Rotary Dynamics - MAELabs UCSD

Rotary Dynamics Assignment – INDIVIDAL ASSIGNMENT
Dynamic Equations of Motion
Show below is a simplified figure of the friction drive and turntable. A drive wheel shown
attached to the motor. If there is no drive wheel, then the radius stays as the that of the
motor shaft, but at this point you should be thinking of adding a drive wheel. This
assignment is to draw the Free Body Diagrams (FBDs) of both the drive wheel and
turntable, and derive the equation of motion.
Drive Wheel
τm
rdw
Motor Shaft
rtt
1
Turntable
Shaft
Use the on-line example of dynamics of a pulley raising a mass for reference:
http://www.maelabs.ucsd.edu/mae156/A/resources/resources.htm#Dynamics
Variable and Parameters
rdw, rtt => radius of drive wheel and turntable
Idw, Itt => moments of inertia of drive wheel (don’t forget motor rotor!) and turntable
θdw, θtt => angles of drive wheel and turntable
τm => motor torque
Assumptions
- The spring preload on the friction drive arm is large enough to prevent slip
between drive wheel and turntable (you can calculate this necessary preload
separately).
- Friction can be neglected (this can be incorporated at a later stage).
- The inertia of the potentiometer can be neglected at this point.

FBD of Drive Wheel FBD of Turntable
Derive the equation of motion of each wheel, i.e. specify the angular acceleration of
each wheel in terms of the variables and parameters shown on the prior page
Equation of Motion of Drive Wheel Equation of Motion of Turntable
2

Show the geometric constraint that relates velocity and acceleration of θdw to θtt.
Combine the equations of motion into a single equation of motion for the system that
defines to the acceleration of the drive wheel, θdw in terms of rdw, r2tt, Idw, Itt, and τm (the
final equation of motion should not have the term θtt). You will use this equation in your
Matlab simulation of the turntable dynamics.
Extra Credit
Modify equation of motion to include the effect of the inertia of the potentiometer pulley.
3