How do I calculate the velocity and acceleration of articular joints of a 2 link robot? (rotation translation)

Hello, I have these transformation matrixes:

T1_0=[cos(q1) -sin(q1) 0 0;...
      sin(q1) cos(q1) 0 0;...
      0 0 1 0;...
      0 0 0 1];

T2_1=[1 0 0 q2;...
      0 1 0 0;...
      0 0 1 0;...
      0 0 0 1];

Te_2=[1 0 0 l1;...
      0 1 0 -l1;...
      0 0 1 0;...
      0 0 0 1];

and the big one

Te_0=[cos(q1), -sin(q1), 0, l1*cos(q1) + q2*cos(q1) + l1*sin(q1)]
[sin(q1),  cos(q1), 0, l1*sin(q1) - l1*cos(q1) + q2*sin(q1)]
[      0,        0, 1,                                    0]
[      0,        0, 0,                                    1]

And I need to make a function where I plot the velocity and the acceleration of the q joints based on their initial and final position.

I really dont know how to start, please help

Answer 1

[Sakshay]

Hello Spulber,

As per my understanding, you are trying to create a 2-Link Manipulator Robot and calculating its Joint Position and Acceleration given the Initial and Goal Configurations.

You can go through the following steps to accomplish the same:

1. Create a robot as a "rigidBodyTree" object using the Transformation Matrices. You can refer to this documentation to build a robot using the same: Build a Robot Step by Step - MATLAB & Simulink (mathworks.com)
2. Simulate the Joint Space Motion of the Robot Manipulator using a specific Control Function. You can refer to this documentation to simulate the same: Simulate Joint-Space Trajectory Tracking in MATLAB - MATLAB & Simulink (mathworks.com). The example, illustrates how to plot the results as well.

You can refer to the documentation on "rigidBodyTree" for more information on that as well:

Create tree-structured robot - MATLAB (mathworks.com)