The inherent compliance and adjustable stiffness of variable stiffness robots endow them with significant potential applications in operating within unstructured environments and interacting with unknown objects. From a structural design perspective, this paper innovatively designs the variable stiffness gripper based on the principle of layer jamming and the synergistic effects of various materials. Combined with rope drive, the gripper achieves a simplified drive mechanism for a multi-layer, multi-material variable stiffness grasping robot. This paper analyzes its kinematics and combines the characteristics of friction, tensile and compression resistance, shear resistance, and elasticity of multi-materials, based on cantilever beam theoretical analysis, the evolution rules of the variable stiffness range of different sheet materials are obtained. Experimental results show that the variable stiffness model can effectively handle unknown objects of various shapes and weights through multiple variable stiffness modes. The multi-layer and multi-material variable stiffness experiment achieves an 18-fold stiffness change.