Module 1·50 min
Free-Body Diagrams
Free-Body Diagrams
A free-body diagram (FBD) is the single most important tool in static analysis. It isolates a body from its surroundings and shows every external force acting on it.
The Isolation Principle
To draw an FBD:
- Select the body you want to analyze
- Remove all supports and connections — replace them with forces
- Draw every external force as an arrow at its point of application
- Label magnitudes and directions (known or unknown)
Common Reaction Forces
| Support Type | Reaction Provided |
|---|---|
| Roller | Force ⊥ to surface |
| Pin/hinge | Force in any direction (2 unknowns) |
| Fixed wall | Force + moment (3 unknowns) |
| Cable/rope | Tension along cable only |
Equilibrium Conditions
A body is in static equilibrium when:
ΣFx = 0 (sum of horizontal forces = 0)
ΣFy = 0 (sum of vertical forces = 0)
ΣM = 0 (sum of moments about any point = 0)
These three equations let you solve for three unknowns.
Example: Robot Arm Link
Consider a forearm link 0.3 m long, weighing 2 N, pinned at one end with a payload of 5 N at the other:
Pin reaction: Rx, Ry (unknown)
Weight: 2 N downward at midpoint (0.15 m)
Payload: 5 N downward at tip (0.3 m)
ΣFx = 0 → Rx = 0
ΣFy = 0 → Ry - 2 - 5 = 0 → Ry = 7 N
ΣM_pin = 0 → -(2 × 0.15) - (5 × 0.3) = 0 ✓ (pin absorbs it all)
The pin must supply 7 N upward. This is the minimum force your actuator must produce.