Analysis and Synthesis of General-Type Goldberg Five-Revolute Mechanism

Abstract

Geometric constraints and formation of general-type Goldberg five-revolute mechanism are outlined through the analytical geometry and its general analytical kinematic closed-form solutions are derived based on matrix algebra. Applying the concept of relative motion and using the coordinate-transformation matrices, we not only present the parametric formulas of its coupler link and coupler point but also provide a procedure for the higher-order analysis of coupler curve. Moreover, this mechanism is used for the dimensional synthesis, function, path and motion generation by the nonlinear programming algorithm. Finally, three numerical examples are given for illustrations and their results of synthesis are separately verified by computer animation with 3D computer graphics.