Selective Precision Synthesis of the Spatial Slider Crank Mechanism for Path and Function Generation

Abstract

A technique for the synthesis of the RRSC spatial slider crank mechanism for path and function generation using the Selective Precision Synthesis method is presented here. Also presented is a closed form analysis technique for this mechanism. The analysis uses the spatial rotation matrices to obtain a fourth order polynomial for the coupler link rotations with the coefficients expressed in terms of the link lengths and input link rotation. This polynomial is solved in closed form to determine the coupler link rotations which are then used to determine the locations of the path point, the output link rotations, and the displacement of the slider at the cylindrical joint. For synthesis, nonlinear inequality constraint equations relating the generated and the desired path points (or slider displacements) are formulated. These constraints define accuracy neighborhoods around each of the “n” prescribed path points (or slider displacements), and are solved using the Generalized Reduced Gradient method of optimization.