Understanding Robot Motion: A Physics Primer

Forward Kinematics

Forward kinematics deals with calculating the position and orientation of a robot’s end-effector (e.g., its hand or tool) given the joint angles. It's essentially solving for ‘where is the tool?’ based on how the joints are moving.

The process involves a series of transformations – rotations and translations – applied sequentially from each joint to the next. Each transformation represents the movement of that joint relative to its parent joint. The final transformation gives you the end-effector's position in Cartesian space (x, y, z).

Position = Σ(Rᵢ * pᵢ) where Rᵢ is the rotation matrix for joint i and pᵢ is the position vector of joint i.

Inverse Kinematics

Inverse kinematics tackles the opposite problem: determining the required joint angles to achieve a desired end-effector pose. It’s about asking, ‘How do I move my joints to reach this specific point?’

Unlike forward kinematics, inverse kinematics often has multiple solutions or no solution at all. Robot design must account for these complexities and choose appropriate strategies (e.g., using constraints).

Solving for θ:  θ = f⁻¹(p) where θ is the joint angle vector and p is the desired end-effector position.

Joint Types & Kinematic Chains

Robots are classified by their joint types – revolute (rotational), prismatic (linear), or spherical. The arrangement of these joints creates a kinematic chain.

A planar robot has two to three revolute joints, while a spatial robot can have six degrees of freedom (DOF) allowing for movement in all three dimensions. Each DOF represents an independent parameter that needs to be controlled.

Degrees of Freedom (DOF) = 3(n-1) where n is the number of joints.

Singularities

A singularity occurs when a robot loses one or more degrees of freedom, meaning it can no longer precisely control its end-effector position. This often happens when all joint angles are zero.

Understanding and avoiding singularities is crucial for robust robot motion planning.

“Zero Velocity Point” (ZVP) – A point where the robot’s frame and base frame coincide, leading to loss of control.”

Frequently asked questions

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Everything above runs in your browser — open Inverse Kinematics (FABRIK) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.