Answer to Question #163910 in Mechanical Engineering for Arpan Chakraborty

Question #163910

Using Grubler's criterion for plane mechanism, prove that the minimum number of binary links in a constrained mechanism with simple hinges is four.


1
Expert's answer
2021-02-16T07:29:34-0500

We know that degree of freedom for a simple mechanism "DOF=3(l-1)-2j"

Grubler's criterion for a plane mechanism applies only to a single DOF.

"1=3(l-1)-2j\\implies3l-2j-4=0"

When we look at the above equation, we find "3l" must be even, and the lowest value which satisfies this equation is "l_{min}=4"

If we consider 2, whatever practically it is not possible. Hence the minimum number of binary links in a constrained mechanism with simple hinges is four.


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