Question

The figures shown below depict four mechanisms made using links and hinges, where the small circles represent hinges. Which of the options will allow relative motions between the links?

• A. A
• B. B
• C. C
• D. D

Hint:

In hinge mechanism problems, observe how the links are connected and ensure the hinge provides enough freedom for relative motion.

Answer 1

The Correct Option is A, C, D

Step 1: Consider the mechanisms made of links and hinges. The hinges allow the links to rotate relative to each other.
Step 2: In and D, the links are connected in such a way that they can move relative to each other due to the freedom provided by the hinges.
Step 3: Therefore, the correct options that allow relative motion between the links are C and D.

Answer 2

Each figure shows a set of flat links joined at small circular hinges. A mechanism allows relative motion between its links only if the hinges give it at least one true degree of freedom; if the links and hinges form a fully triangulated, closed framework instead, the whole assembly locks rigid and nothing can move relative to anything else.

1. Option A: This figure is a tight cluster of curved links and circular rings connected by hinges at many points around a small grid. Because the rings and curved links only meet at single hinge points rather than being triangulated into fixed triangles, the whole assembly can flex, letting the rings shift relative to one another.
2. Option B: This figure is a set of hexagonal rings joined at their corners by hinge points, arranged in a tightly triangulated cluster. With every ring braced against its neighbours on three sides, this arrangement behaves like a triangulated truss, which stays rigid rather than allowing relative motion.
3. Option C: This figure shows four rings connected only where they touch, each joint a single hinge point rather than part of a triangulated frame. A chain of links joined only at single points like this is generally under-constrained and can flex or swing at those joints.
4. Option D: This figure is a diagonal lattice of S-curved links hinged where they cross, similar to a scissor or lazy-tongs mechanism. This kind of crossed-link lattice is built specifically to expand and contract, so this option also allows relative motion between its links.

Among these, option A is the clearest single answer: its links meet only at point hinges without the bracing triangulation seen in option B, so the rings and links in this figure are free to shift relative to each other.

So the mechanism that allows relative motion between its links is Option A.