Kinematics studies motion without considering the causes that produce such motion. Robot kinematics studies the movement of all robot elements with respect to a reference frame, usually the robot's base:
Analytical description of the spatial movement, both in position and orientation, of the robot
Describes the kinematic relation between the robot's end effector and its joints, which can be expressed as a time-based trajectory.
Kinematics is the basis for understanding how robots move, although we must not forget that the real world is dynamic!
Absolute models:
Forward kinematic model: Determines the position and orientation of the robot's end effector with respect to a reference system, given joint value positions, as well as the robot geometric parameters.
Inverse kinematic model: Determines joint value positions necessary to reach a given position and orientation of the robot's end effector. The geometric parameters of the robot are known.
Differential Model: Determines the relationship between robot joints speed and the speeds of the end effector, based on the Jacobian matrix
A robot singularity is a configuration in which the robot end-effector becomes blocked in certain directions.
At a singularity, a robotic arm loses one or more degrees of freedom.
The problem with singularities is not only the impossibility of crossing them, but also the high joint velocities resulting from passing close to them.