Belt scale's error caused idler's deflection by force

For belt scale's error estimation we shall reject constraints (idlers), which will be replaced by their corresponding responses as shown in fig.7. There was added a coordinate system with origin in a point .

The rejected constraints have been substituted by force's responses, that is force , and . Thus, if you recall, -- it is a response of a spring-bias deflected idler and magnitude of this deflection obeys the law:

$\displaystyle N_B=c\Delta y.$
{fig6}
Figure 6: System of force are existing in the mech system with properly counted assumptions. Here is no any response reaction of idler H.

{fig7}
Figure 7: Modernized mech system where constraints(idlers) were thrown off being repalced by its reactions.

Obviously, that .

Further there shall be used "the principle of a solidification" which widely known in theoretical mechanics. As the belt scale system is in an equilibrium we can replace two branches of a flexible string with pivot-joint rods/beams as shown in fig.8. As the system is symmetric we can consider a condition of an equilibrium for its halfs concerning a line of a symmetry $BB\lq$ . In a word it can be split in this place. In fig.9 the new conventional scheme of mech system is presented. There I have tried to depict force keeping a belt scale factor for the further course of operations could be clear.

Figure 8: Modernized mech system where string sections have been replaced by rods having use ``principle of solidification''.

{fig9}
Figure 9: In regard of system's symmetry we can consider a half of one. Increased tension force $\sigma +\Delta\sigma$ is shown dotted.

There are force $\sigma$ and (fig.9) as projections to coordinates' axes of varied (increased) string tension force $\sigma +\Delta\sigma$ . Increased tension $\sigma +\Delta\sigma$ shown dotted. The resultant force of a tension is always directed along a string or in our assumption along a rod. Such force were called as sliding in mechanics and we have "the right" to displace its along a rod as the state of a system's condition will remain the same. Well, we shall take advantage of this "right" and we shall move component of tension force to a point as it shown on fig.10. I am sorry! There are so much force and the point such a tiny, but I think you've seen, what has been conceived.

Figure 10: Belt scale mech system where sliding force have been moved at point