Small-displacement compatibility

Apply constraint-compatible virtual displacements to levers, pulleys, mechanisms, and force-direction optimization.

Open the complete lesson

Advanced engineering statics simulation

Virtual Work Equilibrium Suite

Five distinct, constraint-compatible virtual-work models; efficiency is separated from geometry.

Simulation

Inspect dx/dθ and dy/dθ before applying force equilibrium.

Link length1.8 m

0.3–3.5

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

Generalized link angle40 deg

deg

5–90

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

compatible virtual motion

Required input

kinematic only

Virtual-work residual

0.00e+0 N

Should be near zero

dx/dθ

-2.314 m/rad

dy/dθ

2.758 m/rad

|dy/dx|=2757759995.228

\delta W=\sum \mathbf{F}_i\cdot\delta\mathbf{r}_i+\sum M_i\delta\theta_i=0

Compatibility is derived first; arbitrary independent dx and dy values would violate the mechanism constraint.

Model scope and verification

Scope: Educational rigid-body statics model using the selected geometry, stated idealizations, and displayed SI units.

Acceptance check: Check the governing equilibrium, compatibility, geometry, or limiting-condition statement before accepting the numerical result.

Lever equilibrium Pulley-system virtual work Scissor mechanism Minimum-input-force direction

Related simulations