A Study of Descriptive Vector Statics

Statics is the earliest basic discipline in the natural sciences that is precisely solved by computation, and has formed a relatively perfect research method and knowledge system. Forces are vector quantities and can be represented by lines with (arrows) direction of the force, while arrows may be omitted for graphical simplicity, except where specifically required. A spatial force system can be expressed as a collection of lines, each of which represents a force on an object. The effect of force on an object is determined by three elements: the magnitude, direction, and point of action of the force, which are customarily called the three elements of force, and the vector contains the quantity and direction. The practice of representing the magnitude and direction of a spatial force vector by the Monge orthographic projection method is to draw a horizontal projection of line \(AB\) as \(ab\) , a frontal projection as \(a^{\prime}b^{\prime}\) , and a lateral projection as \(a^{\prime\prime}b^{\prime\prime}\) . The extraordinary feature of Monge's descriptive geometry is the graphical solution of problems of illustrating and solving geometrical elements in three dimensions on two-dimensional drawings. Now assigning force properties to geometric elements and combining them with theorems related to statics results in descriptive vector statics. Vector statics is widely used in engineering calculations, but the process is cumbersome and errors in the calculations are not easy to be detected, while the graphical illustration with projection graphs is both simple and intuitive, and combined with computer graphics, the speed and accuracy of the illustration can also be guaranteed.