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Mechanisms with motion and locking modes can meet the stiffness requirements under specific working conditions after being transformed into specific locking mode configurations. The geometric characteristics of the linkage curve of the spherical 4R mechanism was analyzed, and the correctness of the linkage curve equation of the spherical 4R mechanism was verified through numerical examples. A type of double loops spherical 7R mechanism with locking mode was designed by setting a spherical 3R motion chain in a folding position on the connecting rod of the spherical 4R mechanism. Using screw theory to analyze the instantaneous rotation axis of the connecting rod in a singular configuration of the spherical 4R loop, it was determined that the instantaneous rotation axis of the connecting rod in the spherical 4R loop was coplanar with the axis of the spherical 3R motion chain as a necessary condition for mechanism mode transformation. Using the spherical 4R loop as a generalized rotational pair, the acceleration of the double loops spherical 7R mechanism was analyzed, and the necessary condition for the mechanism mode transformation was obtained, which was that the tangent of the axodes of the connecting rod and the axis of the spherical 3R motion chain were coplanar under the corresponding mechanism configuration of the sharp point of the connecting rod curve in the spherical 4R mechanism loop. This kind of spherical 7R mechanism had lock-in mode. By analyzing the instantaneous rotation of the link in the loop of the spherical 4R mechanism with screw theory, the transformation of the motion mode of the mechanism can be determined. It had a certain application value in the analysis and design of multi-mode mechanism which can meet the requirements of motion and lockin production operation transformation.