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.