Construction and Application of 3D and 2D Type Maps for Linkages

Abstract

The 3D and 2D type maps for planar four-bar and simply RSSR linkages are constructed with illustration of their application. The criteria determining the rotatability of input or output link are developed or reviewed for both linkages. Three-dimensional type maps are then constructed by integrating the tool for numerical analysis and solid modeling software, e.g. MATLAB and PRO/E. The coordinate axes are mainly three ratios of link lengths. The types are classified based on whether the input or output link can make fully rotation. Each type map is composed of five regions representing different types. They are drag link, crank-rocker, rocker-crank, double-rocker, and unassembled. Any cross sections can be taken readily and arbitrarily from the 3D models along any plane or surfaces to get 2D type maps. The constructed type maps are also combined with curves or surfaces representing performances of transmission ratio. With type maps and related surfaces, the design process can be simplified and expedited substantially.