Each joint contributes a specific number of degrees of freedom: a revolute joint and a prismatic joint contribute one each, while a spherical joint contributes three. The total mobility of a mechanism is found by summing joint freedoms and correcting for the constraints imposed by the structure using the Chebychev-Grubler-Kutzbach criterion. The number of degrees of freedom defines the dimension of the configuration space in which motion is planned; forward kinematics maps joint coordinates to the end-effector pose, and inverse kinematics solves for joint coordinates given a target pose. To freely place an end-effector in a full 6-DoF pose an arm needs at least six degrees of freedom; extra freedoms create redundancy used to avoid obstacles and singularities.
DoF answers how many independent control variables are needed to fully describe and control the motion of a robot or rigid body. Without this measure one cannot systematically design a manipulator, judge whether it can reach a required pose, or distinguish under-actuated systems from redundant ones.
Denavit and Hartenberg introduced a matrix notation parameterising joints and links of a kinematic chain, standardising the description of degrees of freedom in robotics.
Number of independently actuated joints that sets the total degrees of freedom of an open kinematic chain.
Kind of joint that determines how many degrees of freedom it contributes to the mechanism.
Number of degrees of freedom required by the task, setting the minimum mobility of the robot.
