The following animation illustrates the principle of force resolution at a wedge. The decomposition of a main force into two flank forces is visualized in real time through an interactive force parallelogram.
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Animation Description
The animation shows a symmetrical wedge with three synchronized elements: wedge geometry, force vectors, and lines of action. The sliders allow adjustment of force and wedge angle, with the force parallelogram adapting automatically.
The flank forces are calculated from the force equilibrium at the wedge:
\[ F_W = \frac{F}{2 \cdot \sin\left(\frac{\beta}{2}\right)} \]
Where:
- \( F \) – Main force (acting perpendicular to the wedge tip)
- \( F_W \) – Flank force (acting perpendicular to the respective wedge surface)
- \( \beta \) – Wedge angle (included angle at the tip)
The dashed lines of action indicate the directions of the forces and form the force parallelogram, whose geometric construction illustrates the resolution 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°): Included angle of the wedge
Physical Background
When a wedge penetrates a workpiece, the applied main force is resolved into two flank forces acting perpendicular to the wedge surfaces. This resolution 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 greater 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 larger. This amplification effect explains the enormous cutting and splitting action of sharp wedges.
Practical Applications
- Cutting tools: Knives, scissors, and axes utilize small wedge angles for high cutting forces
- Fastening technology: Nails and wedges for joining and securing components
- Machining technology: Lathe tools, milling cutters, and drills with defined cutting wedges
- Splitting tools: Log splitters and stone wedges for controlled material separation
Overview
| Title | Forces on the Wedge |
| Target Audience | Teachers and Lecturers |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | MIT |