Trusses, Frames & Internal Force

A machine frame is a load path. The payload loads the end effector; the arm carries that demand through joints and links; the base and anchors carry it into the floor. If an analysis stops before reaching ground, it usually hides a connection or assumes an impossibly floating reaction.

Truss idealization

An ideal planar truss has straight members connected by frictionless pins, with external loads applied only at joints. Each member is then a two-force member in axial tension or compression. At a joint, solve \(\sum F_x=0\) and \(\sum F_y=0\). Start where no more than two member forces are unknown.

For a triangular bracket with a 1 m horizontal member and a 1 m vertical rise, a diagonal at 45 degrees supporting a 500 N downward joint load must supply a vertical component of 500 N. Its axial magnitude is \(500/\sin45^\circ=707\) N. Its horizontal component is 500 N and must be balanced by the horizontal member. Whether each is tension or compression follows from the solved arrow directions.

Real frames depart from this model: joints have stiffness, members carry self-weight, loads may enter between joints, and bending appears. The truss result is still useful if its assumptions match the architecture.

Cut a frame to expose demand

At an imaginary cut through a planar member, show three internal resultants:

• axial force \(N\), normal to the cut;
• shear force \(V\), tangent to the cut;
• bending moment \(M\).

Apply equilibrium to either side. The signs on the opposite face reverse because the separated pieces exert equal and opposite actions. The functions \(N(x)\), \(V(x)\), and \(M(x)\) convert the external load story into the inputs needed for stress and deflection.

Frames, machines, and constraint

A frame contains multi-force members and transmits bending. A machine adds members whose relative motion is intentional. The analysis habit is the same: isolate the full assembly, solve external reactions when possible, then isolate members or subassemblies. Pins internal to the full assembly vanish from its FBD but reappear as equal and opposite forces on the separated pieces.

Load-path review

For a tabletop robot or adjustable monitor arm, draw the load path for three cases: gravity at maximum reach, emergency stop during motion, and a human applying an unintended side force. At every interface ask:

1. What force and moment cross here?
2. Which feature carries each component—bearing, shoulder, bolt preload, weld, key, or friction?
3. What happens if clearance opens or friction is lost?

That review often reveals the real weak point before a stress equation does.