From the comp-444-the_instructors_notebook.pdf
(https://landing.athabascau.ca/pages/view/242986/comp-444-the-instructors-notebook):

Design Question: How many motors, and of what type, would you require to make a fully functional robotic arm that had
a working elbow, wrist, and endeffector (i.e. a simple clamp)? What components would you add if you wanted the clamp
to be able to tell how hard it was grabbing an object such as an egg (i.e. to avoid crushing it)? Discuss your design in your
weblog in detail, especially describing the choice of motor for each joint, the degrees of freedom and the range of motion.

Answer: You would need 4 motors total at a bare minimum. Here's a breakdown of the motors you would require to make a fully functional robot arm:

For the elbow you would use a servo motor. This would make the elbow bend and straighten out similar to how our biceps and triceps control our elbow joint. Range of motion would be 0 to around 150 degrees.

The wrist would be the most complex part this arm (since an anthropomorphic hand and shoulder are not required). To make a wrist you would require two servo motors, one further up the arm (closer to the elbow) since space is limited to "roll" or rotate the wrist in a clock-wis / counter-clockwise otion relative to the elbow joint. Range of motion would be 0 to 180 degrees. The other motor would be a servo as well and this would be the motor what would move your wrist up & down (in other words, control the pitch of the joint). This second servo would be installed rights on the wrist joint since that would be the axis where it would move. Range of motion would be 30 to 120 degrees.

The last motor I think would be one servo motor as well if you were to make a clamping gripper. You would require two gears of the same size on both sides of the gripper mechanism in order to make both sides of the gripper endeffector close its grip on an object. Or you could always use two servo's, one on each side. I think a servo would be the best choice here because you wouldn't need the gears to turn 360 degrees in order for the gripper to work, less then 180 degrees should work well enough and you could also change the gear ratio in order to make the gripper close more or less, or have more or less torque, or close faster or slower etc. With a standard DC it would turn too much and you wouldn't have as much control over how much the motor is turned. 

You would have to measure the current supplied to the servo somehow in order to monitor and control the torque applied by the motor. One method would require using a shunt resistor and OP-amp (and apparently some filtering components due to noise / EMI). Another method would be to use a Hall-effect current sensor IC. Finally, you would probably want to add rubber ends on the endeffector gripper... for more grip.