Utility of Matrix Algebra and Graphical User Interface in Design of Six-Bar Mechanism for Rectilinear Motion Generation

Abstract

Many applications require design of a linkage that executes a rectilinear motion. In this study a synthesis procedure for six-bar mechanism for generation of rectilinear motion is presented. To achieve this goal, matrix algebra is used to describe translation, rotation, and inversion of motion of links. These concepts then are used to implement the classical three-precision point synthesize of a four-bar mechanism with a coupler point that traces a straight line. The motion of this four-bar mechanism is inverted and then is used to synthesize a second four-bar mechanism. The merging of these two four-bar mechanisms forms a six-bar mechanism such that the motion of one link is rectilinear motion. To implement this procedure, a graphical user interface is developed for the ease of exploring the design space. The utility of this approach is demonstrated by designing a linkage for a lift-truck.