Abstract: Two basic principles for the transformation from parallel mechanisms to multi-loop coupled mechanisms with equal mobility are proposed by adding coupled branches. According to the two basic principles, the 3-DOF parallel mechanism 3-(RRR) RR was transformed into a class of symmetrical multi-loop coupled mechanisms with equal mobility. First, the number of kinematic pairs on the coupled branch was determined according to the mobility formula for single-closed loop. Then, to avoid the occurrence of instantaneous mechanisms, the types of kinematic pair on the coupled branches were analyzed. Finally, through the assembly of the coupled branches, a class of three-dof mobile multi-loop coupled mechanisms with first-or second-level coupled nodes was synthesized.