Editing Robot kinematics (section)

==Kinematic equations==
{{See|Kinematic equation}}
A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot.  These [[non-linear equation]]s are used to map the joint parameters to the configuration of the robot system. Kinematics equations are also used in [[biomechanics]] of the skeleton and [[computer animation]] of articulated characters.

Forward kinematics uses the kinematic equations of a [[robot]] to compute the position of the [[Robot end effector|end-effector]] from specified values for the joint parameters.<ref>John J. Craig, 2004, Introduction to Robotics: Mechanics and Control (3rd Edition), Prentice-Hall.</ref>  The reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics.  The dimensions of the robot and its kinematics equations define the volume of space reachable by the robot, known as its workspace.

There are two broad classes of robots and associated kinematics equations: [[serial manipulator]]s and [[parallel manipulator]]s. Other types of systems with specialized kinematics equations are air, land, and submersible mobile robots, hyper-redundant, or snake, robots and [[humanoid robot]]s.

===Forward kinematics===
{{Main|Forward kinematics}}
Forward kinematics specifies the joint parameters and computes the configuration of the chain. For serial manipulators this is achieved by direct substitution of the joint parameters into the forward kinematics equations for the serial chain.  For parallel manipulators substitution of the joint parameters into the kinematics equations requires solution of the a set of [[polynomial]] constraints to determine the set of possible end-effector locations.

===Inverse kinematics===

{{Main|Inverse kinematics}}
Inverse kinematics specifies the end-effector location and computes the associated joint angles. For serial manipulators this requires solution of a set of polynomials obtained from the kinematics equations and yields multiple configurations for the chain.  The case of a general 6R serial manipulator (a serial chain with six [[revolute joint]]s) yields sixteen different inverse kinematics solutions, which are solutions of a sixteenth degree polynomial. For parallel manipulators, the specification of the end-effector location simplifies the kinematics equations, which yields formulas for the joint parameters.