The mechanism ABCD is shown in figure (link BC is fixed). Which of the following is true for this mechanism?

Explanation:

Mechanism ABCD Analysis

• In the context of mechanisms, especially those involving linkages, various configurations can exist such as crank-rocker, double-crank, and double-rocker mechanisms.
• The identification of these configurations depends on the relative lengths of the links and their ability to complete full rotations or limited oscillations.
• For the mechanism ABCD where link BC is fixed, it is essential to understand the movement constraints and capabilities of the other links (AB, CD, and AD) to determine the type of mechanism.
• The classification into crank-rocker, double-crank, or double-rocker mechanisms is based on the Grashof's criterion and the motion of individual links.

Correct Option Analysis:

The correct option is:

Option 1: It is a double-rocker mechanism.

This option correctly identifies the mechanism type for the given configuration. In a double-rocker mechanism, neither of the two links connected to the fixed link (in this case, links AB and CD) can make a complete revolution, and both only oscillate back and forth. Here’s a detailed explanation to support this conclusion:

• Grashof’s Criterion: According to Grashof’s law, for a four-bar linkage consisting of four links, where one of the links is fixed, the system is classified based on the sum of the shortest and longest links compared to the sum of the other two links.
• If the sum of the shortest and longest links is less than the sum of the remaining two links, at least one link can make a complete revolution. If not, the mechanism is a double-rocker.

Assuming the lengths of the links in the mechanism ABCD are such that Grashof’s criterion indicates a double-rocker configuration, it implies that:

• Link AB (or BA) and link CD cannot make a complete revolution around their respective joints B and C.
• Instead, both links can only oscillate within a limited range, qualifying the mechanism as a double-rocker.