RepOlaRap

This is still in draft. I'm just putting down my thoughts and plan to edit it as I proceed with my prototyping:

The Polar RepRap, "RepOlaRap", currently only discusses an X+Y axis robot. I plan on attacking a Z axis once I have a working prototype to test the resolution, positioning accuracy and repeatability, and software complexity for the X+Y.

Structural parts from top to bottom:

Build platform, 14cm radius disk, 15mm thick

 - Hole + thrust bearing at center.
 - MDF?
 - counter top laminate on bottom for hardness, extending out partially to form belt constraint (?)
 - groove for belt placement around perimeter?

Top Bearing Race, ring, radius: 13cm outer, 8cm inner, 4cm thick.

 - 16x 6mm holes drilled every 22.5 degrees, alternating at 9cm and 12cm radius.
 - 16x 5mm stainless steel balls.

Upper Radial Arm Platform, 15mm thick

 - general shape is a disk 14cm diameter, with an offset half a diagonal square 20cm per side extruded outward.
 - MDF?
 - hole drilled for interface bolt from thrust bearing on Build Platform.
 - counter top laminate on top for hardness on area under bearing race.
 - Three cut outs:
    - Two for encoder device and wiring for absolute radial position of Build Platform.
    - One for radial arm bolt + thrust bearing.
 - Build platform motor assembly will attach to this.

Lower Radial Arm Platform, 21cm radius disk, 15mm thick.

 - Hole + thrust bearing at center.
 - MDF?
 - cemented/glued securely to Upper Radial Arm Platform.
 - One long cutout or groove, 1cm x 9cm, for encoder wiring.
 - counter top laminate on bottom for hardness, extending out partially to form belt constraint (?)

Lower Bearing Race, ring, radius: 16cm outer, 11cm inner, 4cm thick.

 - 16x 6mm holes drilled every 22.5 degrees, alternating at 12cm and 15cm radius.
 - 16x 5mm stainless steel balls.

Base, 46cm x 46cm square, 15mm (19mm?) thick.

 - Hole drilled at center for interface bolt from thrust bearing on Radial Arm Platform.
 - MDF?
 - Cut out for encoder device and wiring for absolute radial position of Radial Arm.

Image illustrating XY platform structure:

Model space can be represented as a ring with outer radius of 14cm. The inner radius is defined by the closest approach the extruder can make to the build platform center (typically, this should be < 1mm with proper calibration of the extruder head position.)

My intent to drive the XY platform with closed form inverse kinematics, computed on the host software, and output as a series of stepwise integer splines to the controller firmware. Each step would correspond to some fixed metric, for example, the step pulse send to extrude more filament when extruding, or an arbitrary time unit if simple motion is desired.

Here is a simulated path for a square from model space (3.5mm,3.5mm) to (98mm,98mm) using cubic splines to represent the inverse kinematic motions along each side in segments, with spline segments no greater than 5mm in length. If you zoom in on the top left corner, you'll see that the line deviates enough from straight to be noticable, as you approach the build platform center, smaller spline lengths (and greater communication overhead) are required to reproduce the inverse kinematics accurately enough.