High Speed Motor Control

Overview

The project suggested was to design a system for high speed motor control using the PIC 32. To demonstrate the motor control, a two degree of freedom (2DOF) robot arm was designed to throw and catch one ball with itself.

Team Members

• Sam Bobb (Electrical Engineering senior)
• Daniel Cornew (Mechanical Engineering junior)
• Ryan Deeter (Mechanical Engineering junior)

Mechanical Design

Theory of Parallelogram Design

Equations of Motion

Commanding the arm is much easier for a user to do in x- and y- coordinates than in motor angles or encoder counts. Therefore, equations were required that would translate x- and y- coordinates into angles from horizontal and then into encoder counts. Equations to express the reverse (encoder counts to angles to x- and y- coordinates) were also needed to evaluate the accuracy of the execution with respect to the command path.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = L \cos (\theta_1)\ + \cos (\theta_1+\theta_2)}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = L \sin(\theta_1)\ + \sin(\theta_1+\theta_2)}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \theta _{1}={\frac {-(2L\sin(\theta _{2}))x+(L+2L\cos(\theta _{2}))y}{(2L\sin(\theta _{2}))y+(L+2L\cos(\theta _{2}))x}}}

$\theta _{2}=cos^{-1}\left({\frac {x^{2}+y^{2}-L^{2}-(2L)^{2}}{2L^{2}}}\right)$

Note: In the code, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta_2 \, } is written out explicitly in the equation for Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \theta _{1}\,} , but was defined as above for ease of reading.

Results

It was awesome.