Yudai Suwabe's Portfolio

Motor Speed Control

This assignment focuses on designing a motion speed control system that can deliver an aluminum rod with a rectangular cross-section onto a wooden surface without tipping over.

To achieve the shortest delivery time, the theoretical maximum acceleration was first calculated. The system was then modeled in SolidWorks using a linear motor as the actuator. Finally, a wheel mechanism was implemented to realize the desired motion while maintaining stability.

1. Theoretical maximum acceleration (a_max)

The following Free Body Diagram was constructed.

Following three equations were made.

$$ \Sigma F_{x} = 0 \; \therefore F_{f,A} + F_{f,B} = 0 $$ $$ \Sigma F_{y} = 0 \; \therefore N_{A} + N_{B} = 0 $$ $$ \Sigma M_{A} = 0 \; \therefore -mg \cdot x_{CM} + ma \cdot y_{CM} + N_B \cdot b = 0$$

Where the coordinate of center of mass is

$$( x_{CM}, y_{CM}) = ( \frac{b}{2}, \frac{h}{2} )$$

When the aluminum rod is tipped over, N_b becomes zero. In this case, equation for moment can be simplified into:

$$ a = \frac{g \cdot b}{h} $$

Since height is 1 foot and base side is 1 inch long, theoretical maximum calculation was calculated as;

$$ a_{theo.max} = 11.772 m/s^{-2} $$

. Calculate Theoretical a_max

  • Build V vs t diagram
  • Steeper graph (higher acceleration) will lead to higher force.
  • Build FBD to analyze forces

2. Model system is motion

  • Free body diagram:
    • Horizontal: a_max
    • Vertical: w/2 at two bottom edge of the bar

3. Try on Linear Motor

  • Apply linear motor to bottom base
  • See if a_max is correct.

4. Put complete system in SolidWorks

  • Add wheels in SolidWorks
    • Rotory motor there
  • Get real velocity profile
  • Rack Pinion mate