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In robot kinematics, forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters. [ 1 ] The kinematics equations of the robot are used in robotics , computer games , and animation .
A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. These non-linear equations 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.
In global motion planning, target space is observable by the robot's sensors. However, in local motion planning, the robot cannot observe the target space in some states. To solve this problem, the robot goes through several virtual target spaces, each of which is located within the observable area (around the robot).
The system of six joint axes S i and five common normal lines A i,i+1 form the kinematic skeleton of the typical six degree-of-freedom serial robot. Denavit and Hartenberg introduced the convention that z-coordinate axes are assigned to the joint axes S i and x-coordinate axes are assigned to the common normals A i , i +1 .
From this point of view the kinematics equations can be used in two different ways. The first called forward kinematics uses specified values for the joint parameters to compute the end-effector position and orientation. The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters ...
For each joint of the kinematic chain, an origin point q and an axis of action are selected for the zero configuration, using the coordinate frame of the base. In the case of a prismatic joint, the axis of action v is the vector along which the joint extends; in the case of a revolute joint, the axis of action ω the vector normal to the rotation.
In classical mechanics, the Udwadia–Kalaba formulation is a method for deriving the equations of motion of a constrained mechanical system. [1] [2] The method was first described by Anatolii Fedorovich Vereshchagin [3] [4] for the particular case of robotic arms, and later generalized to all mechanical systems by Firdaus E. Udwadia and Robert E. Kalaba in 1992. [5]
Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: