FOUR LİNK MECHANISMS

Transmission Angle

Force component tending to move the driven link_______________

Force component tending to apply pressure on driven link bearings

Force component tending to move the driven link

Total force applied to the driven link

The optimum value of is 90o . During the motion cycle it deviates from this value. Generally, if this deviation exceeds 40o-50o mechanisms lock.

Transmission Angles for Four Bar Mechanisms

• The minimum and maximum values of the transmission angle may be determined by taking the derivative of cos equation with respect to 12 and equating to zero.

•

• The min. and max. values of will be when

is equal to 0 or .

Transmission Angles for Four Bar Mechanisms (cont’d)

• The min. and max. values of the transmission angle:

• The critical is either min or max , whichever deviates most from 90o.

Crank-Rocker Proportions of a Four-Bar Mechanism

• The link lengths are functions of initial crank angle , (=a3/a2), the given swing angle () and corresponding crank rotation (). For crank-rocker proportions a necessary (but not sufficient) condition is >1.

• Either or may be used as the free parameter and obtain different mechanism proportions.

Crank-Rocker Proportions of a Four-Bar Mechanism (cont’d)

• If is used as free parameter, the link lengths are given as,

where,

t=tan(/2) u=tan[(-)/2] v=tan(/2)

In order to obtain crank rocker proportions there are limits on

swing angle and corresponding crank rotation:

0<<180 90+/2<<270+/2

Crank-Rocker Proportions of a Four-Bar Mechanism (cont’d)

The real lengths of the links are not important. The important thing is their proportions. Therefore, these equations are obtained on the basis of unit length for fixed

link and give the length ratios wrt fixed link.

If is used as free parameter, the link lengths are given as,