The method of analyzing the mechanism in series, parallel and hybrid modes can no longer meet the requirements of analyzing multi-loop mechanisms (MLMs), especially multi-loop mechanisms with passive degrees of freedom(P-DOFs).This study presents an approach to analyzing sub-degree-of-freedom (sub-DOF) relations in a class of MLMs with P-DOFs (P-DOFs) as well as structurally synthesizing these mechanisms. First,the DOFs of mechanisms with P-DOFs are decomposed and combined,and two methods—multi-loop serial connection and multi-loop stacking—are formulated to establish MLMs with P-DOFs.Second, a DOF space (DOF-S) model is generated.Host–parasite (H–P) MLMs are proposed, and various types of parasitism are analyzed. Finally, various DOF distribution patterns in H–P MLMs are analyzed based on real-world examples. The results show the following. H–P mechanisms are a class of MLMs with P-DOFs. For an H–P mechanism, its DOFs can be longitudinally and centrally, transversely and centrally, or comprehensively optimally distributed in the DOF-S by selecting a suitable type of parasitism. The H–P-type palletizing robot prototype developed in this study is able to self-balance. This demonstrates that the comprehensive optimization of DOF distribution is effective. This study enriches the theoretical knowledge on MLMs, which are extensively applied in fields such as aerospace, industrial robotics, and numerical-control machine tools.