Joints for Delta Printer
Contents
Principle and Requirements
TBD
Math / Inverse Kinematic
The predicted nozzle position is given by the software (slicer, G-code) in Cartesian coordinates (X, Y, Z). The firmware has to calculate the position of the 3 vertical carriages so that the nozzle moves to the predicted position. The calculation can be done with 3 “theorem of Pythagoras” (in space).
Math example (simplified)
- DiffX[n] = PredNozzleX - TowerX[n]
- DiffY[n] = PredNozzleY - TowerY[n]
- VertCarriage[n] = Sqrt ( RodLength² - (DiffX[n]² + DiffY[n]² ) ) + PredNozzleZ + ZeroOffsetZ[n]
Error Analysis
The precision of nozzle positioning depends on rod length and a correct nodal point.
In contrast to a cartesian printer the error on a delta printer dependent on the nozzle X/Y position and movement direction. This can result in a curved space and bent printed surfaces.
E.g. a backlash of 0.1 mm in joints can misalign the nozzle up to 1 mm (PositioningError = 2 x Backlash * RodLength / JointDistance)
Other (angle) errors are multiplied by the length of the nozzle (below joints nodal plane).
In result the prcision of the printer depends very much on joint prcision!
TBD
Joint Variants
Cardan Joint
DIY / RepRap Cardan Joint
Most RepRap delta design uses also printed cardian joints. Based on this technique the horizontal drills leaks often on precision. Little variation in joints results in much higher nozzle positioning error.
PROs:
- Very low cost
- Can be printed
CONs:
- Precision depends on manufacturing and assembling. Little manufacturing and assembling error results in a much higher nozzle positioning error
- Design is prone to backlash and misaligned nodal points for vertical and horizontal axis
- Needs more space in construction
Industrial Cardan Joint
There are industrial cardan joints for R/C cars available. Some of them has also plugin adapters with M4 or M5 threads.
TBD
Main Problem: In only 4 directions the joint can be tilt up to 90°. In directions between the usable angle is limited to about 30° (depends on design).
PROs:
- Ready to use
- Less friction
- M4 or M5 mounting threads
- Threaded rods can be used in between
CONs:
- Cost per joint about 12 Euro
- Have to be constructed in e.g. 45° angle to minimize limits
- Have to be mounted in optimal working direction
Rod End Bearing
TBD
Main Problem: At rotation axis the joint is designed for endless rotation. But at the tilt axis the joint is limited by construction. As manufacturer documentation tilt is limited to ±30° (Source: igus.com). To use the maximum (theoretical) reaching area as printing area a tilt angle of 35…40° is necessary. In result you can use only a limited printing area.
PROs:
- Ready to use components
- Threaded rods can be used in between
CONs:
- Limited printing area
- Conical spacer required
Ball-and-Socket Joint
Other variation of the Rod End Bearing but with a limited pivot angle of 25° (Source: igus.com).
Magnetic Joint
- main article: magnet joint
TBD
Note: V2A balls are not magnetic and can not be used!
PROs:
- Precision by design
- No backlash
- Implicit correct and well known nodal point
- Low cost. About 1 Euro per joint
- Simple construction
- Easy assembly
- Easy disconnecting for service and transport
CONs:
- Limited holding force
- In most designs parts have to be glued
- Magnets are sensitive to shock and high temperatures (>80°C)
Magnet Variations
Magnet in Tube
TBD
PROs (additional):
- -
CONs (additional):
- Precision depends on tube cutting and deflashing
Moving Ring Magnet
The bearing balls are glued to the lift and carriage. The ring magnets are part of the rods.
TBD
PROs (additional):
- -
CONs (additional):
- -
Fixed Ring Magnet
The ring magnets are pressed in and glued to the lift and carriage. The bearing balls are part of the rods.
TBD
PROs (additional):
- Depending on design up to (and over) ±90° tilt angle
CONs (additional):
- -
Ball Variations
Ball from Ball-and-Socket Joint
TBD
PROs (additional):
- Screw end
CONs (additional):
- Flat top - limited tilt angle
Bearing Ball
TBD
PROs (additional):
- Implicit high precision
- Very smooth surface
CONs (additional):
- Have to be glued