All objects connected to each other normally share a common joint. The Advanced > Edit > Points > Disconnect command will break off the objects from the joint and will add duplicate joints to each of those objects.
Select the joints to be disconnected from the objects.
Click the Advanced > Edit > Points > Disconnect command.
Tip: This is a very useful command for some special modeling conditions. This feature adds separate joints to objects sharing common joints. After the joint is disconnected, special constraints may be added to those joints. For example, use this feature to add separate joints and then (a) specify moment release constraints between two adjacent edges of shell objects, or (b) add a zero length non-linear link using separate joints at the same location.
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