There are not much methods for humanoid robots to path-plan movements such as piggyback-carry, firefighter-lift or giving a shoulder to support the gait of another. Such methods are essential to apply humanoid robots for rescuing people in emergency, or for taking care of injured/elderly people in the hospital. It is difficult to plan such motions as they require the limbs of the humanoids to be tangled. In this paper, we propose a new method to plan such movements using a criteria based on the Gauss Linking Integral (GLI). The user first specifies the target configurations of the humanoids. The system then detects the tangles made between the bodies, and then plans how the humanoids should move to arrive to the target posture from separate configurations. The motion get entangled is planned by the Rapidly-exploring Random Trees (RRT) expansion. Using our method, it is possible to path-plan complex tangling motions which were difficult by previous methods.