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# Question: an intelligent robot arm which rotates in the horizontal plane...

###### Question details

An intelligent robot arm which rotates in the horizontal plane has a motor inertia of 0.01 kg-m2, arm inertia 7.0 kg-m2.

The motor shaft and bearing has a damping coefficient of 0.01 N-m/s.  The arm and gear mechanism together has a damping coefficient of 3.5 N-m/s.

The intelligent robot arm system design is required to grasp masses ranging from 1 kg to 20 kg, and then rotates through an angle of 150 degrees with minimum oscillatory movements for the entire range of masses as well as shortest time to settle to within 1 degree of the final position.

The intelligent robot has a controller that compares set angle (${\theta }_{d}$ = 150 degrees) with the robot angle ${\theta }_{l}$ and outputs the motor control voltage v as:

$v={K}_{a}\left({\theta }_{d}-{\theta }_{l}\right)+{K}_{b}{\left({\theta }_{d}-{\theta }_{l}\right)}^{2}$

where

• ${\theta }_{d}$ = Desirable angle (rad)
• ${\theta }_{l}$ = Feedback angle from the arm position (rad)
• Ka = First order adjustable constant (V/rad)
• Kb = Second order adjustable constant (V/rad2)

The motor is a 12 VDC motor with a stall torque of 40 Nm, and a no load speed of 4000 RPM.

Which set of system parameters would you recommend?

Formulae applicable to this question:

The torque and rotational speed of a DC motor is given by:

${K}_{m}{T}_{m}+{K}_{o}{\omega }_{m}=v$

where

• v = Voltage (V)
• Tm = Motor torque (Nm)
• Km = Motor torque constant (V/N/m)
• ${\omega }_{m}$ = Rotational speed (rad/s)
• Ko = Motor speed constant (Vs/rad)

Gear ratio n is given by:

$n=\frac{{\theta }_{l}}{{\theta }_{m}}$

• ${\theta }_{m}$ = Angle turned by the motor (rad)
• ${\theta }_{l}$ = Angle turned by the arm (rad)

The robot arm and motor dynamics are defined by Newton’s second law of motion.

Group of answer choices

L = length of robot arm = 0.5 m

n = gear ratio = 20

Ka = first order adjustable constant = 1.5 V/rad

Kb = first order adjustable constant = 0.001 V/rad2

L = length of robot arm = 0.5 m

n = gear ratio = 30

Ka = first order adjustable constant = 0.01 V/rad

Kb = first order adjustable constant = 0.2 V/rad2

L = length of robot arm = 0.5 m

n = gear ratio = 30

Ka = first order adjustable constant = 0.5 V/rad

Kb = first order adjustable constant = 0.1 V/rad2

L = length of robot arm = 1.0 m

n = gear ratio = 30

Ka = first order adjustable constant = 1.4 V/rad

Kb = first order adjustable constant = 0.2 V/rad2

L = length of robot arm = 0.5 m

n = gear ratio = 20

Ka = first order adjustable constant = 1.0 V/rad

Kb = first order adjustable constant = 0.2 V/rad2

L = length of robot arm = 1.0 m

n = gear ratio = 20

Ka = first order adjustable constant = 2.0 V/rad

Kb = first order adjustable constant = 0.3 V/rad2

###### Solution by an expert tutor 