単一板ばね支点の変形

第2近似

抄録

In order to make clear the elastic deformation of a single flat spring fulcrum used in the scales, the authors introduced the fundamental differential equations dl'=dθ/x and xdx=sinθdθ in the first paper¹⁾. To solve these equations, in the case of a small declining angle of scale levers, the authors assumed-sinθ=θ in the same paper. The results were testified experimentally as reported in the second paper²⁾.
In this third paper, to obtain the relations which are necessary in a large inclination angle of levers, the authors solve the fundamental equations by assuming sinθ=θ-(θ³/6).
The effects of the higher order term (θ³/6) upon every quantity which is necessary to design scales are estimated exactly, and it is shown that they are small even when the angle θ is about 0.5 radians.
To verify the theory empirically, the authors examine the relationship between the inclination angles of the flat spring at the upper and lower ends. In this case, they change the inclination angles φ at the upper end from-0.5 rad to +0.5 rad. They also study the shapes of flat springs in various caces by taking photographs of them. The agreement between theory and experiment is satisfactory.