Soft jaws are not only useful to ensure tolerance from part to part, but but are often absolutely necessary to securely clamp a part that is thin walled. Example shown below where the soft jaws have been machined to perfectly fit the OD of the thin-walled part that requires additional operations. This has several benefits: 1 - increases the clamping surface area, 2 - provides a back-stop to register the part depth and flatness in the chuck, and 3 - reduce surface marring where the part is clamped in the chuck since the soft jaws are made from softer material (including plastic at times).
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Here's another example using "Pie-shaped" soft jaws that have been machined to fit the part being clamped:
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