Analysis of the RRSC spatial slider crank mechanism for path generation with prescribed input timing and for function generation are presented here in closed form. A computer aided design technique for the synthesis of the RRSC path generating and function generating mechanisms is also being presented using the Selective Precision Synthesis technique.
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.