Effects of Center-of-Mass Offset on Optimal Wheel Arrangement in a Three-Omni-Wheel Mobile Robot

An equilateral-triangle arrangement with 120° spacing is widely used for omnidirectional mobile mechanisms employing three omni wheels. However, the 120° arrangement itself, driving experiments with variable wheel-placement angles, and mobility evaluations of arbitrary or asymmetric arrangements have already been reported; therefore, the novelty of this study does not lie in proposing the equilateral arrangement. Here, the placement angle of a line-symmetric three-omni-wheel mechanism is treated as a single design variable, and performance measures derived from different physical principles—translational isotropy, worst-case kinematic input effort, three-point support stability, normal-load distribution, and the worst-case required coefficient of Coulomb friction—are analyzed within a common geometric model. For a centered center of mass (CoM), the optimal angles of these independent measures are shown in closed form to coincide at 120°. For a center-of-mass offset restricted to the symmetry-axis direction, a complete planar force-and-moment balance is introduced, accounting for both static load redistribution and the moment generated by the translational force acting at the offset center of mass. Consequently, the support-optimal angle that maximizes support stability and the friction-optimal angle that minimizes the friction requirement separate, and their difference increases with the offset. Thus, this study establishes, in a single analytical framework, both the “unified optimality” by which independent design optima coincide at 120° under symmetric conditions and the mechanical mechanism by which CoM offset breaks that coincidence.