Dyname

In technical mechanics, a dyname is a reduction of the force vectors and moment vectors acting on a rigid body to a resulting force and a resulting moment with respect to a point. If the reference point is chosen so that the force vector and the moment vector are parallel, then the dyname is called a power screw or power winder . The dyname is an important term in screw theory .

The sum of the forces and moments attack at a point O of a rigid body. If the moment is broken down into components perpendicular to the force and parallel to it, the system ( ) can also be described by a so-called dyname or power screw, consisting of: ${\displaystyle {\vec {K}}}$ ${\displaystyle {\vec {M}}}$ ${\displaystyle {\vec {M}}}$ ${\displaystyle {\vec {K}}}$ ${\displaystyle {\vec {M}}={\vec {M}}_{V}+{\vec {M}}_{K}}$ ${\displaystyle {\vec {K}},{\vec {M}}}$

• the torque vector that is too parallel ${\displaystyle {\vec {K}}}$ ${\displaystyle {\vec {M}}_{K}}$
• a on a straight line (the center line) at a distance acting from O parallel shifted force . ${\displaystyle a=|{\vec {a}}|}$ ${\displaystyle {\vec {K}}}$

The equation of the central line is (t real)

${\displaystyle {\vec {r}}={\vec {a}}+t{\vec {K}}}$

with (K is the amount of ) ${\displaystyle {\vec {K}}}$

${\displaystyle {\vec {a}}={\frac {{\vec {K}}\times {\vec {M}}}{K^{2}}}}$

The component of the moment vector that is too parallel is given by ${\displaystyle {\vec {K}}}$

${\displaystyle {\vec {M}}_{K}=p{\vec {K}}}$

with the parameter p of the power screw

${\displaystyle p={\frac {{\vec {K}}\cdot {\vec {M}}}{K^{2}}}}$

The name comes from the fact that on the central line the force causes a translation, the moment of the dyname a rotation around the direction of , so together a screw movement. ${\displaystyle {\vec {K}}}$ ${\displaystyle {\vec {M}}_{K}}$ ${\displaystyle {\vec {K}}}$

literature

• Istvan Szabo Introduction to Technical Mechanics , Springer, 1975, p. 50.
• K.Magnus / HHMüller Fundamentals of Technical Mechanics , Teubner Study Books , 1982, p. 33.