is attached to the camera. Find the following homogeneous transformations: (a) 0T2 , (b) 3T0 and (c) 3T2 [10 marks]

5. The SCARA-type robot shown is in reset position when both arms are aligned along the x-axis.:
[10 marks]
a) Assign the coordinate frames based on the D-H representation.
b) Fill out the parameters table.
c) Write all the A matrices.
d) Write the UTH matrix in terms of the A matrices.

6. Solve the inverse kinematics problem for the following cylindrical robot. [10 marks]

7. A camera is attached to the hand frame T of a robot as given. The corresponding inverse Jacobian of the robot at this location is also given. The robot makes a differential motion,
as a result of which, the change in the frame dT is recorded as given. [10 marks]

a) Find the new location of the camera after the differential motion.
b) Find the differential operator.
c) Find the joint differential motion values associated with this move.
d) Find how much the differential motions of the hand-frame (TD) should have been instead, if measured relative to frame T, to move the robot to the same new location as in part a.

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