Explain in details Hart’s Mechanism?

Hart’s Mechanism:

From Fig,

FC = DE ; CD = EF ;

The point O, A, and B are divide the links FC, CD, and EF in the same ratio.

From similar triangle CFE and OFB,

CE/OF 

OB FC

From Similar triangle FCD and OCA

OB = CE X OF x FC

FD x OA

FC x OC x OA = FD  X OC x FC

OA X OB = CE X OF X FD X OC FC FC = FD X CE X

OC X OF X FC^2

Since the length OC, OF, and FC are fixed, therefore

OA X OB = FD X CE X constant

Now from point E draw EM parallel to CF and EN perpendicular to FD.

Therefore

FD X CE = FD X FM

= (FN + ND) (FN - MN)

= FN2 – ND2 = (FE2 – NE2) – (ED2 – NE2)

= FE2 – ED2

So , Finally

OA X OB = Constant