Newbie implementing one to many many to one relationship

I am attempting to tie a Project to Projectparts to Parts and I
believe the relationship should be one-to-many, then many-to-one. My
goal is to build the Parts table so that this table can grow and the
Parts descriptions can be re-used in different Projects (ultimately
tie this in to an autocomplete plug-in so the user doesn't have to re-
type a part every time, but I'm not there yet). I had the application
working through to the Project - Projectparts relationship, I am now
trying to add the description component from the Part table.

I think I've tracked down my problem to the _projectpart partial of
code that I've implemented for this. Here's the partial:

    <div class="fields">
      <%= f.text_field :qty, :size => 3 %>

      <% f.fields_for :parts do |builder| %> # <======I think
problem is here.
         <%= builder.text_field :description, :size => 50 %>
      <% end %>

      <%= remove_child_link "Delete", f %>

As the code is now, the 'New' view will render, but when I save the
data from the UI, I get an unknown attribute error in my 'Create':

    ActiveRecord::UnknownAttributeError in ProjectsController#create

    unknown attribute: parts

However, when I change the :parts reference to :part, the New screen
will not render & I get a nil object error:

    NoMethodError in Projects#new

    Showing app/views/projects/_projectpart.html.erb where line #10

    You have a nil object when you didn't expect it!
    You might have expected an instance of ActiveRecord::Base.
    The error occurred while evaluating nil.new_record?

So I'm thinking I'm not referencing this correctly. I've tried using
@project.projectpart.description, @project.projectpart & other
variations, but not sure if the model is set up correctly in the first
place (the description is the 'one' at the end of the one-to-many /
many-to-one relationship).

Any thoughts? Thanks in advance.

For reference: