Question

Shown below are four structures made with rigid elements. They are joined at red points by screws (hinges) that allow motion. Identify the structure(s) that is/are NOT rigid. 

• A. zig-zag with many four–bar loops
• B. long Z with a central four–bar
• C. rectangular frame with a hinged V at top
• D. triangle with an internal brace

Hint:

Count triangles. If every loop can be decomposed into triangles, the frame is rigid; any unbraced four–bar makes it floppy.

Answer 1

The Correct Option is A, B, C

Key idea: In a planar pin–jointed framework, a triangle is rigid, but any quadrilateral (four–bar) is a mechanism unless diagonally braced into triangles.
(A): Contains several hinged four–bar loops with no diagonal bracing, so it can shear like a parallelogram ⇒ not rigid.
(B): Has a clear four–bar at the centre; the adjoining bars do not triangulate it ⇒ not rigid.
(C): The outer rectangle is a four–bar and the inner V ends at a hinge, so it does not lock the rectangle; the frame can still deform ⇒ not rigid.
(D): The triangular base and added member triangulate the whole shape; all loops are reduced to triangles ⇒ rigid.
Hence, the non-rigid ones are \(\boxed{(A),(B),(C)}\).