The following animation illustrates how a wedge transfers forces to a workpiece. You can interactively change both the total angle of the wedge (β) and the force F acting from above.
The flank forces act perpendicular to the wedge flanks and are shown as blue vectors in the animation. For a frictionless, symmetrical wedge, the flank force is calculated as:
\[ N = \frac{F}{2 \cdot \tan(\alpha)} \]
Where α corresponds to half the wedge angle (α = β/2).
The principle is simple: The sharper the wedge (smaller α), the greater the resulting normal force N for the same input force F. This explains the high effectiveness of sharp tools.
Influence of Friction
In practice, friction must be considered. The extended formula is:
\[ N = \frac{F}{2 \cdot \bigl(\tan(\alpha) – \mu\bigr)} \]
The friction coefficient μ (pronounced: “mu”) is a dimensionless material property:
- Smooth steel on steel: μ ≈ 0.1
- Rough rubber on asphalt: μ ≈ 1.0
Practical Applications
The desired friction depends on the application:
- Cutting tools (e.g., axes): Minimal friction through polished steel desired
- Clamping wedges (e.g., door wedges): High friction required for secure hold
Additional Examples
- Wood splitting: Typical wedge angles (20-30°) and occurring forces
- Mechanical engineering: Clamping wedges, key joints with specific values
- Construction: Wedge connections in timber construction, historical stone working
- Mountaineering: Clamping wedges with optimal angles for various crack widths
Theoretically, an infinitely sharp wedge would generate infinitely large flank forces. This illustrates the enormous force multiplication potential of the wedge principle.
The optimal wedge geometry depends on the application:
Cutting wedges (knives, chisels):
- Wedge angle: 15-25°
- Minimal friction through polishing
- High hardness of the cutting edge
Splitting wedges (wood, stone):
- Wedge angle: 20-40°
- Moderate friction desired
- Robust construction
Clamping wedges (fastening):
- Wedge angle: 5-15° (self-locking)
- High friction required
- Elastic deformation permissible
Additional Information
| Platform | PC/Mac or Tablet |
| Resolution (min) | 1280 x 720 |
| Development tool | Custom editor: Source code |