TITLE:
The Rolling Wheel Equations without Magic: A Combined Slip-Stiction Approach by the Udwadia-Kalaba Formulation with Constraints Relaxation for a Smooth Simulation
AUTHORS:
Bukoko Ikoki
KEYWORDS:
Rolling Wheel, Friction, Stiction, Slip, Constraints Relaxation
JOURNAL NAME:
Journal of Transportation Technologies,
Vol.11 No.3,
June
24,
2021
ABSTRACT: The Udwadia-Kalaba formulation is proposed to model the dynamics of the
rolling wheel. A unified approach that addresses both the slip and the stiction
in the contact section is considered. Purely rolling constraints are associated
with stiction and are suitably lifted as slip occurs. An extended formulation
for the Uwadia-Kalaba equations of motion is introduced for that matter. It
resorts to the weighted minimum norm and the weighted semi-least-squares
solutions of the constraints equations. This not only allows a bias on
constraints, by an appropriate description of weight functions based on
friction, it also leads to a smooth activation or deactivation of selected
constraints without rewriting the equations of motion or upsetting their
numerical integration.