This paper introduces the Mechacnially prOgrammed Radius-adjustable PHysical (MORPH) wheel, a fully passive variable-radius wheel that embeds mechanical behavior logic for torque-responsive transformation. Unlike conventional variable transmission systems relying on actuators, sensors, and active control, the MORPH wheel achieves passive adaptation solely through its geometry and compliant structure. The design integrates a torque-response coupler and spring-loaded connecting struts to mechanically adjust the wheel radius between 80 mm and 45 mm in response to input torque, without any electrical components. The MORPH wheel provides three unique capabilities rarely achieved simultaneously in previous passive designs: (1) bidirectional operation with unlimited rotation through a symmetric coupler; (2) high torque capacity exceeding 10 N with rigid power transmission in drive mode; and (3) precise and repeatable transmission ratio control governed by deterministic kinematics. A comprehensive analytical model was developed to describe the wheel's mechanical behavior logic, establishing threshold conditions for mode switching between direct drive and radius transformation. Experimental validation confirmed that the measured torque-radius and force-displacement characteristics closely follow theoretical predictions across wheel weights of 1.8-2.8kg. Robot-level demonstrations on varying loads (0-25kg), slopes, and unstructured terrains further verified that the MORPH wheel passively adjusts its radius to provide optimal transmission ratio. The MORPH wheel exemplifies a mechanically programmed structure, embedding intelligent, context-dependent behavior directly into its physical design. This approach offers a new paradigm for passive variable transmission and mechanical intelligence in robotic mobility systems operating in unpredictable or control-limited environments.