Answer to Question #163910 in Mechanical Engineering for Arpan Chakraborty

Question

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

Answer 1

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.