Forward kinematics

The reverse process, that computes the joint parameters that achieve a specified position of the end-effector, is known as inverse kinematics.

The kinematics equations for the series chain of a robot are obtained using a rigid transformation [Z] to characterize the relative movement allowed at each joint and separate rigid transformation [X] to define the dimensions of each link.

[3][4] This convention positions the joint frame so that it consists of a screw displacement along the Z-axis and it positions the link frame so it consists of a screw displacement along the X-axis, Using this notation, each transformation-link goes along a serial chain robot, and can be described by the coordinate transformation, where θi, di, αi,i+1 and ai,i+1 are known as the Denavit-Hartenberg parameters.

The kinematics equations of a serial chain of n links, with joint parameters θi are given by[5] where

The forward kinematic equations can be used as a method in 3D computer graphics for animating models.

Three of these joints (the shoulder, wrist and the base of the thumb) have more than one degree of freedom, all of which must be taken into account.