INVERSE KINEMATICS OF A ROBOTIC MANIPULATOR

Inverse kinematics has one of the most difficult problems for a robotic manipulator.
Below are the problems of a Robotic Manipulator.

1. Singularities.
2. The possibility of no solution.
3. The existence of multiple solutions.

• Singularities.

Singularity is a place of  infinite acceleration.

• The possibility of No Solution.

A point outside the workspace of the robot has no solution.

• The Existence of Multiple Solutions.

Redundancy of movement caused by redundant links.

Example

1DOF pendulum desired endeffector positionP  given as an (x,y)  location.

Inverse kinematics of 1DOF?considering pendulum.
Question
1.what is  θ1?
ans:

given position is (x,y).

θ1   is obtained by tan^-(y/x)

In  MatLab

atan2(Y,X)

Check this link.

http://web.eecs.umich.edu/~ocj/courses/autorob/autorob_10_ik_closedform.pdf