Robotic kinematics
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I have thought about the further development of the robot:
- the 5 axis robot is a special case of a 6 axis robot, the 4th axis being fixed
- build a 6 axis robot, which includes special work modes like 5 axes and a vertical hotend
I'll let the 5 axis robot code exist until I have calculated the 6 axis robot and built a prototype. For the 6 axis robot's 4 th axis, the rotating arm, I'll try the idea https://www.youtube.com/watch?v=2YC-0C8oPUo which is based on an expired patent https://patents.google.com/patent/US5954611
In the long run, I'll try to DIY harmonic drives. -
I've thought about how to design the kinematics for the 6 axis robot. Developing the firmware, I want to follow the following ideas. If someone doesn't agree or has additional main topics, please tell me:
- following the Denavit-Hartenberg (DH) transformation https://en.wikipedia.org/wiki/Robotics_conventions#Denavit–Hartenberg_line_coordinates and the DH parameters: https://en.wikipedia.org/wiki/Denavit–Hartenberg_parameters
- the DH parameters are set directly with M669 parameters
- implement kinematics, inverse kinematics, speed and accel calculations
- to calculate inverse kinematics, store current workmodes of the arms and stay when possible inside it
- possibility to set the robot into classical 3d printing mode (5 axis robot mode): 4th axis 0 degree always, 5 th axis such that 5th arm is vertical, 6th axis and arm rotates horizontal, so the hotend is vertical always
- collision detection and avoidance
- simulation to check whether the planned object is creatable with given constraints
- homing, calibration, measure accuracy and precision proposals
- in a later release railed version and bending corrections
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@joergs5
bye! it's been a long time since I let myself be heard! I would like to know if you are continuing the robot arm project, I have had many commitments, but now that it is better I would like to continue building a prototype! -
@tony73 I've researched the last threee months how to build a good robot, and your timing is perfect, as I restarted building it this weekend.
The robot is now 6 axis, as you proposed some time ago. When the 4th axis fixed at 0 degree, it's the same like the 5 axis robot before. But 6 axes allow all positions (xyz and rotations by xyz).
Robot's properties are
- 6 axis, the parameters following Denavit-Hartenberg parameters
- harmonic drives and belt drives as alternatives
- encoder for position control and homing
- brakes at the hinges
- toolchanger at the tip
- calibration tool by 2 actuators at robot's base
The encoder is an absolute encoder. I'm still not sure whether it's fast enough for the 1HCL to support closed loop, but I'll try. If it's not fast enough, two encoders for every hinge is still possible.
In a separte thread was a discussion that using the full potential of non planar printing, better slicers are needed. This will be a necessary next step.
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@tony73 there's a chinese saying from Lao Tzu: "A journey of a thousand miles begins with a single step". Let's start with two steps this week.
Everyone who wants to build a robot from scratch is invited to follow my descriptions and building the objects needed. I'll try to offer alternative ways to produce them, from needing easier/less or more/expensive tools. Using easier tools may mean lower quality or more time needed.
The goal is to manufacture in a DIY way all mechanical robot's parts, including harmonic drives, encoders and toolchanger.
The first steps are preparation steps to be able to manufacture small parts and control their quality. The following two parts help achieving those goals:
differential screw
@mrehorstdmd has brought to my attention differential screws: two screws matched together and having different pitch result in a high resolution small movement. Resolution is 0.125 µm for one step of a 400-step stepper for the configuration I've selected.
The differential screw will be needed for
- calibration robot and/or bed (2 needed)
- focus 1:1 lenses (3 needed)
- manufacturing of the teeth of the harmonic drives
- manufacturing the cross roller bearings
- tasks in the teststation
Documentation: https://forum.duet3d.com/topic/25448/differential-screws-robot-series
1:1 lens
It is possible to make images with the resolution of the camera sensor's pixel size! I've detected it in https://www.raspberrypi.org/forums/viewtopic.php?t=59889 and is also known as coupling lenses, macro stacking or coupled reversed lenses. It is not reverting one objectiv, but coupling two of them (or two lenses reverted). The maximum resulution is for a Raspberry OV5467 e.g. 1.4 µm and ESP32-CAM's OV2640 pixel size is 2.2 µm! I will also use Canon EOS CMOS sensors, they have pixel size of about 4.3 µm, but with lower noise.
The lenses will be needed for
- checking teeth quality of the harmonic drives
- checking roller quality of the cross roller bearings
- absolute optical encoder reading
- quality control in general, e.g. of printed objects
I will create a new thread and place the link here to describe the two steps.
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@joergs5
I'm here, waiting for you to publish the instructions! I would like to know if the prototype you built of the 5-axis robot, were you able to print objects with it? -
@tony73 said in Robotic kinematics:
were you able to print objects with it?
the robot was ready for printing, but the arms were vibrating/swinging so much that I didn't want to do it. I wanted to avoid demotivation and take a step back, improving all parameters. Later, after disassambly, I had the idea that the only action to take was to speed down and set acceleration very low to solve it (today I would try input shaper...). But I was a bit frustrated, because I want to build a good 3D robot printer, which can also be used for light router tasks, grinding, 3D scanning and similar tasks. In fact, I want two robot arms which work together.
Another reason why I didn't start printing was, printing bad quality would not help motivating other users to build a robot. That's a reason, why I want to achieve building the robot with tools every user has and at the same time a good quality robot. I know it's difficult. Differential screw and 1:1 lenses are means for micromanufacturing with low cost, and a good start.
But anyway, my view with all printer types is, stability and precision is key to good prints, and I am working and researching for this goal.
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@tony73 I started documentation of the differential screw, lenses and harmonic gears now in https://forum.duet3d.com/topic/25448/differential-screws-11-lenses-harmonic-gear-robot-seriesto give an overview which tools are needed. Images and detailed instructions of building will follow.
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@joergs5
hi,I looked at the project of the differential screw and read the various measures, but I cannot understand how it would be assembled, I do not know this type of reducer. I think I understand that there are pulleys, screws and a linear guide, if built with high precision can the backlash be zero or very low? -
@tony73 said in Robotic kinematics:
if built with high precision can the backlash be zero or very low
The differential screw documentation is not finished yet. I'll describe all details and steps. A general description of differential screws: https://en.wikipedia.org/wiki/Differential_screw The first image shows how I'm building it, rotated to vertical, with stepper driving the rotation being in the middle and the dark gray parts being two big blocks.
If Differential screws stay at one flank, it has no backlash. This can be reached by pushing it into one direction always.
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@tony73 I've changed the title of the description to produce differential screws, because I added lenses and harmonic gear to the thread, the new link is https://forum.duet3d.com/topic/25448/differential-screws-11-lenses-harmonic-gear-robot-series
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I've started documentation of the 6 axis robot now in https://duet3d.dozuki.com/Wiki/Configuring_RepRapFirmware_for_a_SixAxisRobot?revisionid=HEAD
If someone finds a serious error, please tell me. I will refine the description and add functionality the next weeks. -
The documentation https://duet3d.dozuki.com/Wiki/Configuring_RepRapFirmware_for_a_SixAxisRobot?revisionid=HEAD is now in a fairly stable version. If an important parameter is wrong or missing, please tell me. I'll base the firmware development on those parameters, forward kinematics is ready, inverse kinematics comes next. The development is based on RRF 3.4.
What will be missing in this release is a rail system to move the robot as a whole, calculation arm bending and collission detection. This will come in a later release.
It will probably make sense to maintain the 5-axis-robot code, because it supports a special parallelogram structure with 4 axes which provides higher precision for 3D printers.
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@tony73 I've just finished the jacobian and inverse jacobian code today to calculate inverse kinematics with nice small matrix code. I can start implementing the kinematics file now. Then I will test the code.
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@joergs5 it would be great if you would include a diagram of the hole arm to help explain it.
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@t3p3tony I hesitate to publish commercial robots to avoid image license problems, but when I have a prototype again, I will post images and explanations. Until then, for Kuka KR5 are some good articles with explanation of Denavit-Hartenberg parameters.
Some authors rotate by Y without explanation, I am still struggling sometimes. I'll document examples.
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@joergs5 sure, it does not have to be a commercial robot - maybe the cad of your implementation?
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@t3p3tony => DH will be described, see my next post.
Implementing a visual method in DWC would be a nice possibility to show the configuration.
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@t3p3tony I've found a youtube video with a reuse license: https://www.youtube.com/watch?v=nwj0xR21ldo and use the robot images from there. It's a nice typical 6 axis robot. I'll create a separate document to explain parameters to set for robots, based on this video.
The documentation will be in https://duet3d.dozuki.com/Wiki/Denavit-Hartenberg_parameter_for_Robots?revisionid=HEAD
The video above is a good video to understand part of the DH parameters, so it is useful to watch it. In the video, the last column's values are joint 5 minus pi/2, joint 6 is 0. I am using different methods to get the Jacobian, however.
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The robot documentation is available at the new documentation site now at https://docs.duet3d.com/User_manual/Machine_configuration/Configuring_RepRapFirmware_for_a_Robot_printer and the explanation with examples of the Denavit-Hartenberg parameters are at https://docs.duet3d.com/User_manual/Machine_configuration/Configuring_Robot_DH_parameters
I wish to implement and push to David the firmware code for 3.5, so it's time to do it calmly and well tested.
