Robotic Arm Control β: Inverse Kinematics for 2 DOF

[ffp]

βHi, I'm working in a project with an arduino mega 2560 controling a robotic arm with 2 DOF moved by servo motors.

I want to make the arm lift vertically about 20 cm as if it would carry a transformer to a pole. I was thinking in inverse kinetics (don't know if that's the name in english) to make it.

This means:

dθ= J^-1 * dh

Where dθ is the matrix of the angle vriations, J is the jacobian matrix and dh is the variation of height.

I'll try to ilustrate the problem:... ______(l2)_____
...\......|
...\ ......| h
.(l1)..\......|
...\....|
--------------------------------
.....d

l1 is the first apendice with 9.2cm and the angle between it and the horizontal line is α, which starts as 30°.
l2 is the second apendice with 9.7cm and the angle between it and the horizontal line is β which starts as 0º.
h is the height of the tip of the arm and starts as 6cm and goes until 15cm.
d is the distance between the robot base and it's tip and is constant at 5cm.

Correct me if I'm wrong but wouldn't the jacobian matrix J be:

l1*cos(α) l2*cos(β)

l2*sin(α) -l1*sin(β) ?

 

[Navin A S]

Also, do you think it would be better to use the jacobian transposed matrix JT or just jacobian matrix J ?The answer to your question depends on the application. If you need to find the joint angles that correspond to a given end-effector position and orientation, then you would typically use the Jacobian matrix J. If you need to find the end-effector velocity given joint velocities, then you would typically use the transpose of the Jacobian matrix JT.