This paper concerns the problem of designating criteria for assessing the possibility of a collision between the elements of serial manipulators with three rotary joints allowing to flex the segments in common plane oriented by rotating the fourth connection. The issue of contactless and efficient functioning of described group of manipulators has been considered in the spatial system. Equations were derived determining the possibility of a collision between selected segments of both manipulators. Collision detection model isn’t based on the information from the tactile sensors, but only on the relative position between the segments of manipulators. Based on the parameters defining the collision, the search for method of impossible collision was set on designing level, in order to minimize the time needed to examine all possible scenarios of collisions between segments. The results were included in development of methods and algorithms for planning and controlling movements of finger modules in anthropomorphic manipulator during grasping objects of indeterminate shape.