Navic209 created this robot arm which you can guide by hand and it will "learn" to repeat that motion.
From project description:
Inspired by the Baxter robot, this arm can be trained to move with your own hands. Once the train button is pressed, youd. move the arm and gripper as needed while the Arduino stores the positions in EEPROM. After that the arm will replay the motion as needed.
The motion sensing is done by Adafruit Analog Feedback Micro servo: http://www.adafruit.com/products/1450
Arduino programming:
https://github.com/vectrasoft/TrainableRoboticArm
Gripper of robot arm:
http://www.thingiverse.com/thing:71797
Robot arm:
http://www.thingiverse.com/thing:34829
VectraSoft by Navic209
https://sites.google.com/site/vectrasoft/projects/
https://sites.google.com/site/vectrasoft/projects/trainable-robotic-arm
Update:
here is a new video showing improvement with smoother movement
