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.

翻译：本文介绍了一种机械编程式半径可调物理（MORPH）轮，这是一种完全被动的变半径轮，其内部嵌入了用于扭矩响应式变形的机械行为逻辑。与依赖执行器、传感器和主动控制的传统变速系统不同，MORPH轮仅通过其几何形状和柔性结构实现被动适应。该设计集成了一个扭矩响应耦合器和弹簧加载的连接支柱，可在80毫米至45毫米之间机械地调整车轮半径以响应输入扭矩，无需任何电气元件。MORPH轮提供了三种在先前的被动设计中很少同时实现的独特能力：（1）通过对称耦合器实现无限旋转的双向操作；（2）在驱动模式下具有超过10 N的高扭矩承载能力，并实现刚性动力传输；（3）由确定性运动学控制的精确且可重复的传动比控制。我们开发了一个全面的分析模型来描述该轮的机械行为逻辑，建立了在直接驱动和半径变换两种模式之间切换的阈值条件。实验验证证实，在1.8-2.8公斤的轮重范围内，测得的扭矩-半径和力-位移特性与理论预测高度吻合。在不同负载（0-25公斤）、斜坡和非结构化地形上的机器人层级演示进一步验证了MORPH轮能够被动调整其半径以提供最佳传动比。MORPH轮是机械编程结构的一个范例，它将智能的、与环境相关的行为直接嵌入其物理设计中。这种方法为在不可预测或控制受限环境中运行的机器人移动系统，提供了一种用于被动变速和机械智能的新范式。