Robotic kinematics

3DPotter

where your endstops are located, we can discuss which value to set for the angles. You can describe by making images of the 3

I started to set up the axis angle limits and homing offset for the arm. as shown in the first video the axis seem to be moving incorrectly. The second video explains where the endstops are located and how the machine triggers them.

config g

Video 1
Video 2

JoergS5

@3dpotter let's first discuss that your actuators are not X,Y,Z world coordinates, but axis 1,2,3, and to verify that your 3 actuators are rotating correctly:

Please test Axis 1 with
G1 H2 X10
H2 means to move the first axis individually.

Same with axis 2 and 3 with G1 H2 Y10 and G1 H2 Z10.

Please be aware that G1 H2 commands ignore the endstops, so you can run them with impossible angles.

You can verify that the axes are rotating in the correct direction. Please see documentation: https://duet3d.dozuki.com/Wiki/Configuring_RepRapFirmware_for_a_FiveAxisRobot?revisionid=HEAD#Section_Construction

axis 1 positive is counterclockwise
axis 2 and 3: rotating upwards is positive

If you later say G1 X10, this has a different meaning: it means to rotate all 3 axes so that the world coordinate X changes by10.

I've explained the difference of X as axis 1 and X as world coordinate in
https://forum.duet3d.com/topic/17222/duet3d-3-custom-delta-printer-inconsistant-motor-problems/14
In respect to algorithms, robot kinematics is similar to a delta: the actuators are connected by trigonometric functions and result in X, Y, Z world (cartesian) coordinates.

If the rotation of a stepper is incorrectly, you can change it in the config by changing:
M569 P0 S0
to
M569 P0 S1
or other round for the S0/S1 values. P0 is axis1, P1 is axis 2, P2 is axis 3.

JoergS5

@3dpotter the next thing to check is when your endstop are triggering:

axis 1 often triggers if the robot looks straight to the direction of the nozzle/gripper, which would be 0 degree
axis 2 would be 0 degree if the axis 2 arm is horizontally
axis 3 like axis 2

But please check first that the steppers are rotating in the correct directions and the rotation degrees are correct: if you say G1 H2 10, it should rotate 10 degree counterclockwise, e.g. If not, config must be changed. I often take an easy to recognize rotation like 90 degree to check the setting, but the arms must have enough space to make this rotation.

tony73

@3dpotter
Hello! how does the configuration on the robot proceed? I am building a 5-axis robot, but the work is slow! if you have time to write how it goes with yours, it will be of great help!

JoergS5

This post is deleted!

JoergS5

This post is deleted!

JoergS5

I remember that I have a separate thread about building the prototype. I move the posts there, and this thread is for firmware topics.

The prototype description is here: https://forum.duet3d.com/topic/20209/robot-type-1-45-cm-belt-gear-direct-drive-r0

JoergS5

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.

JoergS5

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

tony73

@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!

JoergS5

@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.

JoergS5

@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.

tony73

@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?

JoergS5

@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.

JoergS5

@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.

tony73

@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?

JoergS5

@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.

JoergS5

@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

JoergS5

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.

JoergS5

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.