# Rieter

### Preliminary remarks

#### Index

Fig. 90 – Resolution of forces in the force parallelogram

In the following explanations, certain inaccuracies have been deliberately accepted; for example, representation exclusively in two dimensions when the actual process is three-dimensional.

The intention is not to present either exact scientific theory or a detailed basis for calculations. Rather, the aim here is to provide the textile specialist involved in everyday practice with an understanding of the interrelations and in particular to bring out the interplay of forces. For this purpose, simplified models have been used; there is much literature available on scientifically exact usage  [18, 20, 21].

The whole treatment is based on the parallelogram of forces, the normal “school” presentation of which is repeated here briefly for completeness (see Fig. 90).

If a carriage is to be moved forward on rails, it can be pulled directly in the direction of the rails (as FT).

In this case the whole of the force contributes to the forward movement. This is no longer true if the force is directed with a sideways inclination (pulling in direction FF). Now only a part of the total force exerted (FF) will contribute to the forward movement (FT).

Part of the force FF ( i.e. the force FR) will press the carriage against the rails at an angle of 90° to the direction of movement. This component is lost as far as forward motion is concerned. The pulling force FF can therefore be resolved into two components, the tangential force FT, which draws the carriage forward, and the radial force FR. Accordingly, if the carriage is to be moved forward with the required force FT and the pulling force is effective at an angle $\alpha$, then the pulling force must have the magnitude FF (friction forces being neglected here). These forces can be represented graphically and measured or calculated in accordance with the formula:

$F_F = \frac {F_T}{sin\alpha}$