Your boundary determines which forces belong. Your moment reference determines their torque contributions. A force can create zero moment about one point and still remain essential.
Name the System
Boundary
- System: Identify the isolated segment.
- Environment: Identify everything outside it.
- Contact: Add forces exerted on the system.
- Gravity: Include the segment’s weight.
Forces
- Muscle: State whether forces are resolved individually.
- Joint reaction: Include the support force.
- Load: Add the external force at its application point.
- Action–reaction pair: Keep the opposite force on the other body.
Moments
- Reference: Name the point or axis.
- Distance: Use the perpendicular moment arm.
- Direction: Define the positive rotational sense.
- Equilibrium: Apply only when the stated motion permits it.
Free-body diagrams include external forces acting on the selected body. Forces exerted by that body belong on another diagram. OpenStax: drawing free-body diagrams.
Choose One Joint Representation
| Representation | Include | Avoid |
|---|---|---|
| Resolved-force model | Individual muscle forces and joint contact reaction | Adding a net muscle moment that already represents those forces |
| Lumped joint model | Net joint force and net joint moment | Re-adding the same individual muscle contributions |
| Ideal pin support | Reaction components at the pin | Inventing a resisting couple unless the model specifies one |
Work Through a Defined Example
Model: A horizontal forearm–hand segment at rest. Muscle action enters as an external upward force. All forces lie in one plane.
| Quantity | Value | Direction |
|---|---|---|
| External hand load | 50 N | Down |
| Load moment arm | 0.30 m | From elbow |
| Segment weight | 20 N | Down |
| Weight moment arm | 0.15 m | From elbow |
| Muscle moment arm | 0.03 m | Perpendicular |
| Joint reaction | Unknown | At elbow |
Choose counterclockwise moments as positive.
Moment equilibrium about the elbow:
Fmuscle × 0.03 − 50 × 0.30 − 20 × 0.15 = 0
Fmuscle × 0.03 = 18 N·m
Fmuscle = 600 NVertical force equilibrium:
Ry + 600 − 50 − 20 = 0
Ry = −530 N
The joint reaction acts downward in this simplified model.The elbow reaction creates no moment about the elbow. It still appears in force equilibrium. OpenStax: static-equilibrium methods.