Robot kinematics

Robot kinematics describes how joint positions determine a robot’s configuration and how that configuration determines the position and orientation of its links and end effectors, without modeling forces.

Forward kinematics: The calculation of a robot’s link and end-effector poses from its joint positions. It maps specified joint values to the resulting end-effector pose.
Rigid-body transformation: A transformation combining rotation and translation that maps coordinates between rigid-body frames. Link poses are composed from transformations between neighboring frames.
Robot manipulator: A robotic mechanism of linked segments and joints designed to position or move an end effector. Its linked structure is the standard setting for joint-to-pose calculations.
Robot dynamics: The study of forces, torques, and motion in robots, including the effects of mass and inertia. Unlike kinematics, dynamics explains the forces required to produce motion.
Inverse kinematics: The calculation of joint positions that place a robot’s end effector at a specified pose. It solves the reverse mapping needed to reach a target pose.
Rotation matrix: An orthogonal matrix with determinant one that represents a three-dimensional rotation. It represents the orientation component of a link or end-effector pose.
Robot motion planning: The computation of a collision-free path between configurations or task states for a robot. Kinematic reachability and constraints shape the paths a planner can use.
Screw theory: A mathematical framework that represents rigid-body motions and forces using six-dimensional screws. It offers a compact alternative for describing spatial robot motions.
Denavit–Hartenberg parameters: A convention for representing the relative geometry of successive robot links and joints with four parameters. These parameters encode link geometry for a forward-kinematics chain.
Homogeneous coordinates: An augmented coordinate representation that expresses translations and linear transformations as matrix operations. They let rotation and translation combine in one pose matrix.

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