I wrote this post to help me get my mind around the differences between traditional 3D printers vs Delta robots, and the math involved in figuring out movement.
(tl;dr The resolution of a single arm on the Rostock printer I’m building varies from 11 to 60 steps/mm across the print bed)
What I find interesting is that with a Delta bot, the resolution changes depending on where you are on the print bed.
With printers that use a Cartesian coordinate linear motion system (i.e. X, Y, Z motors), the resolution of the printer is the same no matter where you’re printing. For example, my ORDish Bot printer has a resolution of approximately 53 steps/millimeter on both the X & Y axis, and 2015 steps/millimeter along the Z.
(Both X & Y axis use 20 tooth gears, 3mm pitch belts, and stepper motors with 200 steps/revolution in 1/16 microstepping mode. The Z axis uses 16 TPI threaded rod and the same motors.)
Looking at a single arm of a Delta Bot, one end of the arm moves up and down (attached to some form of linear motion element), and the other end moves horizontally (attached to a print head). This forms a right triangle, with the arm as the hypotenuse. The hypotenuse length is fixed, and the length of either side can be calculated from the other via the Pythagorean theorem.
The printer I’m currently building is based on Johann’s original Rostock dimensions, with an arm length of 250mm. Moving the print head across the platform (but keeping it on the platform) moves the other end of the arm up & down, at heights ranging from 165mm (print head is farthest from the linear motion element), 218mm (middle of platform), and 245mm (closest to linear motion element)
A little playing around with the Pythagorean theorem shows that a 1mm vertical movement at those points results in print head movements of 0.87mm, 1.76mm, & 4.69mm. Using the same pulley/belt/motor combo as my ORDish bot translates to resolutions of 60, 29, 11 steps/mm. The farther away the print head is from the linear motion element, the higher the resolution.
This is just looking at one arm... When the print head is in an area of higher resolution of one arm, it’s at lower resolution of the other arms, and visa-versa.
If anybody has a good way of describing the resolution, please let me know.
All these numbers are approximate, and should be taken with a grain of salt...