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 (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_1 = \frac{-(2 L \sin(\theta_2)) x + (L + 2 L \cos(\theta_2)) y} {(2 L \sin(\theta_2)) y + (L + 2 L \cos(\theta_2)) x}}
• 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 = 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 (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_1 \, } , but was defined as above for ease of reading.

Results

It was awesome.