How do I create a form that is signed (on hard copy) after printing?

When you say signed, do you mean to say that it is signed by the person who filled up the form? If so you can insert an e-signature widget or smooth signature widget on your form. This way after it gets printed or converted to PDF, a signature will appear on the form. 

Here are the links to the signature widgets which you can use:

https://widgets.jotform.com/widget/signature

https://widgets.jotform.com/widget/smooth_signature

You can see here how to add widgets to your jotform: How to Add a Widget to your Form

In addition, you can also make use of the Adobe eSign widget - which uses Adobe Document Cloud e-Sign Services (formerly echosign). Please see and test the widget here: http://widgets.jotform.com/widget/adobe_esign

This Blog post offers some helpful information to get started: http://www.jotform.com/blog/148-Announcing-the-Adobe-Document-Cloud-eSign-Widget

But if this is not what you mean, please let us know.

Thanks.