FRAMES AND MACHINES A group of students has designed a toggle press to crush alu

Question

FRAMES AND MACHINES

A group of students has designed a toggle press to crush aluminum cans to use in the student lounge. The press consists of handle EFG, 3 bars(BD, CD, DE), and a piston at B that moves vertically within cylinder A. When an upward force P is imposed on the handle, a crushing force of 100 lb develops at the piston. Points B, C, D, E. and F are pinned connections. Assume smooth walls between the piston and cylinder. Draw ALL FBD's necessary to solve this problem. Find the force P and the forces in members BD, CD, and DE.

Explanation / Answer

Mechanical Advantage = Fb / Fa = a / b = Crushing load / P

To, find P, resolve forces along x and y directions.

By using sine law

Fa / sin A = Fb/ sin B = Fc/ sin C

So, from the given figure we can designate

the values of Fa = Fde, Fb = Fbd and Fc =Fdc

So, from the given geomentry of figure, the angles

A = 78+67 = 145

B = 90+(90-78) = 102

C = 90+ 90-67 = 113

So, here Fa / sin 145 = Fb / sin 102 = Fc / sin 113

But the value of Fb = Crushing force / sin 67

So, Fb = Fbd = 100 / 0.9205 = 108.63lb

FRom the sine law stated above we can calculate the Fa and Fc values as

Fa = Fde = 63.68 lb and Fc = Fcd = 102.23 lb

Now, the value of P = 2*Fde/(8-0.5) = 63.68/3.75 = 16.98 lb

Now, the mechanical advantage can be found out by MA = Crushing load / p

MA = 100/16.98 = 5.8892

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