Effect of friction on the planar elastica constrained inside a circular channel with clearance

In this paper we consider the effect of friction force on the contact behavior of an elastica inside a circular channel with clearance. The elastica is partially clamped at both the input and output ends of the channel. Coulomb friction is assumed to be present at the output end and on the constraining walls. Focused is placed on the relative motion between the input end and the output end of the elastica. Shooting method is adopted to solve for the quasi-static behavior of the elastica movement. Four types of contact patterns between the elastica and the constraining channel walls may occur when the input end moves in and out of the channel; they are rolling point contact, combined rolling and sliding point contact, rolling line contact, and sliding line contact. When the input end undergoes a sinusoidal motion, the output end either ceases to move at all, or follows exactly the input end motion. These two phases of output end motion occur subsequently, one immediately after the other. In general, the output end lags behind the input end. Experimental observations on the lagging phenomenon at the output end confirm the theoretical prediction.