Asymmetric Behavior in the Geometric Model of a Transformable Four-Legged Wheel Mechanism

Transformable wheels offer a geometric means of extending the reach of wheeled locomotion systems, but their design requires explicit relationships between transformation parameters and singularity constraints. This study presents a geometric and kinematic model of a transformable four-legged wheel driven by a trajectory-disc mechanism. Closed-form expressions describe follower displacement, disc rotation, pivot position, leg rotation, and the maximum theoretical leg-tip position. Three geometric cases, comprising two asymmetric cases and one symmetric case, are examined using a scalar Jacobian and the design constraint ΔXr