MORPH Wheel: A Passive Variable-Radius Wheel Embedding Mechanical Behavior Logic for Input-Responsive Transformation

TL;DR

The MORPH wheel addresses the limitation of fixed-transmission wheels by embedding mechanical logic directly into a passive, variable-radius wheel. It achieves bidirectional operation, high torque transmission, and deterministic transformation through a torque-response coupler, connecting struts, and compliant springs, without sensors or actuation. An analytical model defines threshold conditions for mode switching, and bench-top tests plus robot demonstrations validate the radius variation and torque–transmission behavior across loads and terrain. This work demonstrates a new paradigm of mechanically programmed adaptation, enabling energy-efficient and robust mobility in unpredictable environments. Future work will refine geometry, durability, and multi-wheel integration to broaden real-world applicability.

Abstract

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.

Figures (16)

• Figure 1: Mechanically prOgrammed Radius-adjustable PHysical (the MORPH) wheel: Passive variable-radius wheel embedding mechanical behavior logic for input-responsive transformation.
• Figure 2: Mechanically programmed structure of the MORPH wheel. (a) Structural composition of the the MORPH wheel, consisting of a torque-response coupler, connecting struts, springs, tire segments, and central hub. (b) Operating principle of torque-response coupler mechanism.
• Figure 3: Mechanical behavior logic of the MORPH wheel: (a) Wheel rolling in diverse environments: output force is sufficient for direct wheel rotation ($F_{out} > F_{res}$). (b) Passive wheel radius variation: torque-response coupler reconfigures wheel geometry ($F_{out} < F_{res}$ and $F_c > F_s - W_w$). (c) Wheel behavior under programmed conditions.
• Figure 4: Wheel displacement analysis for tire segment design. (a) Geometric relationship between tire segments showing the variation in central height ($h_c$) and wheel displacement amplitude $A$ in the fully expanded state. (b) Wheel displacement amplitude as a function of the number of tire segments $n$ and radius ratio ($\rho_c$ = 1.2–2.0), demonstrating that six segments maintain vibration below 5$\%$ of maximum wheel radius.
• Figure 5: Configuration of the connecting strut mechanism. Two symmetric slider–crank mechanisms are installed per tire segment, each equipped with a torsional spring (k = 2.14 N·mm/deg) at the upper joint.