Model

Construction

Prismatic control was achieved by 2 VEX continuous-rotation servo motors that couple to the Etch A Sketch's knobs. The left knob assembly is responsible for controlling motion in the Etch-a-Sketch's y-axis while the right one is responsible for controlling motion in the x-axis.

We used an Arduino Duemilanove microprocessor to control the motors and a start/stop button. Additionally, we used MATLAB in coordination with the Robotics Toolbox to calculate the information sent to the motors to enable the robot to achieve the desired shape or curve.

Image Rotation

The images may be rotated about the world x-, y-, and z-axis by theta_x, theta_y, and theta_z respectively. The rotation matrix is as follows:

Velocity Calculation

In theory, our motors run backward (down and left) when the PWM signal is between 0 and 89, remain stationary when the signal is at 90, and run forward (up and right) when the signal is between 91 and 180. However, given the fact that our motors are imprecise and have backlash, the “dead” zone is larger than expected. We conducted tests to determine the relationship between the drawing velocity and the PWM signal. The following charts show these relationships. Series 1 corresponds to the left motor (y-axis) and Series 2 corresponds to the right motor (x-axis). It should be noted that behavior differs for each motor in the different directions.