Clicking Javascript link in a web application

In the app is a table (see attachment).  In the first column there is an edit link for each row.  I need to write a script that clicks the edit link, performs a task, and then moves onto the next row where it repeats.

The problem is that I can't figure out how to click the edit link.  I don't want to use mouse coordinates because they change depending on the data (column widths and row heights and such).

It's in IE but the edit link itself is a javascript link.  When I right click the edit links and select properties, I see something like javascript:openOrderForm('6484166', '219021');