I am trying to select the motor for a robot arm with six degrees of the freedom robot arm. What should I do to select the motors and which type of motor I should select?
First you need to specify your target payload and then the target velocity/acceleration for moving this payload.
After this, I would start with an inverse kinematic model of the robot (incl. higher order models for velocity and acceleration). A kinematic model can map end effector position, velocity and acceleration to joint position, velocity and acceleration.
Based on this, you can develop a dynamic model of the robot. This will have the role of translating the target payload mass, position, velocity and acceleration to joint torques, velocities and accelerations. Please note that this is position dependent, so you might want to find the worst case position. Also, a different worst case configuration is expected for all joints.
Based on the maximum joint performance you should calculate the power needed for the joints to narrow down possible motors and get to the required torque and velocity/acceleration using a motor and a gearbox combination. Please note also that the drive amplifier used for the motor will also have an affect on the dynamic performance of the motor (but in many cases this is negligible).
The above modelling does not necessarily have to be analytic modelling. Numerical simulation can also be used, but care must be taken when identifying worst case configurations.
Motor selection cannot be generally solved. It is always a case by case decision. For hobbyist robots RC-Servos can be an easy way to start and get into robotics. One step towards complexity would be to use a DC motor with a simple drive amplifier. In commercially available industrial robots PMSMs (Permanent Magnet Synchronous Motors) are the most often used motor types.