The joints of multi-arm robot were simplified into entities, each of which consists of a cylinder and two hemispheres jointed at two ends of cylinder respectively (radius of cylinder is equal to radius of hemisphere). For 2 entities in arbitrary situation, graph transform was conducted. One of them was transformed into vertical state and the center of underside circle of cylinder for the entity coincides with the origin of 3-D right-angled coordinate system after graph transform. Afterwards, according to the theory of solid analytic geometry and the interferences of orthographic projections of 2 entities on coordinate plane, 5 possible cases in which two entities in 3-D space don't interfere with each other are found out and corresponding judgment conditions are given out. Finally, an approach is presented to detect collision between the joints. Numerical experiments show that average detection speed of the method is faster than that of previous related algorithms.