As for the dimensional twisted members at the shoulder of the roof system, sectionalized break lines replace ideal curve, and the main axis of the section of each member is deflected.

Based on a proportional valve-hydraulic cylinder system, this paper puts forward the problem of implementing cushioning and positioning at any point in full-stroke by using ideal curve.

This paper gives a general equation for the ideal curve of crane beam with joint support, then further discusses the effect of elastic support on the curve, and gives the complement equation.