This paper aims at exploring a new parallel machine as a configuration integration, and developing this new configuration into a series. The moving platform of this parallel machine (spindle) replaces the swivel ball joints with joint rings. In the machine processing, the rigidity of the spindle parts can be enhanced. The layer of joint rings will increase holding points of spindle components and reduce singularity of the parallel machine. The comprehensive method of machine will be used in this paper which is based on the azimuthal characteristic. Each chain of the machine will be splitted into a single opened chain for research, analyzing the azimuthal characteristic of each kinematic pair. A union method is also used to work out the motion output equation of each chain. Different chain combination and intersection method will be applied on the basis of the verification of a 5-strut parallel machine to build the parallel machine of four degrees of freedom with joint rings.