Question

A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB \( \perp \) CE and FD \( \perp \) CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is

• A. a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG
• B. a non-Grashof chain with all oscillating links
• C. a Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF
• D. on the border of Grashof and non-Grashof chains with uncertain configuration(s)

Hint:

To check if a four-bar linkage is a Grashof chain, apply the Grashof condition: \( S + L \leq P + Q \), where \( S \) is the shortest link, \( L \) is the longest link, and \( P \) and \( Q \) are the other two links.

Answer 1

The Correct Option is A

Step 1: Apply the Grashof Condition.
For a four-bar mechanism to be a Grashof chain, the sum of the shortest and longest link lengths must be less than the sum of the other two link lengths. In this case, the mechanism satisfies the Grashof condition, as the link AG, AB, and CDEF can rotate completely about the ground link FG.
Step 2: Analyze the Linkage.
The four-bar linkage includes 3 revolute pairs and 1 prismatic pair. The links AG, AB, and CDEF are capable of full rotation, which implies that they meet the criteria for a Grashof chain. The ground link FG remains fixed, and the other links can rotate completely.
Step 3: Conclusion.
The mechanism follows the Grashof condition and allows for full rotation of the links AG, AB, and CDEF about the ground link FG. Final Answer: \[ \boxed{\text{a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG}} \]