The figure below shows four mechanisms made using links and hinges. If circles represent hinges, which of the option(s) will allow relative motions between the links?
To determine which mechanisms allow relative motion between the links, we need to examine each mechanism's arrangement of links and hinges.
1. Understanding Hinges: Hinges are pivot points around which connected links can rotate. If all links and hinges in the mechanism are appropriately arranged, relative motion is possible.
2. Evaluating Each Mechanism:
: This mechanism has links connected in a way that forms a movable chain, allowing relative motion through rotation about the hinges.
: Similarly, this mechanism's links and hinges are arranged to permit relative rotational motions between connecting links.
: This mechanism might have fixed or constrained links that don't allow for relative rotational movement, possibly due to an improper configuration that creates redundancy or immobility.
: This mechanism permits relative motion, likely through strategic placement of hinges, avoiding any constraints that might limit movement.
3. Conclusion: The mechanisms that allow relative motion between the links are:
