Print 3D

Edit:10 nov. 2019, Cre:19 oct. 2015

Delta Design

A few notes about delta design (which may also apply for other printers)

While I expensed significant amount of time to design the D-Box, which was following unrealised other designs, I made a few mistake because of lack of thinking. My experience with the Fisher delta was quite positive, notably looking closely to the tradeoffs they made in order to get the minimum cost.
The design and use of OpenScad Delta simulator was of great help to understand the delta geometry design.

Any design is the result of tradeoffs, which depends from the objectives of the designer. A large machine, for many reasons, cannot be as fast as a smaller one. We cannot buy industrial grade equipment because of cost. Safety is something fairly neglected by board, firmware and printer designers, because it take time to study and add some cost.
upscaling a printer is something which basically don’t work, because none of the applicable physical law is linear.
High speed printing imply particular configuration of the hotend, which drive to stringing.


  • Arm angles
two arm angles qualify a delta design
  • The angle of the arm relative the the vertical when effector is at center
  • The minimum angle of the arm relative to horizontal when effector is at its furthest point from centre
There are rule of thumbs while designing a delta printer, which is the arm angle when effector centred shall be 60° and minimum angle shall be at least 20°.
A low angle make fast carriage travel at large diameter print and reduce the effector stability. Printer which are designed for lower angle than 20° as the Fisher are not quite usable at their maximum specified diameter. Low angles are chosen because they allow shorter arms, hence give a higher usable area.
Indeed, it may be benefiting to increase the minimum angle to improve printer behaviour at large diameters.
  • Effector offset
The effector offset is the distance between arm pair horizontal axis articulation on effector and the center of effector. Larger effector offset allow slightly shorter arms as the effector could go a bit further away. The benefit is limited and large offset have bad effects on effector stability, so this is to be avoided.
Arm angle when effector is centred
If you choose to have longer arms, the angle are higher than 60°. In fact, the aim is the minimum angle, the rest angle being a result of other parameters.
  • Carriage offset.
The carriage offset is the distance between the column and the arm pair horizontal articulation axis. The reference (column axis, column face or other) is arbitrary, but the more appropriate geometrically is the center of the sliding system, where no momentum is created on carriage by vertical loads.
Carriage offset create a moment which tend to rotate the carriage around an horizontal axis. For most carriage design, the stability around this angle is quite good and increasing the carriage offset have limited effect.
It is interesting to have a larger carriage offset as it allow arm length reduction, hence larger usable height. It shall be noted however that if this offset is large, the maximum diameter is reached with the arm going over the vertical while effector is near the column. Depending the firmware, this may be doable or not. As an example, the first version of the delta simulator was fooled while the arm angle was exceeding vertical. An example of a machine operating with this condition is the Rostock max, which drives me to correct the simulator algorithm.

Factors influencing travel

  • Part cooling fan space
Good printing need sufficient part cooling, so you will find on printers multiples fans around hotend to blow a lot of air on the printed part. Unfortunately, on delta printers more than on others printers, these fans creates obstacles with the columns and especially the belts, which very significantly reduce the usable area. Way too often, the usable diameter given don’t take into account the fans, as fan setup is generally considered user responsibility.
But good cooling is not necessarily creating a tempest on your part. A more focused flow, straight below the hotend, may be more efficient, more silent and will take a lot less space. Some have done very focused flow with straws. One of the best system is a ring distributing flow homogeneously around and below the hotend. But designing properly such ring is not an easy task. Fluid mechanic is not easy and not always very intuitive. It is important to distribute the flow just below the hotend and not on it, as flowing air cool the hotend and creates a lot of perturbations in the temperature control. In some cases, it also can significantly limit the highest reachable temperature.
Others have tried cooling from an external fan with a duct guiding air to the head. This does have some advantages.
Proper part cooling is key in good printer design.
  • Belt position
Belts are also a seriously limiting factor in usable space. Often, for ease of design and manufacture they are installed at some distance from the columns, inducing loss of a lot of usable space.
Some designs as the Rostock max bury the belt in the column, which is the best you can do, with the penalty of added pulleys and complexity.
It is also possible to have the belt on one side, but this creates a side momentum which need a carriage design stiff in this axis if you don’t want to have parasitic movements due to the carriage rotation.
A rarely seen solution, but interesting as it uses a space often already taken if the carriage have counter-plates, is to set the belts behind the columns. This allow simple belt installation, but needs a more complex motor support.

See on reprap wiki the page Delta geometry (that I created)

(c) Pierre ROUZEAU
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