Question: an intelligent robot arm which rotates in the horizontal plane...
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 ( = 150 degrees) with the robot angle and outputs the motor control voltage v as:
- = Desirable angle (rad)
- = 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:
- v = Voltage (V)
- Tm = Motor torque (Nm)
- Km = Motor torque constant (V/N/m)
- = Rotational speed (rad/s)
- Ko = Motor speed constant (Vs/rad)
Gear ratio n is given by:
- = Angle turned by the motor (rad)
- = Angle turned by the arm (rad)
The robot arm and motor dynamics are defined by Newton’s second law of motion.