Tension transmission via an elastic rod gripped by two circular-edged plates

Abstract

The equilibrium of static friction in tension transmission by an inextensible elastic rod gripped by two plates with round edges was modeled and solved analytically. To proceed, we established equilibrium equations in the deflected and circular edged regions, respectively, and then combined the results together. In both deflected and circular edged region, the condition of cantilever beam with clamped end maintaining a continuous contact was assumed to avoid corresponding mathematical complexity. As a result, we expressed the gripping force in terms of the contact angle, the inclined angle of load, the radius ratio and the initial tension in our results. More specifically, a more precise but still analytical relationship between the incoming and outgoing tensions including the effect of the rod bending rigidity was derived through the analysis of the circular edged region; it turned out that the radius ratio is the only parameter representing the bending rigidity in the tension ratio. To analyze the deflected region, the classical elastica analysis in terms of an elliptic integral was adopted. Based on the results, the effect of radius ratio and frictional coefficient on the derived force ratio was investigated. As a result, the bending rigidity can be ignored above the range of ρ ≈ 100 . But the tension transmission decreases by 29.1% relative to the classical case at the range of ρ ≈ 5 . In addition, the effect of inclined load on the derived gripping force was also investigated.