Higher-order curvature analysis of planar curves enveloped by straight-lines

The main focus of this paper is on higher-order curvature analysis of curve envelopes generated by planar motion of straight-lines. Classic Burmester theory mainly deals with curvature properties of moving point trajectories. When compared with this case, very few investigations dedicated to curvature properties of envelopes generated through planar motion are on the record.In the present paper, for planar curve envelopes generated by straight-lines, the analytical expressions of curvature ratios lambda(1) and lambda(2) have been deduced in terms of Bottema's invariants. The theoretical findings are used to propose a new algorithm for the kinematic synthesis of linkages for fourth-order curve generation through the envelope of a moving straight-line.The paper offers two kinematic synthesis applications of the theory herein developed. For a planar four-bar, at a given position, is computed the coupler driven straight-line generating envelopes with prescribed third and fourth-order curvature ratios. (C) 2018 Elsevier Ltd. All rights reserved.