Synthesis of a spatial 3-RPS parallel manipulator based on physical constraints using hybrid GA simplex method

This paper presents dimensional synthesis of a 3-RPS parallel manipulator according to the limitations on the actuating link lengths and on the range of motion of the spherical joints. The synthesis of the manipulator consists of determining the dimensions of a moving platform and a fixed base along with the directions of revolute joint axes such that a point on the moving platform passes through a set of prescribed positions in space. The dimensions of the moving platform are determined using a hybrid optimization method called GA–simplex method. While determining the dimensions of the fixed base, the limitations on the motion of the joints are considered to design a practical manipulator. The synthesis procedure presented confines to that class of problems where the number of prescribed positions required to complete a task is more than the number of positions a parallel manipulator can offer. The practical applications include automated assembly, contour machining, etc. A numerical example for the synthesis with ten positions is presented. This paper also presents direct kinematic equations for the manipulators with non-equilateral triangular platforms in order to validate the results of the numerical example.