Attempt to get as much distance from the problem as possible.
Make the excursion about 5-10 minutes.
Include some physical activity if the energy level of the group is low.
Give the group some rationale for why an excursion might be helpful.
If necessary, provide a model or example to help demonstrate it.
The following are just some of the worlds that you can ask people to be a part of.
Science Fiction Astronomy
Storyboard excursions are where a story is started, usually by the facilitator, and everyone tries to make the story more ridiculous, and have more twists in it as the story goes on. I prefer to keep the story as visual as possible.
These are generally needed for groups of low energy. You can do anything from aerobics to charades (where they have to pick a physical activity).
These are where you ask the group to go outside and ask them to focus on something that grabs their attention. They then need to talk about this object when they return. I find it best if they asked lots of questions about life as that object, what its role is, how it feels etc without linking it to the problem. Take everyone though this, possibly taking notes, and then remind them of the problem and the facilitator goes over the comments made whilst they in/out listen to link back to the problem.
I would group under here all the excursions where you ask people to describe something within their experience, and could include
Favourite smell & associations that go with it
Most rewarding experience
Favourite sound & associations that go with it.
It is sometimes very effective to get the resources to be various components of the problem. For example, when looking at “How to get a seal around a moving wire” one person could be the wire, another the seal, another gas trying to get through the seal etc.