Reddit mentions of Arduino Robotics (Technology in Action)

There are tons of projects! There are hacker groups and forums for literally every type of project out there on the internet. Read up on what other people have done in order to get ideas and avoid costly mistakes. I have no idea what you're into, but here are some things that I would like to build.

diy go kart:
http://www.diygokarts.com/
http://www.instructables.com/id/Intro-44/

drones:
http://diydrones.com/

Amateur telescope + exoplanets
https://www.youtube.com/watch?v=Bz0sBkp2kso

Rocketry (be careful!)
http://www.apogeerockets.com/Advanced_Construction_Videos/All
https://www.youtube.com/watch?v=12fR9neVnS8

Robotics
http://arduino.cc/en/Main/Robot
http://makezine.com/projects/building-a-simple-arduino-robot/
http://www.amazon.com/Arduino-Robotics-Technology-Action-John-David/dp/1430231831

Sterling engine
http://diystirlingengine.com/

A lot of cool projects mainly involve electronics and programming, but can still provide valuable skills for a mechanical engineer.

Magnetic levitator
http://hackaday.com/2013/12/05/avr-atmega-based-pid-magnetic-levitator/

Robotics simulator
http://gazebosim.org/

Motion sensing camera
http://www.instructables.com/id/Raspberry-Pi-Motion-Sensing-Camera/

Weather station
http://www.weather.dragontail.co.uk/index.php?page=station_setup

Note*
Some of the projects are more expensive and difficult than others. Keep in mind that the parts list doesn't always include the tools you will need to put stuff together.

For books, I recommend:

• http://www.amazon.com/Arduino-Robotics-John-David-Warren/dp/1430231831/
  
  
• http://www.amazon.com/Robot-Building-Beginners-Technology-Action/dp/1430227486/

If you're willing to spend $30, this book will teach you everything you need to know.

If you're looking to get some hands-on experience I recommend getting started with Arduino, building projects.

There's lots of beginner's tutorials online. You can buy your parts from Sparkfun Electronics.

I just ordered myself this book to help with some more advanced concepts!

If you get stuck with anything technical or need any help finding resources, feel free to PM me.