Question

using grublers criterion for plane mechanism prove that the minimum number of binary links in a constrained mechanism with simple hinges is four

Answer 1

Answer:

We know that degree of freedom for a simple mechanism DOF=3(l-1)-2jDOF=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=01=3(l−1)−2j⟹3l−2j−4=0

When we look at the above equation, we find 3l3l must be even, and the lowest value which satisfies this equation is l_{min}=4l

min

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=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.

Step-by-step explanation: