Agnewgraph

Agnewgraph I is a device that traces Spirograph curves (technically, hypotrochoids). Unlike other systems that compute and plot hypotrochoids mathematically, Agnewgraph I operates a physical Spirograph much as a human being does.

Agnewgraph I

Agnewgraph I in action
 
In order to do so, Agnewgraph I contains two electromechanical subsystems—a force-sensing pen and a pen transport mechanism—plus a Parallax Propeller chip as the brains.

Force-sensing pen
 
The force-sensing pen consists of a pen mounted to an upside-down analog joystick. The joystick has springs to return it to its neutral position. A force exerted at the pen tip will displace the joystick from neutral. Measuring the resistances of the joystick's potentiometers yields a fair approximation of the force vector at the pen tip. (As it happens, the joystick's springs are not stiff enough for Spirographic purposes so I augmented them with some rubber bands.)

The pen transport mechanism consists of two improvised linear actuators, each consisting of a stepper motor, some aluminum tubing, and some Kevlar thread wound around the motor shaft. The actuators pivot around two fixed points and they meet at the pen.

"Linear actuator" close-up
 
The two actuators act almost as an X-axis and Y-axis. However, the "axes" are obviously not independent (being joined at the pen) and any resemblance to orthogonality diminishes rapidly outside a very small sweet spot.

 
Not really X, not really Y
 
The only benefit of this design is ease of construction, but that's a really big benefit for me.

Fortunately, Agnewgraph I's algorithm does not require precise X-Y positioning; instead, it uses feedback from the force-sensing pen to determine where the pen should go and whether it's really getting there.

The final component of Agnewgraph I is a Parallax Propeller microcontroller. The Propeller executes the Spirograph tracing algorithm while reading the joystick potentiometers, producing the stepper motor control pulses, and generating a video display of the force vectors (target and actual).

 
Propeller video display
 
The black line is the measured force, the blue line is the target force. The algorithm is quite simple: the Propeller commands the motors to move the pen to minimize the difference between the force at the pen tip and a target force vector. (The red arrows indicate which way the linear actuators are moving.) Once the measured force matches the target, the target vector is rotated slightly and the process repeats. The net effect is to duplicate what Spirograph users do with their fingers.


Future work

Agnewgraph I can trace curves inside the ring but doesn't work outside the ring. I have some ideas on that but I think it will require a new design (Agnewgraph II).


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