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Delta Geometry Simulation

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Neil Jansen edited this page May 2, 2014 · 4 revisions

Purpose

Delta geometries are not as straight-forward as Cartesian designs. Accuracy and rigidity depend on the delta geometry (length ratios between joints, etc) and the rotational accuracy of the stepper motor. The problem is complicated by the fact that different geometries have different work areas. Either we can use trial-and-error to find a decent geometry, or we can simulate it and let the computer "find" us a decent set of ratios.

We shall simulate the "FirePick Delta Hacker/Developer Edition" geometry below.

Delta Geometry Calculations

Shamelessly borrowed from this page: Trossen Robotics - Delta robot kinematics

Delta Simulation Program

Was written in Labview 2011 Student Edition. Unfortunately this is a proprietary and very expensive development environment, so until I have time to re-write it in something more Open-Source friendly, it probably won't be released.

Input Requirements

  • Z work area (mm) = >100mm
  • Minimum XY work area radius = 150mm *Note: Enough to circumscribe a 214mmx214mm square (RepRap standard heated bed size)
  • Acceptable Error = 0.05mm *Note: sufficient to place 0201 components accurately

Number of monte-carlo iterations: 1000

Results

78 out of 1000 iterations successfully met the accuracy requirement at all points in the work area.

Analysis:

  • Longer 're' (parallelogram joint / shin) values seem to be preferred.
  • All passing iterations had an 'rf'/'re' ratio between 0.25 to 0.45.
  • My program doesn't take into account collision detection, so always make sure it's not outputting a physically impossible geometry.

##Conclusion For the 300mm x 300mm base, use the following geometry and machine settings:

  • End effector (e) = 115 mm
  • Base (f) = 190.526 mm
  • Length of parallelogram joint (re) = 270 mm (cut from 12", standard length carbon fiber Kossel rods)
  • Length of upper joint (rf) min = 90mm center-to-center
  • Stepper motor steps per revolution = 200
  • Stepper motor microstepping ratio = 16x
  • Timing belt # of teeth (motor) = 16 Designed for these GT2 16T pulleys
  • Timing belt # of teeth (arm) = 150 *Note: Sort of a misnomer. We actually use a smooth pulley here but listing them as if they were a teeth count makes the ratio easier.
  • Max theta = 80 degrees
  • Min theta = -80 degrees

This will give a work radius suitable for a RepRap Mk2B sized heated bed plate and a Z height of 80mm (more if printing a tall, skinny part).

TODO: Post pictures of simulation results

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