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I am talking about robots like this one: http://www.meccanotec.com/step781b.JPG
How would a person know what type of motor to use in design of such a robot? What I want to understand is that stepper motors have different step sizes, different torques among other things. How do we determine what type of stepper motor is most suitable to be used in a given robot?
Math is the short answer. You need to figure out what you want the motor to do, i.e. how much it needs to lift, amount of torque etc. You also need to consider how it is going to be powered. If its going to run on a battery you may want to get a motor that will do the minimum work required to save battery life. If it's going to run on standard AC power from a wall outlet, this won't be as much of a concern. Your robot arm design will also change the values of the power/torque needed because of leverage. If it's going to be belt driven, direct drive etc will all figure into this too.
My suggestion for a small robot arm would be to start with a kit where the parts have been matched for compatibility and go from there. If not a kit nema 17 motors are probably enough for what you need, but they come in all different specs.
The nice thing about steppers is that they can be stopped and started at specific places in they're rotation pretty easily.
Again, unless you're really good at math and physics, a kit is the way to go as a beginner.
Just realized how old this is, whoops.
The key phrase in your question is "most suitable". Only you can define what this means.
Generally you need to understand the requirements of your project -- in hard numbers -- before you can make design decisions like which motors to use. How much weight will need to be moved by the robot? How fast will it need to move? How precisely? And so on.
