Kinematics DH parameters

[VidyaPuri]

Greetings, first of all awesome work with the robot!

So i was going through your code for kinematics and DH parameters and i can not figure out how did you position the coordinate systems for base. The d1(BASE=110mm) parameter is understandable, but for the r1(FOOT=40mm) it does not seem right. For my robot the distance between these two is somewhere between 2.5mm-3mm. It might be that there is size difference between the robots (SainSmart 6dof).

Also i am wondering how did you solve the issue regarding the shoulder and elbow servos and the pulley that connects the servo and the elbow joint. They are limiting each other and if one rotates the other has to move as well. I can't figure it out how to solve this. If you could just direct me in the right direction.

thank you very much, V

[wedesoft]

Hi, Sorry for the lack of documentation. I attached a sketch which hopefully answers your firdt question. Regarding the shoulder and elbow angle: I had to use some trigonometry to figure those out.

Regards Jan

Am 8. Juli 2018 16:38:30 GMT+01:00 schrieb VidyaPuri notifications@github.com:

Greetings, first of all awesome work with the robot!

So i was going through your code for kinematics and DH parameters and i can not figure out how did you position the coordinate systems for base. The d1(BASE=110mm) parameter is understandable, but for the r1(FOOT=40mm) it does not seem right. For my robot the distance between these two is somewhere between 2.5mm-3mm. It might be that there is size difference between the robots (SainSmart 6dof).

Also i am wondering how did you solve the issue regarding the shoulder and elbow servos and the pulley that connects the servo and the elbow joint. They are limiting each other and if one rotates the other has to move as well. I can't figure it out how to solve this. If you could just direct me in the right direction.

thank you very much, V

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[wedesoft]

Hi, Here is the diagram.

Regards Jan

Am 8. Juli 2018 16:38:30 GMT+01:00 schrieb VidyaPuri notifications@github.com:

Greetings, first of all awesome work with the robot!

So i was going through your code for kinematics and DH parameters and i can not figure out how did you position the coordinate systems for base. The d1(BASE=110mm) parameter is understandable, but for the r1(FOOT=40mm) it does not seem right. For my robot the distance between these two is somewhere between 2.5mm-3mm. It might be that there is size difference between the robots (SainSmart 6dof).

Also i am wondering how did you solve the issue regarding the shoulder and elbow servos and the pulley that connects the servo and the elbow joint. They are limiting each other and if one rotates the other has to move as well. I can't figure it out how to solve this. If you could just direct me in the right direction.

thank you very much, V

-- You are receiving this because you are subscribed to this thread. Reply to this email directly or view it on GitHub: https://github.com/wedesoft/arduino-sainsmart/issues/2

-- Diese Nachricht wurde von meinem Android-Gerät mit K-9 Mail gesendet.

[VidyaPuri]

Hi, where is it?

"Regarding the shoulder and elbow angle: I had to use some trigonometry to figure those out." in which part of the code did you solve it?

thank you, Vid

[wedesoft]

Sorry, the email attachment didn't work. Here is the diagram:

[wedesoft]

Here is a link to the inverse kinematic source code (it is in kinematics.rb).

[wedesoft]

There are also tests for the inverse kinematics.

[VidyaPuri]

Thank you very much for the diagram! It clears some of my issues.

Now since i have no prior knowledge of Ruby, i am trying to descipher the inverse method of Kinematics class. What is the input of that inverse method (matrix) and what is it made of?

Thank you very much!

[wedesoft]

The input of the inverse kinematics method is a 4x4 homogeneous transformation matrix:

r11 r12 r13 t1
r21 r22 r23 t2
r31 r32 r33 t3
0    0    0    1

with the nine rji being a rotation matrix and the 3 tj values a translation vector.

[wedesoft]

Note that the standard Ruby Matrix and Vector class are extended in the matrix_ext.rb file.

[wedesoft]

The angle for the elbow servo is the elbow angle minus the shoulder angle (see kinematics.rb line 85).

[VidyaPuri]

Thank you for your answers! is there any specific book or paper that you used for calculating inverse kinematics? i was deriving it through your code and for the first three angles i get it right (and is the same way as it is in the book i am using) but for the RPY of the end effector i get lost.

thank you for your help! Best regards, V

[wedesoft]

Hi, I don't have a book for this. Basically I compute head_matrix to contain only the rotations of the gripper relative to the arm.

[VidyaPuri]

So i was trying to find out how you got to this part:

head_matrix = Matrix.rotate_y(shoulder_angle - elbow_angle) Matrix.rotate_z(-base_angle) matrix

and the closer i got to it was that Matrix.rotate_y (shoulder_angle-elbow_angle)=Matrix_rotate_y(shouler_angle)*Matrix_rotate_y(-elbow_angle) since in the literature it goes like this: Which is constructed from three rotation matrices.

and what is this adapter matrix, what does it mean?

adapter_matrix = Matrix[[0, -1, 0, 0], [0, 0, -1, 0], [1, 0, 0, 0], [0, 0, 0, 0]]

[wedesoft]

The adapter matrix is just a matrix to swap coordinate axes.

[VidyaPuri]

I see, so you rotated the coordinate axes for Rot(y,90) and Rot(z,-90) from J3 to J4.

wrist_matrix = Matrix.rotate_x(-pitch_angle) Matrix.rotate_z(-roll_angle) adapter_matrix * head_matrix

and what are these rotate_x and rotate_z rotations? Why these particular ones?

[wedesoft]

I have to admit that this part was a bit of trial and error. I used unit tests to ensure that the result is correct though. Matrix.rotate_x and Matrix.rotate_z are rotation matrices around the x and z axis. The idea is to determine a wrist_matrix which only contains the rotation of the wrist (i.e. separated from pitch and roll angle).