Sunday, September 9, 2007

Kinematics of a Robotic Arm

I dropped the idea of designing a robotic arm initially due to the kinetics.. :P
I found the reverse kinetics tough enough that I surrendered and dropped the very idea of a robotic arm.
Still I do feel I will start working on this project some day (in my undergraduate only)

Robot Kinematics is the study of the motion of robots. In a kinematic analysis the position, velocity and acceleration of all the links are calculated without considering the forces that cause this motion.

Robot kinematics are mainly of the following two types: forward(or direct) and inverse kinematics.

Forward Kinematics (angles to position)
What you are given: 1.The length of each link
2.The angle of each joint

What you can find: The position of any point
(i.e. it’s (x, y, z) coordinates

Serial chains:

The solution is always unique: one given joint position vector always corresponds to only one single end effector pose. The FK problem is not difficult to solve, even for a completely arbitrary kinematic structure.

Methods for a forward kinematic analysis:

  • using straightforward geometry
  • using transformation matrices

Parallel chains (Stewart Gough Manipulators):

The solution is not unique: one set of joint coordinates has more different endeffector poses. In case of a Stewart Platform there are 40 poses possible which can be real for some design examples. Computation is intensive but solved in closed form with the help of algebraic geometry.

Inverse Kinematics (position to angles)
What you are given: 1.The length of each link
2.The position of some point on the robot

What you can find: The angles of each joint needed to obtain
that position

In contrast to the forward problem, the solution of the inverse problem is not always unique: the same end effector pose can be reached in several configurations, corresponding to distinct joint position vectors. A 6R manipulator (a serial chain with six revolute joints) with a completely general geometric structure has sixteen different inverse kinematics solutions, found as the solutions of a sixteenth order polynomial.

(Detailed tutorial for analysis and solving to come later)


Anonymous said...

i needed help in solving the inverse kinematics of an arms with 3 revolute joints....

Pankaj Chopra said...

As I said earlier.. we are having problems with the kinetics ourselves.
But we will cover it up soon and post the detailed tutorial.

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