If this is a DC servo motor red & blk for power, the green should go to your central ground point, you should ideally set up a central star point ground where all the earth grounds and shields go to.
Also have bonding conductor from the frame of the machine.
The main reason for gearing is to use a more economically viable drive and motor, with a servo you usually have the luxury of sizing a small motor with high gearing to take advantage of the flatter rpm/torque curve of the servo.
The alternative to little or no gearing is a much larger servo and drive.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.