A geometric and analytic technique for the determination of the instantaneous screw axes in single-DOF spatial mechanisms

Abstract

In single-degree-of-freedom (single-DOF) mechanisms, the location of the instantaneous screw axes (ISAs) of the relative motions between any two links depends only on the mechanism configuration. In the literature, this property together with the Aronhold-Kennedy (AK) theorem was exploited to devise geometric and analytic techniques that determine ISAs in planar mechanisms, where the ISAs are located by the instant centers (ICs). Despite the fact that an extended Aronhold-Kennedy (EAK) theorem has been demonstrated for spatial mechanisms, too, since 1959, the spatial counterpart of these techniques has not been proposed, yet. Relating ISA locations to the mechanism configuration is important during the mechanism design and provides a deeper comprehension of the mechanism motion by disclosing the role each link plays. Here, a geometric and analytic technique based on the EAK theorem is presented for the ISA determination in single-DOF spatial mechanisms. The proposed method is indeed the extension to spatial mechanisms of those techniques used for the IC determination in planar mechanisms. The effectiveness of the proposed technique is also illustrated through two relevant case studies.