Editing Robot kinematics (section)

==Fields of study==
Robot kinematics also deals with [[motion planning]], '''singularity avoidance''', '''[[Redundancy (engineering)|redundancy]]''', '''collision avoidance''', as well as the kinematic synthesis of robots.<ref>J. M. McCarthy and G. S. Soh, [https://books.google.com/books?id=jv9mQyjRIw4C&q=geometric+design+of+linkages ''Geometric Design of Linkages,''] 2nd Edition, Springer 2010.</ref>
<!--this is described in the article on forward kinematics.  While dealing with the kinematics used in the robots we deal each parts of the robot by assigning a frame of reference to it and hence a robot with many parts may have many individual frames assigned to each movable parts. For simplicity we deal with the single manipulator arm of the robot. Each frames are named systematically with numbers, for example the immovable base part of the manipulator is numbered 0, and the first link joined to the base is numbered 1, and the next link 2 and similarly till n for the last nth link.-->
<!--this is described in the previous section.  ===Forward position kinematics===
The forward position kinematics (FPK) solves the following problem:
"Given the joint positions, what is the corresponding end effector's pose?"
=== 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 end effector 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]].{{Citation needed|date=October 2011}} -->
<!--this is described in the previous section.  ===Inverse position kinematics===
The inverse position kinematics (IPK) solves the following problem: "Given the actual end effector pose, what are the corresponding joint positions?"
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 joint]]s) with a completely general geometric structure has sixteen different inverse kinematics solutions, found as the solutions of a sixteenth order polynomial for best result.
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