To restate: You have three tables: Assets, People, Projects
It's not clear whether assets are assigned to people or to projects ( and then the project is assigned to people), but the basic principle can be used for all such "assignments".
One way to assign assets to people (and this works to assign them to projects also), is to use a join table with an effective date field ( or possibly two date fields).
Add a table named People_Asset.
Define these relationships:
People::__pkPeopleID = People_Asset::_fkPeopleID
Assets::__pkAssetID = People_Asset::_fkAssetID
For help understanding the notation that I've used: Common Forum Relationship and Field Notations Explained
By putting a "date assigned" and a "date released" pair of date fields in People_Asset, you can use finds and/or portal filters to find the current assignemtns for a person or an asset, but you still have the historical record of past assignments.
Here is what I have thus far see image...
In the assets table if I change the project and / or the person I would like a historical record i.e. would like to know all the projects and persons this asset has been associated with.
Thank you for all the help!