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Question: a robot arm which rotates in the horizontal plane has...

Question details

A robot arm which rotates in the horizontal plane has a motor inertia of 0.01 kg-m2, arm inertia 5.0 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 robot arm system design is required to grasp a 20 kg mass and rotates through an angle of 150 degrees with positioning error less than 2 degrees without oscillatory movements. 

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)

Voltage generated by a differential amplifier is given by:

v = K a ( θ d θ l )

where

  • θ d  = Desirable angle (rad)
  • θ l  = Feedback angle from the arm position (rad)
  • Ka = Amplifier adjustable constant (V/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 = 2

Ka = differential amplifier adjustable constant = 1 V/rad

L = length of robot arm = 0.2 m

n = gear ratio = 2

Ka = differential amplifier adjustable constant = 0.1 V/rad

L = length of robot arm = 0.2 m

n = gear ratio = 3

Ka = differential amplifier adjustable constant = 0.1 V/rad

L = length of robot arm = 0.5 m

n = gear ratio = 2

Ka = differential amplifier adjustable constant = 0.1 V/rad

L = length of robot arm = 0.5 m

n = gear ratio = 3

Ka = differential amplifier adjustable constant = 1 V/rad

L = length of robot arm = 0.5 m

n = gear ratio = 3

Ka = differential amplifier adjustable constant = 0.1 V/rad

 

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