Repelling-screw-based geometrical interpretation of dualities of compliant mechanisms

Abstract

This paper provides a geometrical insight into the dualities of compliant mechanisms via repelling screws. A method for the construction of the repelling screw system is proposed. By means of screw theory and linear algebra, the closed-loop relationships among the twist/wrench spaces of both actuation- and constraint-screw systems are identified, upon which the kinematics, statics and stiffness/compliance of both full- and limited-mobility compliant mechanisms are analysed. The internal correlations between repelling screws and dualities of mechanisms are investigated, which reveals both orthogonal and dual properties of mechanisms with either parallel or serial configuration. The repelling-screw-based representation is applied to describing the permitted motions and restricted constraints of the mechanism. In addition, a novel and systematic approach for parallel-to-serial/serial-to-parallel transformation is proposed, which retains the capability of changing the constraints and relative dimensions of the target configuration to better suit a specific task. A few examples conducted demonstrate the feasibility of the proposed approach and the effectiveness of the repelling-screw based interpretations of mechanism geometries.