The following animation illustrates the principle of force distribution on a wedge. The division of a main force into two flank forces is visualized in real-time through an interactive force parallelogram.
Links
Description of the Animation
The animation shows a symmetrical wedge with three synchronized elements: wedge geometry, force vectors, and lines of action. The sliders allow the force and wedge angle to be changed, with the force parallelogram adjusting automatically.
The flank forces are calculated from the force equilibrium on the wedge:
\[ F_W = \frac{F}{2 \cdot \sin\left(\frac{\beta}{2}\right)} \]
With:
- \( F \) – Main force (acting perpendicular to the wedge tip)
- \( F_W \) – Flank force (perpendicular to the respective wedge surface)
- \( \beta \) – Wedge angle (opening angle at the tip)
The dashed lines of action show the directions of the forces and span the force parallelogram, whose geometric construction illustrates the decomposition of the main force.
Interactive Controls
The following parameters can be adjusted using the sliders:
- F (0–100 N): Magnitude of the main force
- β (5–90°): Opening angle of the wedge
Physical Background
When a wedge penetrates a workpiece, the applied main force is decomposed into two flank forces that act perpendicular to the wedge surfaces. This decomposition follows the principle of the force parallelogram: the two flank forces form the sides of a parallelogram whose diagonal corresponds to the main force.
The smaller the wedge angle β, the larger the flank forces become relative to the main force. At an angle of 30°, the flank forces are already twice as large as the main force; at 10°, approximately six times as large. This amplification effect explains the enormous cutting and splitting action of sharp wedges.
Practical Applications
- Cutting tools: Knives, scissors, and axes use small wedge angles for high cutting forces
- Fastening technology: Nails and wedges for joining and fixing components
- Machining technology: Lathe tools, milling cutters, and drills with defined cutting wedges
- Splitting tools: Log splitters and stone wedges for controlled material separation