What are the physical minimums required to avoid infringement of an existing patent?

There are no physical mins. It is an element by element comparison. Additionally there is the doctrine of equivalents to consider - even if you don't have the exact same elements.

There are no "physical minimums" required to avoid infringement of an existing patent. Infringement of patent claims is determined by whether the accused product falls within the scope of the patent claims. Determining the existence of patent infringement can be an extremely complex matter. It would be a rare circumstance where a layperson would be qualified, even with online instruction, to determine whether an accused device actually infringes a patent.

The name of the game is in the claim Judge Giles S. Rich. Well, if you want to avoid patent infringement you have to avoid two things. First, the claim language. If a patent states. We claim... XYZ "comprising": A, B and C elements. You will infringe A, B and C, even if you include a D element, and if you do not use a B element you will be infringing on A and C. You have to compare the claims to your technology, claim by claim. Second, the doctrine of equivalents. This is when the equivalent element performs substantially the same function in substantially the same way and produces substantially the same result. The function-way-result test. If the claim states "comprising," and if the function (purpose) is to open a box using element tool A, and if your technology uses element B, but causes the box to open (the result) in a similar way. Then you are infringing under the doctrine of equivalents. This is avery complicated matter and I suggest you seek legal advice from a licensed patent attorney.

Infringement is determined by the "claims" appearing at the end of the patent. They determine whether materials used, appearance, features, and measures lead to infringement. Therefore, one cannot answer your question without knowing what the patent says.