Question

Two consecutive frames describe the old (T1) and new (T2) positions and orientations of the end of a 3-DOF robot. The corresponding Jacobian, relating to dz, ?x, ?z, is also given. Compute the values of joint differential motion ds1, d?2, d?3 of the robot that caused the given frame change. T1 = ?0 0 1 10?, T2 = ?-0.05 0 1 9.75?, J = ?5 10 0? ?1 0 0 5 ? ?1 -0.1 0.05 5.2 ? ?3 0 0 ? ?0 1 0 3 ? ?0.1 1 0 3.7 ? ?0 1 1 ? ?0 0 0 1 ? ?0 0 0 1 ?

          Two consecutive frames describe the old (T1) and new (T2) positions and orientations of the end of a 3-DOF robot. The corresponding Jacobian, relating to dz, ?x, ?z, is also given. Compute the values of joint differential motion ds1, d?2, d?3 of the robot that caused the given frame change.
T1 = ?0 0 1 10?, T2 = ?-0.05 0 1 9.75?, J = ?5 10 0?
     ?1 0 0 5 ?       ?1 -0.1 0.05 5.2 ?      ?3 0 0 ?
     ?0 1 0 3 ?       ?0.1 1 0 3.7 ?      ?0 1 1 ?
     ?0 0 0 1 ?       ?0 0 0 1 ?

Two consecutive frames describe the old (T1) and new (T2) positions and orientations of the end of a 3-DOF robot. The corresponding Jacobian, relating to dz, ?x, ?z, is also given. Compute the values of joint differential motion ds1, d?2, d?3 of the robot that caused the given frame change.
T1 = ?0 0 1 10?, T2 = ?-0.05 0 1 9.75?, J = ?5 10 0?
?1 0 0 5 ? ?1 -0.1 0.05 5.2 ? ?3 0 0 ?
?0 1 0 3 ? ?0.1 1 0 3.7 ? ?0 1 1 ?
?0 0 0 1 ? ?0 0 0 1 ?

Added by Joel O.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

09/17/2023

Step 1

The Jacobian matrix relates the differential changes in the robot's end effector position (dx, dy, dz) to the differential changes in the robot's joint variables (ds, do, do). Show more…

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Two consecutive frames describe the old (T1) and new (T2) positions and orientations of the end of a 3-DOF robot. The corresponding Jacobian, relating to dz, ͂x, ͂z, is also given. Compute the values of joint differential motion ds1, dθ2, dθ3 of the robot that caused the given frame change. (14 marks)