MDF Rose Engine 2.0

Geo(metric chuck) Screen

Purpose: This screen allows for the creation of a rose or single stage geometric chuck patterns (see also, Wikipedia Rose (mathematics) -- the math explaining how the variables work is explained there).

The B axis is only available when it is set to Linear in the B Axis Configuration page

The geometric mathematics behind this movement are explained by Dr. Frank Farris in his "Wheels on Wheels on Wheels-Surprising Symmetry" paper. There is also a nice article on this at Wolfram MathWorld.

Key Note: There is some pretty heavy duty math going on here, and some of the combinations of n and d get into calculations which can take the Teensy some time. The result is that it can not be run as fast on the Z axis as with other operations.

★

200 is the recommended starting point for the Max Speed on the Z axis
(and also start at 50% on the slider).

n	the numerator	Rose curves for various values of n & d

d	the denominator

k	the ratio, ⁿ/_d

Spindle Revolutions

Number of revolutions the spindle should make before stopping. This functionality is useful for producing patterns like the one to the right.

If this is set to zero (0), the movement of the cutter will continue until the stop button is pressed.

This field was introduced in version 19.

Axis Amplitude

Sets height (distance along Z or X Axes) of each lobe and is dependent upon value entered in the Preferences Screen for Distance/360

B Radius

This is the distance from the center of rotation to the location where the force is applied to drive the rotation.

This field is only visible when moving on the B axis.

Speed

The controls on the left and right side of the screen are for controlling the respective stepper motor's speed and acceleration.

To change the Max Speed, touch the number, and you will be presented with the Number Pad Screen.

The slider is a red bar that can be moved up to increase the speed, or down to decrease it. The percentage shown in the bar (100% on the left, 29% on the right) shows the percentage of the Max Speed at which the stepper motor is set to run.

There is a slider for the stepper motor on each axis, and they operate independently.

The top number is the max speed for the respective axis' stepper motor. This is measured in pulses / second. The MDF Rose Engine 2.0 are set to 6,400 pulses / revolution, so a max speed of 8500 would equate to \[ \begin{align} MaxSpindleRPM & = \frac{8,500 \, \frac{\mathrm{pulses}}{\mathrm{sec}} \times \, 60 \, \frac{\mathrm{sec}}{\mathrm{min}}} {6,400 \, \frac{\mathrm{pulses}}{\mathrm{rev}} \times \, 9 \, \frac{\mathrm{motor \, revs}}{\mathrm{spindle \, revs}}} \\ & = 8.9 \, \mathrm{RPM} \end{align} \]

The other stepper motor (in this case, on the Z axis) directly drives the motion. Thusly, a max speed of 7200 would equate to \[ \begin{align} MaxRPM & = \frac{7,200 \, \frac{\mathrm{pulses}}{\mathrm{sec}} \times \, 60 \, \frac{\mathrm{sec}}{\mathrm{min}}} {6,400 \, \frac{\mathrm{pulses}}{\mathrm{rev}}} \\ & = 68 \, \mathrm{RPM} \end{align} \]

Thusly, at 29%,the motor's speed is \[ \begin{align} RPM & = MaxRPM \times \, 0.29 \\ & = 20 \, \mathrm{RPM} \end{align} \]

And if the lead screw has a pitch of 2mm and 4 starts, it will move 8mm per revolution. At the set speed, this is \[ \begin{align} Movement Speed & = RPM \times \, 8 \frac{\mathrm{mm}}{\mathrm{rev}} \\ & = 160 \, \frac{\mathrm{mm}}{\mathrm{min}} \end{align} \]

Acceleration

The bottom number (6000 on the left; 5000 on the right) is the acceleration for the stepper motor.

To change this value, touch the number, and you will be presented with the Number Pad Screen.

Limit Switches

Limit switches cannot be used with this function. They can only be used from the Main Screen or One Screen.

Specific Axis Notes

Axis	Comments
Spindle	Movement continues until the identified movement distance is completed, or the stop button (shown to the right) is used.
Z	Movement on this axis is the same as for the spindle.
X	Movement on this axis is the same as for the spindle.
B	The fields on this screen are used with the fields and settings on the B Axis Configuration screen to calculate how long to run the stepper motor to achieve the desired rotation. Movement on this axis is the same as for the spindle.