Glossary term
Free-Body Diagram
A diagram that isolates a body or component and shows the external forces, moments, reactions, and selected coordinate system acting on it.
Definition
methodA diagram that isolates a body or component and shows the external forces, moments, reactions, and selected coordinate system acting on it.
A free-body diagram is the first formal step in statics and dynamics. It defines the system boundary, load path, unknown reactions, and sign conventions before equations of equilibrium or motion are written.
A free-body diagram isolates one body from its surroundings and replaces those surroundings with external forces and moments. It is a modelling tool, not merely a sketch. The diagram defines what is included in the body, what is excluded, and how interactions cross the boundary.
Engineering role
Free-body diagrams are used in statics, dynamics, structural analysis, machine design, robotics, vehicle dynamics, biomechanics, and aerospace loads work. They help engineers derive equilibrium equations, calculate reactions, identify load paths, size members, and avoid double-counting forces.
What to include
A good FBD shows applied loads, support reactions, weights, contact forces, friction forces, cable tensions, spring forces, pressure resultants, moments, inertial forces when using dynamic equilibrium formulations, and a coordinate system. Internal forces are not shown unless the body has been cut to expose them.
Boundary choice
The chosen boundary determines the unknowns. Isolating a whole assembly may reveal external reactions; cutting through a member may reveal internal shear, moment, and axial force; isolating a single link may reveal joint forces. Good analysis often uses several FBDs at different levels of the system.
Equations
For static equilibrium, the sum of forces and moments must be zero. For dynamics, force and moment resultants are related to mass acceleration and angular acceleration. The FBD must match the assumptions of the equations, including planar versus three-dimensional motion, friction model, rigid versus deformable body, and inertial reference frame.
Common mistakes
Common mistakes include omitting a reaction, drawing forces on the wrong body, double-counting action-reaction pairs, and mixing internal and external forces. Another frequent error is starting calculations before drawing the FBD; this usually hides sign-convention mistakes and unsupported assumptions.