Johns Hopkins University
EN.530.420 Robotic Sensors and Actuators
HW2: DC Motors
DRB Kraemer
Due Fri 29 Sep 5pm via Canvas
Given the DC permanent-magnet motor and battery which is modeled by the below electrical and mechanical
parameters below, determine the following:
System parameters:
VOC = 9V,
Rbattery = 2Ω
Rmotor = 8Ω
L = 1x10-3 H
kT = 0.02N m/Amp
kbemf = 0.02V/(rad/s)
J = 1x10-4 kg m2 (includes mass moment of inertia of motor armature and the wheels’ inertia)
kD = 1x10-6 N m/(rad/s)
For your analysis assume that the wheel friction on the surface is su cient to prevent
slipping.
Show work, including relevant Free-Body Diagrams (robot, and wheel).
1) Will this motor be able to drive a robot with total mass of 0.25kg up a 15° inclined plane? Assume that the
motor drives a 5 cm diameter wheel directly.
2) Will this motor be able to drive a robot with total mass of 0.25kg (again, the motor drives a 5 cm diameter
wheel directly) on a level surface at a speed of 10 m/s? Show work.
3) Will this motor be able to drive a robot with total mass of 0.25kg (again, the motor drives a 5 cm diameter
wheel directly) up a 13° inclined plane at a speed of 10 m/s? Show work.
4) Will this motor be able to drive a robot with total mass of 0.4kg up a 11° inclined plane at a speed of 1 m/s, if
the motor drives a 5 cm diameter wheel directly? Show work.
5) Will this motor be able to drive a robot with total mass of 0.4kg up a 11° inclined plane at a speed of 1 m/s, if
the motor drives a 5 cm diameter wheel through a 2:1 gear box? Show work.
Rbatt
+ VOC
Rmotor
L
Tm
ω
Im
Vbemf +
J
TLoad
ffi
Battery
6) Using a spreadsheet or similar tool, plot the steady-state efficiency of the motor (without gears) as a function
of the load torque.
Let the load torque vary from 0 to stall.
You can normalize the load torque by the stall torque.
Describe briefly what the plot tells you.