The following interactive animation illustrates the principle of force decomposition on the wedge.

## Description

The animation is based on the following assumptions:

The tip of an ideal wedge is infinitely small. The workpiece only comes into contact with the sides of the wedge. The main force is distributed over both sides. The lateral forces (also known as cheek forces) create a parallelogram of forces. The lines of action of the lateral forces are orthogonal to the sides. The geometric sum of the lateral forces corresponds to the amount of the main force.

The shape of a parallelogram half is identical to the shape of the wedge itself. This means that all angles of the parallelogram are known.

The angle γ (gamma) in the sketch corresponds to the angle β. As the sum of all angles in a triangle is 180 degrees, the angle α can be easily calculated.

In a symmetrical wedge, the following right-angled triangle always results on the left-hand side (in mirrored form also on the right-hand side):

The lateral force can be calculated using the following formula:

## Special case: Asymmetrical wedges

An asymmetrical wedge can also be shown in the animation. The halves of the force parallelogram also correspond to the wedge shape for the asymmetrical wedge (the wedge shape also appears rotated by 90 degrees here).

The following therefore applies:

The following applies to alpha angles:

and

The following applies to the delta angles:

and

This means that all angles are known. An unknown side can be determined using the transformed sine theorem.

## General information

Basically, the smaller the angle β or the point of a wedge, the wider the force parallelogram for the same main force. This relationship explains the enormous cutting and splitting effect of wedges. Extremely high lateral forces can occur with a very thin wedge (e.g. a nail or a knife).

In the case shown, the wedge penetrates the workpiece from above. There are also cases where the wedge acts on a surface at an angle (e.g. with a plane or a drill cutting edge). Depending on the material of the workpiece and the orientation of the wedge, a chip is created on the workpiece.

## Note on use

After starting the application, you can view the animation in full-screen mode. To do this, click on “View” and then on “Full screen”:

To exit full screen mode, press the Esc key.

## Overview and download

Title | Force distribution on the wedge |

Target group | Teachers and lecturers |

Platforms | Microsoft® Windows® Apple® Macintosh® |

Features | Full screen mode lossless zoom Large screens and projection screens supported |

Licence | Freeware |

Download | Contact |

## Contributors

C. Hein, S. Rikowski

## Sources

Authoring tool (control elements supplied): *Adobe Animate*

## Share

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