This paper describes a ball-shaped wrist with six degrees of freedom of industrial robot

the wrist is high in repeatability

large in orientation

and compact in size. Based on the kinematics analysis of the wrist

the author has studied the relationship between the repeatability and the kinematics parameter error of each joints of the wrist

from which a complete mathematical model of the wrist is prodacal.Using this error model

we can optimize the distributions of accuracy of the wrist

and design the mechanical constraction and control system of the robot. The author introduced the optiming method that mokes the robot having properties such as quickcr response

higher accuracy and so on.