===== Lego Robotic Manipulator =====

**Closed Form Solution**
 
 We can project the the manipulator in a 2D plane , wz , where w is the plane where the target is located.Using algebra a closed form solution for the inverse kinematics problem can be found for this particular Lego Manipulator.
 
 Given the target coordinates in world coordinates , we can solve for the base angle A0 and the joint angles A1,A2,A3.  The angle from the base can be easily found using:

{{ ::axis2.jpg?direct |}}

Projecting the manipulator in the wz plane , the problem now is 2D , and the closed form solution can be found using algebra.

{{ ::axis_lego.jpg?direct |}}

{{youtube>Ue8vInMqgBE?large}}

{{ ::legoman1.jpg?direct |
}}

{{ ::legoman2.jpg?direct |}}