Co

c\2e dv2

dtT"

Therefore:

At the instant the bolt motion starts, <->=0. Hcncc, the relation between the initial accelerations of the masses reduces to:

This relation shows that if 6/ is small, the acceleration of the linkage mass Ma will be much greater than the acceleration of the bolt mass Mj. For example, if <9=4°, sin 0—0.0698 and the acceleration of mass Ma will be greater than the acceleration of mass Mi by a factor of 7.17. In other words, the inertia reaction of a mass located at point B is 7.17 times greater than for the same mass located at point A.

Actually, the mass multiplying effect is further increased by the fact that the bolt acts through the linkage at a great mechanical disadvantage. Fig. 1-46 shows a vector diagram of the forces in the linkage. The inertia reaction of mass M* is equal to M2 (dV2/dt) directed perpendicular to arm BC. This force is in equilibrium with the indicated forces exerted at point B by the linkage arms. Taking component perpendicular to arm BC gives the force Pi in arm AB as:

dt sin 2 0

Taking horizontal components at point A gives the relation between P2 and the force Pi exerted on arm AB by the bolt

Substituting the value of P2 into this expression gives:

cos 0

As previously explained, at the instant the bolt motion starts:

0 0

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