Are you looking for format or a physical method?
Physical method can be anything from a paid service (if your company has Quickbooks, look into the Time Tracking function) to a custom spreadsheet to paper time sheets. I've done dumb spreadsheets that are essentially just paper with manual entries - those are annoying and easy to put off and get stuck trying to remember what you worked on Tuesday afternoon of last week. Then I built a smart timer (I think I posted on here somewhere) where I enter the project I'm working on and the kind of task and click a button when I start and when I finish. At the end of the day, another button totaled all of my time for each project (so even I switched back and forth, it would give me a single time entry for my time sheet. Now, I have a paid service that's part of my project management software that allows me to track project, task, and other attributes. For something small and simple, look for things like Harvest and Harpoon, and type "time tracking software" into google and explore the plethora of options.
As far as format goes, it depends on your end goals. If you want to see what kind of system is more profitable so you can focus your marketing efforts in that direction or seeing which are least profitable to explore efficiency and/or training improvements (or both), then breaking it up by system would make perfect sense. If you just want to make sure people are working a certain amount, then just having an 'engineering' task would probably suffice.