Joints for Delta Printer

Delta

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 precision of the printer depends very much on joint precision!

TBD

Joint Variations

Cardan Joint

DIY / RepRap Cardan Joint

Most RepRap delta design uses also printed Cardan 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
• Rotational stiffness add stability on effector

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

USED BY:

• Rostock

Industrial Cardan Joint

Industrial Cardan

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

CHECK:

• Check other manufacturers for wider tilt angle

Rod End Bearing

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

CHECK:

• Check other manufacturers for wider tilt angle

USED BY:

• Kossel
• 3DR

Ball-and-Socket Joint

Other variation of the ‘Rod End Bearing’ but with a more limited pivot angle of 25° (Source: igus.com).

Magnetic Joint

Magnetic Joint Example 1

main article: magnet joint

TBD

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

Magnet in Tube Variant

A cylindrical magnet is glued and/or pressed in a tube. The magnet should not touch the steel ball but should also be as near as possible to the ball to get maximum force. The edge of the tube is sliding over the steel ball.

The ‘tube’ can also be drill in the construction.

PROs (additional):

• -

CONs (additional):

• Precision depends on tube cutting, drilling and deflashing

Moving Ring Magnet

Moving Ring Magnet Variant

The steel balls are mounted (glued) to the lift and effector. The ring magnets are part of the diagonal rods.

PROs (additional):

• -

CONs (additional):

• -

CHECK:

• Long time abrasion of magnets is unknown

Fixed Ring Magnet

Fixed Ring Magnet Variant

The ring magnets are glued and/or pressed in to the lift and effector. The steel balls are part of the diagonal rods.

PROs (additional):

• Depending on design up to (and over) ±90° tilt angle

CONs (additional):

• -

CHECK:

• Long time abrasion of magnets is unknown

USED BY:

• Wood-D

Ball Variations

Note: Stainless steel (V2A) balls are not magnetic and can not be used!

Ball from Ball-and-Socket Joint (DIN 71802)

TBD

PROs (additional):

• Screw end

CONs (additional):

• Flat top - limited tilt angle

Bearing Ball

Bearing balls are produced with a very high precision. Even if you get class B merchandise the precision much higher than you need for the delta joints.

Note: Look for “slingshot balls” on eBay.

PROs (additional):

• Low cost (100 pieces for about 10 Euro)
• Implicit high precision
• Very smooth surface – less friction, no abrasion
• Available in all sizes

CONs (additional):

• Have to be glued

USED BY:

• Wood-D

Ball from Photo Tripod Ball Head

TBD

PROs (additional):

• Screw end
• Big balls with big magnets for high force

CONs (additional):

• Expensive

CHECK:

• Is ball material magnetic? (Could be chromed brass)

Other Joints

TBD (Feel free to add other variations)