The consequences of structures such as rings in molecules is readily apparent with models, and as you say, the flexibility of the molecule becomes more restricted compared to open chain molecules (I'm thinking of organic molecules such as alkanes). Double bonds have a similar effect because rotation about a double bond such as that in alkenes does not normally occur; thus the molecule is "stiffer". This helps explain why saturated fats, with no carbon-carbon double bonds, are solids (such as Crisco) while unsaturated fats, which contain carbon-carbon double bonds in their carbon chains, tend to be liquids (such as vegetable oils). The stiffer carbon chains in the unsaturated vegetable oils do not interact with each other as effectively as the interactions between the more flexible chains in saturated fats.
A double bond affects the geometry about the involved atoms also, which are usually described as being sp2 hybridized with the sp2 hybrid orbitals pointing towards the corners of a trigonal plane and the remaining p-orbital perpendicular to the plane. This of course has immediate consequences with regard to the overall structure of the molecule. When p-orbitals on adjacent atoms overlap in the side-to-side fashion characteristic of pi-bonding, a "pi-cloud" results above and below the plane of the bonds formed with the sp2 orbitals (see drawings of ethylene, for example). The electrons in this pi-cloud are more spread out, extending far out in space from the atoms, making them more accessible in reactions via contact with other reactant molecules. Carbon-carbon double bonds are reactive towards electron-poor sites in other molecules (which are called electrophiles in these reactions), giving a class of alkene reactions called electrophilic additions.
That's the general idea! A good model set really helps one to see the effect on molecular structure and flexibility.
Steve
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