Dynamics

The study of how forces and torques produce motion — how much acceleration a given torque causes.

Dynamics is the branch of classical mechanics that studies the relationship between force and motion, grounded in Newton's second law, F = ma. Robot dynamics extends this to multi-joint systems, commonly written as M(q)q̈ + C(q,q̇)q̇ + g(q) = τ, where q is the vector of joint angles, q̇ and q̈ are joint velocity and acceleration, M is the mass matrix (each link's inertia reflected back to the joints), the C term captures Coriolis and centrifugal forces, g is the gravity term, and τ is joint torque. Computing acceleration from known torques is called forward dynamics, which a physics engine solves at every simulation step; computing the torques needed to produce a desired motion is called inverse dynamics, used for gravity compensation and torque control. Kinematics only deals with geometry; picking up a heavy object, moving quickly, and balancing on legs all require dynamics.

ExampleWhen an arm holds an object perfectly still, q̇ and q̈ are both zero, so the equation reduces to g(q) = τ — inverse dynamics then just gives the torque each joint needs to counteract gravity, including the object's weight.

Also called

Robot Dynamics

Related

Forward Dynamics · Inverse Dynamics · Mass Matrix · Rigid-Body Dynamics · Kinematics · Physics Engine

Sources

Wikipedia: Dynamics (mechanics)
MIT Underactuated Robotics: Multi-Body Dynamics（manipulator equations）
MuJoCo Documentation: Computation（forward / inverse dynamics）