Using instantaneous invariants of the curvature theory in motion generation synthesis of 4R mechanisms with higher-order coupler point kinematics

Abstract

This paper aims at exploiting the unique characteristics of instantaneous invariants and pole locations in synthesizing motion generation four bar (4R) planar mechanisms with higher-order coupler point kinematics (i.e. specifying coupler point velocity and/or acceleration in addition to its position and coupler orientation). The proposed methodology targets to ease the complexity of such design problems by reducing the number of non-linear governing equations that are solved to generate the desired dyads of the final 4R mechanism design. The new approach integrates graphical and analytical techniques to synthesize 4R mechanisms with prescribed coupler point position, velocity, and acceleration. Two case studies are presented; the first presents the synthesis of a motion generation 4R with 3 prescribed coupler point positions and 2 prescribed coupler point velocities; the second presents the synthesis of a motion generation 4R with 2 prescribed coupler point positions, 2 prescribed coupler point velocities, and 1 prescribed coupler point acceleration. When compared to classical kinematic-based approaches, the proposed method prominently reduces the size and complexity of the set of governing non-linear equations.