Introduction

Kinematics is the study of motion — position, velocity, and acceleration — without worrying about the forces that cause it. For a robot arm or mobile robot, kinematics is what lets you answer: "if my joints are at these angles, where is my end-effector?" and the reverse: "I want my end-effector here — what joint angles get me there?"

These two questions are forward kinematics and inverse kinematics, and almost everything else in this page builds on that distinction.

Key Concepts

• Forward Kinematics (FK) — given joint angles/positions, compute the pose (position + orientation) of the end-effector. Always has a unique solution — it's just applying a chain of transformations.
• Inverse Kinematics (IK) — given a desired end-effector pose, compute the joint angles that achieve it. Often has multiple solutions, sometimes none (unreachable pose), and can be analytically or numerically solved.
• Denavit–Hartenberg (DH) parameters — a standard convention for describing the geometry of a robot's links and joints so FK can be computed systematically.
• Transformation matrices — 4x4 homogeneous matrices combining rotation + translation between coordinate frames; the core building block of FK.
• Workspace — the set of all points an end-effector can reach; distinguishing reachable vs dexterous workspace matters for arm design.

Applications in Robotics

• Robot arm control (industrial arms, manipulators) — IK is how you tell an arm to "pick up the object at this point"
• Mobile robot odometry — relating wheel rotations to robot displacement
• Any simulation environment (Gazebo, MuJoCo) computes FK constantly under the hood

Resources

Books

Papers

Repos