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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 (θ d = 150 degrees) with the robot angle θ l and outputs the motor control voltage v as:

v = K a ( θ d θ l ) + K b ( θ d θ l ) 2

where

  • θ d  = Desirable angle (rad)
  • θ 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 ω m = v

where

  • v = Voltage (V)
  • Tm = Motor torque (Nm)
  • Km = Motor torque constant (V/N/m)
  • ω m  = Rotational speed (rad/s)
  • Ko = Motor speed constant (Vs/rad)

Gear ratio n is given by: 

n = θ l θ m

  • θ m = Angle turned by the motor (rad)
  • LaTeX: \theta_lθ 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

 

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